Solution Manual for Math and Science for Young Children 9e Rosalind Charlesworth, Ph.D

Instructor Manual for all Chaptes Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 1: Development, Acquisition, Problem Solving, and Assessment

TABLE OF CONTENTS Purpose and Perspective of the Chapter ................................................................................................... 2 Chapter Objectives ..................................................................................................................................... 2 What’s New in This Chapter ..................................................................................................................... 2 Chapter Outline .......................................................................................................................................... 2 Additional Resources ................................................................................................................................ 10 Primary Sources ...................................................................................................................................... 10

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this chapter is to provide an understanding of concept development in science, technology, engineering, and mathematics (STEM), emphasizing the importance of foundational exploratory activities in infancy and toddlerhood. It explores the integration of arts into STEM (STEAM) and highlights the significance of adhering to principles and standards outlined by professional organizations and national curriculum guidelines. Constructivism, rooted in the theories of Piaget, Vygotsky, and Bruner, is discussed as a framework for children’s intellectual autonomy and knowledge construction. The chapter also outlines various learning experiences, including naturalistic, informal, and adult-guided, considering factors such as learning styles, cultural background, and digital technology’s role in STEM education. Additionally, it delineates the six steps in the Curriculum Planning Cycle, emphasizing problem-solving and inquiry as central processes, and underscores the importance of assessment integrated with instruction and tailored to individual needs, with a focus on observation, interview techniques, and equitable assessment methods.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 1-1

Define concept development, and identify the concepts children are developing in early childhood.

1-2

Describe three types of learning experiences, and give an example of each.

1-3

Create and integrate lessons and activities using the six steps in instruction suggested in this chapter.

1-4

Understand the reasons for development of the National Assessment Standards.

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WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: ●

Addition of developmentally appropriate practices and STEM

●

Addition of the topic Digital Technology Today

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CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

I. Concept Development (01.01; PPT Slide 3)

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a.

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i. In early childhood, children actively acquire fundamental concepts and process skills such as one-to-one correspondence, counting, classifying, measuring, and applying the scientific method. ii. As children grow and develop physically, socially, and mentally, their concepts also evolve, beginning in infancy as they explore the world with their senses and gradually develop spatial sense and understanding of concepts like size, weight, shape, time, and space through exploration and interaction with their environment.

Relationships Between Science, Technology, Engineering, Math, and Art (STEM and STEAM) i. Fundamental concepts developed in early childhood form the basis of understanding in science, technology, engineering, and math (STEM). ii. Anxiety surrounding teaching these subjects can be alleviated by referring to specific chapters that provide overviews of materials and activities for young children.

Understanding the interrelationships between STEM components and the importance of process skills is essential for problem-solving across disciplines.

Rationale for Standards and Common Core Curriculum Guidelines i. National professional organizations such as NCTM, NRC, and NAEYC have developed standards and guidelines for teaching in various subject areas, including mathematics, science, and early childhood education, which serve as frameworks for educators to develop core curricula aligned with these standards. ii. These standards, such as Next Generation Science Standards (NGSS) and Common Core State Standards for Mathematics (CCSSM), provide performance benchmarks and developmental placement of key concepts and skills, aiming to promote a deeper understanding of concepts and processes through interactive learning experiences.

The Movement Toward National Core State Curriculum Standards i. As of 2023, 40 states have retained common K–12 curriculum standards, with a growing focus on standards for early childhood education up to age 5, aiming for a balanced approach that includes math, literacy, science, art, and social/emotional development. ii. The CCSSM and the NGSS provide structured frameworks designed to enhance mathematical understanding and scientific exploration, integrating scientific and engineering practices with crosscutting concepts across grade levels.

National Standards for Professional Preparation i. Standards for Professional Preparation, particularly in early childhood education, as outlined by NAEYC, cover six key areas including child development, family engagement, assessment, culturally appropriate teaching practices, academic content integration, and professionalism. NAEYC Standard 5 emphasizes the importance of knowledge and application of academic content, including mathematics, science, and visual arts, for designing and implementing developmentally appropriate curriculum in early childhood settings.

Constructivism i. Jean Piaget’s theory of constructivism posits that individuals construct their own understanding by linking new experiences with existing knowledge, forming conceptualizations that make sense to them. ii. Piaget identified four periods of cognitive development: the sensorimotor period (birth to about age 2), the preoperational period (ages 2 to 7), the concrete a

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operations period (ages 7 to 11), and the formal operations period (ages 11 through adulthood), each characterized by distinct cognitive milestones and advancements such as object permanence, symbolic play, conservation, and abstract problem-solving abilities. f. The Learning Cycle i. The Science Curriculum Improvement Study (SCIS) materials utilize a Piagetian-based learning cycle approach, reflecting the idea that science education should engage students in hands-on exploration, data collection, and conceptual invention. ii. This learning cycle, encompassing exploration, concept development, and concept application phases, guides curriculum development and teaching strategies, with teachers facilitating exploration by providing developmentally appropriate materials and environments for students to construct their own understanding of scientific concepts, such as shapes in a lesson example. g. Adapting the Learning Cycle to Early Childhood i. Bredekamp and Rosegrant (1992) adapted the learning cycle for early childhood education, comprising four processes: Awareness, Exploration, Inquiry, and Utilization. ii. Each process involves children gradually constructing understanding through sensory experiences, guided by adults who facilitate exploration, guide inquiry, and provide opportunities for application. iii. The cycle progresses as children encounter new situations, beginning with awareness and advancing through exploration, inquiry, and utilization, aligning with their developmental stages.

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h. Multimodal Creative Inquiry i. Recent work has explored the use of multimodal creative inquiry as a means to enhance meaning-making in early childhood education. Multimodal creative inquiry engages various learning processes, including linguistic, visual, kinesthetic, aural, and spatial modalities, grounded in Vygotskian cultural–historical theory. ii. This approach, which builds upon the learning cycle, enriches play-based learning by integrating physical and digital play spaces, offering a transformative learning experience for children.

II. Types of Learning Experiences (01.0; PPT Slide 29) i. Children learn best when they engage in meaningful and familiar situations, actively constructing knowledge and discovering relationships within their environments. ii. There are three types of learning experiences: naturalistic, where children control choice and action; informal, where children choose activities with adult intervention; and adult-guided, where adults choose the experience and provide direction. iii. These experiences align with both Piagetian constructivist and Vygotskian views, with naturalistic experiences fitting the constructivist approach and informal and adult-guided experiences aligning with Vygotskian theory. iv. All three types of experiences can be integrated into lessons structured around the learning cycle and multimodal creative inquiry, catering to different learning styles and cultural backgrounds. a. Naturalistic Experiences i. Naturalistic experiences occur spontaneously as children engage in their daily activities, serving as a primary mode of learning during the sensorimotor period and remaining valuable for older children as well. ii. Adults play a supportive role by providing a stimulating environment and observing children’s activities, responding with encouragement, descriptions, or elaborations. iii. Examples of naturalistic experiences include counting pennies, observing plant leaves, sorting objects by color, mixing colors while painting, drawing the moon, and experimenting with measuring cups to understand volume and shape relationships. b. Informal Learning Experiences i. Informal learning experiences are not preplanned and occur spontaneously when the adult senses an opportunity to scaffold the child’s learning. ii. These experiences often involve the adult providing support or reinforcement during a child’s naturalistic exploration, such as counting fingers or discussing size comparisons initiated by the child. c. Adult-Guided Learning Experiences i. Adult-guided experiences involve preplanned lessons or activities conducted by the adult, either with individuals or groups, at specific times. ii. These experiences may follow a structured learning cycle or consist of focused instruction aimed at addressing specific learning objectives, such as practicing counting or exploring concepts like shape matching. d. Diverse Learning Styles a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. In planning learning experiences, it’s crucial to consider individual learning styles, which can encompass modalities like auditory, visual, or kinesthetic preferences as well as temperamental characteristics and strengths in particular areas identified by Howard Gardner’s theory of multiple intelligences. ii. To accommodate this variety, integrating curriculum areas rather than teaching them separately is increasingly emphasized, with a focus on interconnectedness and flexibility in addressing different learning styles and purposes. e. STEM and Equity in the Classroom i. In planning and instruction, it’s essential to consider diversity not only in multimodal learning styles but also in race, ethnicity, social class, gender, out-ofschool experiences, and special needs. ii. The reform movement in mathematics and science classrooms emphasizes active student engagement in constructing, discussing, and questioning knowledge, requiring teachers to be attuned to each student’s learning style and abilities, while equity in education demands culturally relevant instruction and high expectations for all students, including English Language Learners and those from lower socioeconomic backgrounds. f. Helping Children with Special Needs and Non-Typical Development i. A significant amount of research has focused on the quantitative development of typical young children, providing valuable insights for instructional practices. ii. However, it’s equally important to address the development and instruction of children with special needs or non-typical development in STEM fields. iii. Strategies such as cooperative learning groups and computer activities have shown promise in enhancing mathematics skills for all children. Tailored approaches are necessary to support the diverse needs of gifted students and those with learning disabilities and aim to promote confidence and positive learning experiences.

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g. Digital Technology Today i. Digital technology is rapidly evolving and will increasingly play a significant role in the learning experiences of young children, presenting challenges for educators in homes and schools. ii. While access to technology remains a concern for many, teachers are urged to embrace new technologies and explore their effectiveness in facilitating children’s learning. iii. With the rise of various digital platforms, educators must stay informed about technological advancements and make informed decisions about integrating technology into educational programs.

III. Six Steps in Instruction/Curriculum Planning Cycle (01.03; PPT Slide 36) i. STEM education in early childhood has gained prominence, emphasizing problemsolving and inquiry-based instruction, where both teacher-developed and childgenerated problems are essential. ii. Teachers play a facilitating role, supporting students within their zone of proximal development, while creativity is highlighted as crucial for STEM, evolving into STEAM by integrating the Arts. iii. The instructional process follows a cyclical approach, focusing on assessment, reflection, implementation, and adaptation to ensure effective teaching and learning. a. Assessing i. Children should undergo individual assessment through methods such as interviews and observation during their regular activities to gauge their existing knowledge and abilities before planning instruction. ii. Specific task assessments involve tasks like counting objects, comparing quantities, ordering objects by size, and solving math problems using manipulatives, drawings, or writing, tailored to different age groups to assess their mathematical understanding and problem-solving skills. b. Reflect and Plan i. When planning instruction for young children in STEM, it’s crucial to choose objectives tailored to each child’s existing skills and knowledge level. Objectives should be selected based on individual needs, considering factors like counting abilities and sorting skills. ii. When planning experiences, instructors should prioritize naturalistic activities and gradually introduce informal and adult-guided experiences as children progress through developmental stages, always ensuring materials are developmentally appropriate and conducive to hands-on exploration. iii. Additionally, when selecting materials, it is important to consider their sturdiness, versatility, alignment with learning objectives, and developmental appropriateness, ensuring a progression from concrete to abstract experiences. c. Implement Strategies i. After objectives have been identified and plans and materials are in place, the next step is implementation, which involves teaching. Epstein (2014) advocates for Intentional Teaching, a balanced approach that combines child-guided and adult-guided teaching and that is guided by specific goals and objectives.

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ii. Teaching occurs when planned experiences using selected materials are put into operation, with the duration varying depending on the complexity of the concept and the child’s age and ability. iii. For instance, the concept of time is acquired gradually through naturalistic activities and informal experiences, with some children grasping it quickly while others may take longer, necessitating flexible and individualized instruction. d. Reflect on Implementation i. Even with careful planning, an activity might not succeed initially. In such cases, it is crucial to analyze the situation by asking questions such as whether the children were interested, if the task was appropriate for their skill level, if they understood the instructions, and if the materials were suitable and engaging. ii. Further assessment may be necessary, and adjustments to the method or materials might be needed for a successful outcome. Evaluation involves determining what the child has learned, which can be done through formal questions, tasks, specific observations, and informal inquiries to tailor future activities to the child’s needs and interests. e. Problem Solving and Inquiry i. Problem solving and inquiry are integral to STEM education, fostering critical thinking and reasoning in children’s approach to mathematical problems and scientific investigations. ii. In science, technology, and engineering, problem solving is driven by curiosity, encouraging students to explore and inquire. Teachers create environments that support problem solving and inquiry, as seen in examples like kindergarten students exploring rocks or preschoolers working on physics problems. iii. The process involves identifying a problem, determining outcomes, exploring solutions, and evaluating results. iv. In mathematics, problem solving is emphasized in the Common Core State Standards, promoting active learning and heuristic approaches. Problem types vary from routine to nonroutine, with children engaging in activities like addition problems and creative solutions to real-life scenarios.

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IV. National Assessment Standards (01.04; PPT Slide 42) i. Assessment in early childhood education aims to gauge children’s knowledge, skills, and attitudes in mathematics and science, supporting both learning and identifying those who may need additional assistance. ii. Assessment methods include observation, questioning, and interviews and are integrated into everyday activities to provide valuable feedback for teachers and students alike, promoting a positive attitude towards math and science while fostering individualized instruction. a. Assessment Methods i. Teachers employ observation and interviews as assessment methods to evaluate a child’s developmental level, utilizing teacher-developed tasks for everyday assessment and planning. ii. While initial screening instruments offer a broad overview of educational assessments, they are supplemented by individualized assessments using concrete materials and verbal or motor responses, with paper-and-pencil tests reserved for later developmental stages. b. Assessment Tasks i. The assessment tasks provided in each content chapter and in Appendix A cover the developmental concepts from infancy through the primary grades. Tasks are tailored to nine developmental levels, ranging from basic sensorimotor skills to more advanced skills expected by the end of the primary grades. ii. These tasks encompass individual interviews as well as observational assessments, focusing on sensory and motor development, language acquisition, and mathematical concepts relevant to each developmental stage. c. Assessment Task File i. Teachers should maintain a personalized collection of assessment tasks tailored to the diverse needs and developmental stages of individual children and groups.

This collection can be organized digitally or in a paper format, allowing for easy addition, revision, or removal of tasks. ii. Tasks typically involve concrete materials, pictures, or virtual manipulatives, with Appendix A providing a range of tasks for download. Each child progresses at their own pace, and tasks should be adjusted accordingly, with a sample recording sheet provided for tracking individual progress and instructional needs. d. Record Keeping and Reporting i. Portfolios serve as systematic collections of student work, providing evidence of understanding and growth through ―authentic‖ assessment in various real-world contexts. ii. Organized in folders with hanging files or expanding legal-size file pockets, portfolios include dated pieces of work selected through regular student-teacher conferences, fostering student reflection and self-evaluation. iii. Examples of portfolio items range from written descriptions of investigations to drawings, reports, diagrams, journal entries, and recorded data such as videos or audio recordings. e. Maintaining Equity i. Highlight the importance of using culturally appropriate assessment methods and making modifications for children with diverse needs, emphasizing the need for ongoing collaboration between professionals and family members. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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ii. Assessments for English Language Learners should consider language proficiency and may involve a dual-language approach for instructional guidance. iii. For children with special needs, assessments should be comprehensive and involve a multidisciplinary team, while day-to-day assessment remains the responsibility of the teacher, ensuring authentic evaluation and timely referrals to specialists when needed.

V. Summary [return to top]

ADDITIONAL RESOURCES PRIMARY SOURCES ●

Bohart, H. & Procopio, R. (Eds.) (2018). Spotlight on Young Children: Observation and Assessment. Washington, DC: National Association for the Education of Young Children.

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Charlesworth, R., & Leali, S. A. (2012). Using problem solving to assess young children’s mathematics knowledge. Early Childhood Education Journal, 39(6), 373–382.

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Fairbanks, A. M. (2013, May 22). Digital trends shifting the role of teachers. EducationWeek. www.edweek.org.

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Froschauer, L. (2013). The role of science standards in early childhood education. In A. Shillady (Ed.), Exploring Science (pp. 72–74). Washington, DC: National Association for the Education of Young Children.

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Koestler, C., Felton, M. D., Bieda, K. N., & Otten, S. (2013).

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Connecting the NCTM process standards & the CCSSM practices. Reston, VA: National Council of Teachers of Mathematics.

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Science for all. (2014), Science and Children [Focus Issue] 51(5).

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Turrou, A.C., Johnson, N.C., & Franke, M. (2021). The young child and mathematics, 3rd ed.

Washington, DC: National Association for the Education of Young Children.

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Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 2: Basics of Science, Technology, and Engineering

TABLE OF CONTENTS Purpose and Perspective of the Chapter Chapter Objectives

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Chapter Outline

12

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Additional Resources 18 Primary Sources ...................................................................................................................................... 18

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to equip educators with the necessary knowledge and skills to effectively teach science by integrating key principles outlined in national standards. Participants will gain an understanding of the significance of the science framework and standards, appreciate the symbiotic relationship between science and literacy, and grasp the dual nature of science as both inquiry and engineering design. Through exploration of various content areas of science, participants will deepen their understanding of how science concepts are developed and learned, enabling them to incorporate this understanding into their teaching practices. Additionally, participants will learn to assess, plan, teach, and evaluate science instruction in alignment with national standards, ensuring that their teaching practices uphold the highest educational standards and promote student success in science education.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 2-1

Recognize and explain the importance of the science framework and standards, the relationship of science and literacy, science as inquiry and as engineering design, and the content areas of science.

2-2

Understand how science concepts are developed and learned and incorporate this understanding in your practice.

2-3

Assess, plan, teach, and evaluate science instruction in line with national standards.

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CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and, therefore, by topic) so that you can see how all the content relates to the topics covered in the text.

V. The Framework and Standards for Science Education (02.01; PPT Slide 3) i. With the evolution of STEM education, science is now categorized into four core areas, encompassing physical sciences, life sciences, earth and space sciences, and engineering, technology, and applications of science. ii. The integration of engineering and technology in science education represents a significant conceptual shift, emphasizing problem-solving skills and fostering a lifelong curiosity for scientific exploration and engineering solutions. i. Science as Inquiry and Engineering Design i. Inquiry-based learning, rooted in children’s questions, is a foundational approach in science education, fostering the development of scientific understanding and critical thinking skills. ii. Through inquiry, students engage in active exploration, utilizing scientific reasoning to construct explanations, communicate findings, and cultivate a deeper appreciation for the nature of science, technology, and engineering. j. Process of Inquiry a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. Science process skills, integral for students to navigate new information through hands-on experiences, are foundational and progressively develop over time, starting with basic skills like observing and measuring in pre-K and primary grades. ii. Mastering these fundamental skills lays the groundwork for more complex processes, such as inferring and predicting, enabling students to engage in sophisticated experimentation as they progress through their education. k. Science Process Skills Used in Inquiry  Through the utilization of inquiry processes, individuals engage in problem-solving and gradually build their understanding of scientific inquiry, enhancing their abilities to think critically and analyze phenomena.  Employing observation, comparison, and classification, students develop foundational skills essential for scientific exploration, enabling them to identify patterns, make connections, and organize information effectively as they investigate the world around them. i. Observing ii. Comparing iii. Classifying iv. Communicating v. Inferring vi. Predicting vii. Hypothesizing and Controlling Variables = Investigation l. Developing Scientific Attitudes Used in Inquiry i. In cultivating scientific attitudes such as curiosity, skepticism, and a positive approach to failure, educators lay the groundwork for lifelong habits essential for effective problem-solving and critical thinking. ii. Encouraging students to question, explore, and maintain an open mind fosters a positive self-image and resilience, nurturing skills vital for both scientific inquiry and navigating life’s challenges.

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m. Engineering Design i. The integration of science and engineering in education bridges scientific inquiry with engineering design, tapping into children,s inherent creativity and problemsolving instincts, particularly evident in activities like building sandcastles and constructing forts. ii. Beginning in kindergarten and progressing through elementary school, students engage in the engineering design process, from defining problems and developing solutions to comparing alternatives, fostering critical thinking and practical application of STEM concepts. n. Science Content Knowledge and Learning and the Development of Literacy i. Despite the challenges teachers face with packed schedules, the argument for incorporating science into daily lessons is compelling: neglecting science education is a costly omission. ii. Integrating STEM and literacy activities not only deepens technical understanding but also enhances communication, critical thinking, and empathy skills among children, fostering holistic development essential for success in a rapidly evolving world. o. Appropriate Science Content i. The science curriculum for pre-K can be tailored to match students’ interests, while in kindergarten through high school, it aligns with the specifications outlined in the Next Generation Science Standards (NGSS) and A Framework for K-12 Science Education. Although the content is important, the manner in which science is taught holds significant value, with emphasis placed on integrating engineering design into scientific inquiry to nurture problem-solving skills and critical thinking. ii. The primary grades emphasize four main science areas—life science, physical science, earth and space sciences, and engineering, technology, and applications of science—setting the stage for comprehensive STEM education. p. Important Developmental Factors i. Taking Science to School (Committee on Science Learning, 2007) identifies four overarching themes that shape knowledge growth beyond pre-K, which will be further explored in Section 2-2 of this chapter. ii. As primary grade children build upon their pre-K knowledge, it becomes evident that cognitive achievements during infancy and toddlerhood lay the groundwork for future understanding. iii. Elementary school science learning often delves into intricate details of previously explored concepts, such as gear action or digestion, as children employ concrete thinking to deepen their understanding. iv. Navigating through misconceptions can actually be a crucial step in cognitive development, as it allows children to progress toward more accurate understanding of scientific concepts during their primary and elementary years.

II. Concept Understanding in Young Children (02.02; PPT Slide 12) i. Young children often construct magical explanations to make sense of the world, such as believing chickens lay eggs and pigs lay bacon, or that the sun follows them on walks.

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a.

b.

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d.

ii. Piaget and Vygotsky’s research on children’s beliefs underscores the understanding that learning is an internal process where misconceptions are a normal part of development, and children must progress through stages naturally, supported within their Zone of Proximal Development.

Enhancing Awareness i. To help children understand abstract concepts, focus on aspects they can grasp, and utilize visual aids, observation, drawing, and discussion to enhance their awareness. ii. Encouraging children to observe, draw, and discuss their observations promotes awareness and understanding of various phenomena, such as weather patterns or animal characteristics, fostering curiosity and engagement in learning.

Teacher Magic and Misconceptions i. Children need ample time to engage with materials and explore concepts, as misconceptions can arise at any stage of development. ii. Even as children progress through developmental stages and move away from magical explanations, concrete experiences remain crucial for concept development, highlighting the importance of hands-on interaction and multimodal creative inquiry.

Self-Regulation and Concept Attainment i. The process of self-regulation in concept development involves encountering discrepant events, leading to a state of disequilibrium where learners actively seek new information to reconcile their understanding. ii. By accommodating and assimilating new information, students modify their existing cognitive structures, moving from a state of confusion to a deeper understanding of concepts.

Discrepant Events i. Discrepant events create a state of curiosity and readiness for learning in students by challenging their existing understanding. ii. By leveraging these events, teachers can engage students in investigative activities that deepen their understanding of concepts, such as the role of smell in food appreciation or the behavior of water and ice during freezing and melting processes.

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e. Using the Learning Cycle to Build Concepts i. The learning cycle, based on Piaget’s equilibration process, provides a framework for designing lessons that align with how children naturally learn, promoting assimilation and accommodation of new concepts. ii. Discrepant events, like those utilized in the learning cycle, stimulate curiosity and place students in a state of disequilibrium, fostering inquiry and exploration. iii. By incorporating exploration, concept development, and concept application phases, teachers can guide students through a process of self-regulated learning, encouraging them to actively engage in inquiry-based activities and develop problem-solving skills from an early age. f. Strategies That Encourage Inquiry i. The inquiry-based approach to early childhood science education emphasizes active engagement in constructing ideas and explanations, fostering curiosity and critical thinking skills. ii. Children are encouraged to ask questions, conduct investigations based on systematic observation, and communicate their findings, promoting the development of scientific inquiry skills from an early age. iii. By providing opportunities for hands-on exploration, discussion, and reflection, educators can support children in constructing their own knowledge and understanding of the world through multimodal creative inquiry.

III. Integrating Science into the Curriculum (02.03; PPT Slide 22) i. Children benefit from encountering concepts through diverse and extended experiences, such as post-visit activities following a zoo trip or integrating science with other subjects like art, music, and literacy. ii. By incorporating hands-on exploration, creative play, and interdisciplinary connections, educators can create rich learning environments that engage children in active inquiry and facilitate their understanding of scientific concepts. a. Children Learn in Different Ways i. To accommodate diverse learning styles among kindergarten students, a teacher plans science activities that cater to individual preferences, such as group discussions and solitary work. ii. By incorporating visual, auditory, and interactive elements into lessons about flamingos, the teacher ensures engagement and understanding across the class while integrating science with other subjects.

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b. Organizing for Teaching Science i. When planning science lessons, begin by assessing students’ existing knowledge and interests, then determine the essential content and the most effective organization of learning experiences using techniques like webbing to visually outline concepts and activities across subject areas and instructional methods. ii. The activity plan serves as a vital tool for structuring experiences to foster concept development, incorporating adaptability and a focus on science concepts, material manipulation, and reinforcement through supplementary activities and interdisciplinary connections, with an illustrative example provided in Figure 26, the bubble machine. iii. When planning an activity, it’s crucial to define the main concept to be taught and formulate clear objectives that specify the desired behavior of the students, followed by organizing materials and preparing the necessary steps for implementation, including an engaging initiating experience and opportunities for extension to reinforce learning. c. Assessment Strategies i. To ensure effective teaching, assessment should be integrated into lesson plans to gauge student understanding and progress, allowing for adjustments in teaching strategies based on ongoing observations and feedback while also validating students’ existing knowledge and addressing any misconceptions through varied assessment strategies. d. Evaluating the Investigation Plan i. The investigation should be critically evaluated by considering whether it relates to children’s prior knowledge, incorporates various science process skills, aligns with developmental appropriateness, integrates other subject areas, utilizes reading and writing activities that complement hands-on learning, incorporates diverse instructional strategies, encourages active inquiry, provides opportunities for investigation and problem-solving, includes both open-ended and narrowly focused questions, ensures assessment strategies to evaluate application of learning, utilizes local resources, and ultimately addresses developmental appropriateness, student interest, effectiveness of activities, understanding of students, and desired learning outcomes. Reflection and assessment data should guide judgments about the effectiveness of teaching.

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e. Three Basic Types of Science Investigations and Units i. Some teachers prefer to compile resource files containing a diverse range of activities and suggestions tailored to a specific science topic. ii. This allows for flexibility in meeting the needs and interests of children, while others opt for more concise teaching plans detailing exactly what will be taught, including objectives, materials, activities, and evaluation procedures, often with initiating and culminating experiences. iii. Textbook units may also be utilized to supplement learning, although they may not always align with children’s interests. a) Effective questioning involves starting with narrowly worded, convergent questions to build confidence and then transitioning to open-ended, divergent questions to stimulate discussion and critical thinking, ensuring that students remain engaged and motivated throughout the learning process.

IV. Summary [return to top]

ADDITIONAL RESOURCES PRIMARY SOURCES 

Bredekamp, S., & Rosegrant, T. (1992). Reaching potentials: Appropriate curriculum and assessment for young children (vol. 1). Washington, DC: National Association for the Education of Young Children.

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Bredekamp, S., & Rosegrant, T. (1995). Reaching potentials: Transforming early childhood curriculum and assessment (vol. 2). Washington, DC: National Association for the Education of Young Children.

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Charlesworth, R. (2014). Understanding child development, 9th ed. Belmont, CA: Wadsworth Cengage Learning.

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Duschl, R., & Grandy, R. (Eds.) (2008). Teaching scientific inquiry: Recommendations for research and implementation. Rotterdam: Sense Publishers.

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Harlan, J., & Rivkin, M. (2007). Science experiences for the early childhood years: An integrated affective approach, 9th ed. Upper Saddle River, NJ: Merrill/Prentice-Hall.

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Lederman, N. G., Lederman, J. S., & Bell, R. L. (2005). Constructing science in elementary classrooms. Boston: Allyn & Bacon.

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NSTA, National Science Teachers Association. (Member Draft, December 2013). NSTA Position statement: Early Childhood Science Education. www.nsta.org.

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NSTA, National Science Teachers Association. (2002, July). Position statement: Elementary School Science. www.nsta.org. a

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

Weiss, T. H. (2013, Summer). Any questions? Science and Children, 50(9), 36–41.

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Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 3: Prekindergarten and Kindergarten Concepts and Skills: Mathematics—One-to-One Correspondence, Number Sense, Logic/Classification, Comparison, Early Geometry

TABLE OF CONTENTS Purpose and Perspective of the Chapter Chapter Objectives

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20

What’s New in This Chapter 20 Chapter Outline

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Additional Resources 30 Primary Sources ...................................................................................................................................... 30

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to provide educators with a comprehensive understanding of foundational mathematical concepts and skills aligned with national standards, encompassing one-to-one correspondence, number sense, logic and classification, comparison, and shape concepts. Participants will learn to understand, assess, plan, teach, and evaluate these essential mathematical concepts in accordance with established standards, ensuring effective instruction and student mastery. Through exploration of diverse teaching strategies and assessment methods, participants will develop the expertise to create engaging and developmentally appropriate learning experiences that foster mathematical understanding and proficiency in students. By aligning instruction with national standards, educators will be equipped to support the mathematical growth and success of all learners in their classrooms.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 3-1

Understand, assess, plan, teach, and evaluate one-to-one-correspondence concepts aligned with national standards.

3-2

Understand, assess, plan, teach, and evaluate number and number sense concepts aligned with national standards.

3-3

Understand, assess, plan, teach, and evaluate logic and classification concepts aligned with national standards.

3-4

Understand, assess, plan, teach, and evaluate comparison concepts aligned with national standards.

3-5

Understand, assess, plan, teach, and evaluate shape concepts and early geometry aligned with national standards.

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WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Expectations and Characteristics of Shape

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Added section: Sample Assessment Tasks

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Added section: Sample Activities

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Added section: Figures for Illustration of Concepts and Skills

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CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

VI. One-to-One Correspondence (03.01, PPT Slide 4) i. One-to-one correspondence, although not explicitly mentioned in CCSSM, is emphasized by the National Council of Teachers of Mathematics (NCTM) as crucial for rational counting, a foundational skill for early mathematics. ii. It entails matching objects to numbers and is essential for understanding equivalence and conservation of number, serving as a prerequisite for rational counting rather than mere rote memorization of number names. a. Pre-Assessment Observation i. To gather informal insights into children’s understanding, observe their behaviors during various activities, noting instances of natural one-to-one correspondence such as when they assign objects like chairs or mittens to each individual, and utilize diverse tools, including digital and virtual manipulatives, to aid their problem-solving skills, with interview assessments provided for further evaluation. b. Activities i. Naturalistic Activities a) Naturalistic activities in early childhood involve the development of oneto-one correspondence skills, beginning with infants’ sensorimotor exploration of grasping objects, progressing to toddlers’ understanding of fitting objects into corresponding spaces and arranging items in sets, such as placing one toy animal in each container or setting the table for themselves and a stuffed bear with matching utensils. ii. Informal Activities a) Daily informal one-to-one correspondence activities, such as distributing items to a group and ensuring everyone has what they need, provide ample opportunities for children to practice this skill, aiding in problemsolving and fostering equitable participation, while informal rules and interventions based on one-to-one correspondence, such as distributing toys equally among children or enforcing limits on resources like swings or juice cups, help manage social situations and promote fairness in shared activities and resources. iii. Adult-Guided Activities a) When planning adult-guided activities for one-to-one correspondence, educators should consider a wide range of materials and adhere to the six steps from concrete to abstract, while also taking into account five key characteristics such as perceptual qualities, number of items, and concreteness, ensuring materials are developmentally appropriate and safe for children, particularly those under 3 years old. c. Supporting Children with Special Learning Needs i. Engaging in one-to-one correspondence games, such as matching activities and finger plays, not only enhances perceptual-motor skills and vocabulary a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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acquisition but also provides valuable support for children with language delays by incorporating labeling and questioning techniques to encourage speech development. d. Support for English Language Learners i. Engaging English Language Learner (ELL) students, particularly Spanish speakers, in bilingual finger plays and counting games fosters math vocabulary development for all children, while paired learning experiences between multilingual classmates not only support math skills but also enhance language acquisition and social-emotional growth, as illustrated by the interaction between two emergent bilingual kindergarteners during a math card game. e. Informal Post-Evaluation i. Informal evaluation methods involve observing children’s responses during adult-guided activities and learning center play, assessing their ability to distribute items one at a time, organize materials according to shapes and quantities, and match objects to their designated locations, while a more formal assessment can be conducted using similar procedures to evaluate children’s learning outcomes.

VII. Number Sense and Counting Standards and Description (03.02; PPT Slide 10) i. According to CCSSM and NCTM/NAEYC guidelines, by the end of kindergarten, children should count to 100 by ones and tens, write numbers up to 20, count objects up to 20, and compare groups of objects, while preschoolers should progress from counting small groups to counting by tens, identify small groups of items quickly, work with patterned items, and begin to understand basic addition and subtraction concepts.

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a. Number Sense and Its Relationship to Counting i. Number sense, crucial for understanding quantities and counting, encompasses the perception of benchmarks like 5 and 10. Number sense aids in estimating quantities and predicting academic success with subitizing, the ability to instantly recognize ―how many‖ items are in a group, including perceptual and conceptual subitizing, which play a foundational role in developing number sense from infancy through preschool years.  Rote and Rational Counting (1) Rote counting involves reciting numerals from memory, while rational counting involves matching each numeral to an object in a group, requiring coordination of eyes, hands, speech, and memory; by the end of kindergarten, children typically become proficient in both rote and rational counting, which lay the foundation for understanding numbers and their relationships, though developmentally appropriate activities and materials, along with naturalistic and informal instruction, are crucial for fostering these skills. b. Informal Pre-Assessment i. The adult should observe children’s spontaneous activities, noting their ability to recognize small groups without counting and their accurate use of rational counting, such as counting objects independently, while also documenting these naturalistic and informal interactions for formal assessment, utilizing sample tasks provided in the chapter and appendix. c. Activities i. Children engage in naturalistic activities where they practice rote counting and begin to grasp number concepts, such as recognizing quantities up to two or three, using number names for division, and expressing desires for more items, indicating early numerical understanding and language development. ii. Informal activities offer numerous opportunities for rote and rational counting instruction, such as counting while waiting for the school bus or counting objects during everyday tasks like putting on shoes, setting the table, or distributing toys, facilitating children’s numerical understanding through frequent, short practice sessions and encouraging problem-solving skills through open-ended questions. iii. Adult-Guided Activities  Adult-guided activities for teaching counting skills include using rhymes, songs, and finger plays, practicing rote counting through clapping and rhythmic activities, introducing groups of zero to four items before progressing to larger groups, engaging children in counting games and problem-solving challenges, and utilizing various resources such as computer software and interactive games to reinforce counting skills. d. Supporting Children with Special Needs i. Typically developing children learn counting and number sense through informal experiences, books, and rhymes, but some require additional teacher-guided activities. ii. These may include verbalization through finger plays, multisensory experiences such as jumping on a trampoline while counting, and structured activities like a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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counting objects into containers or completing self-correcting puzzles to develop counting skills and number sense. e. Informal Post-Evaluation i. Informal evaluation of children’s counting and number sense can be conducted during adult-guided activities and center time by observing their application of learned concepts and asking questions about their actions. ii. Formal evaluation involves tasks like those in Appendix A, with questions focused on children’s ability to count accurately, understand one-to-one correspondence, recognize quantities without counting, make estimates, and apply counting strategies consistently.

VIII. Logic and Classification Standards for Science and Math (03.03; PPT Slide 20) i. The Core Curriculum State Standards for Mathematics (CCSSM) emphasize the ability of children to classify objects and count the number of objects in categories, while NGSS science standards focus on developing logical thinking through sorting, classifying, and organizing data about objects. ii. Children construct logical groups based on common criteria, gradually organizing materials by criteria that become apparent to adults as they develop, and they learn to group items based on various attributes such as color, shape, size, material, pattern, texture, function, and association. a. Informal Pre-Assessment i. The adult should observe and document children’s play activities, noting whether they engage in sorting and grouping behaviors with their play materials, such as organizing pegs by color or separating snacks by shape. ii. Formal assessment can be conducted using tasks provided at the end of the chapter and in Appendix A.

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b. Activities

i. Naturalistic Activities 





Naturalistic activities for young children involve sorting and grouping objects, which is fundamental to their play and exploration of the world around them.

From infancy, they begin to categorize people and objects based on their experiences, such as distinguishing between caregivers and strangers or identifying items that alleviate teething pain.

As they grow older, children engage in activities like putting objects into containers and organizing their play materials based on their preferences and interests, demonstrating their developing ability to sort and group items by various criteria.

ii. Informal Activities 





Informal activities to promote sorting and grouping skills involve adults acknowledging and encouraging children’s efforts through nonverbal cues like nods or smiles, as well as verbal reinforcement.

By labeling children’s activities and asking questions about their sorting and grouping choices, adults help expand their vocabulary and understanding of classification concepts.

As children develop language skills, they can articulate their sorting strategies and reasons behind their groupings, enhancing their ability to categorize objects effectively.

iii. Adult-Guided Activities 

Adult-guided activities aimed at teaching sorting and grouping skills, essential for classification, encompass various materials and exercises, transitioning from real objects to representations like cutouts or pictures.  One-to-one correspondence is integral to these activities, as children match objects in equal numbers or sort them into different groups.  Classification, a key skill in science, involves recognizing patterns and order, mirroring how scientists observe the world. c. Supporting Children with Special Needs

i. Copley, Jones, and Dighe (2007) propose various strategies to cater to the requirements of children with special needs and those with atypical development. ii. Advanced learners might require more stimulating activities to prevent boredom, including tasks involving number symbols, chart creation, or advanced computer programs. iii. Children facing delays can benefit from accommodations tailored to their needs, leveraging their strengths while addressing areas of difficulty. iv. Using multisensory experiences, breaking concepts into smaller components, and utilizing special technology are some effective approaches, as elaborated in Section 3-2, with further discussion in Chapter 12. d. Support for English Language Learners a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. Support English Language Learner (ELL) students by simplifying language, repeating rhymes and chants, and using visual aids to aid recognition. ii. Engage them in classification activities to expand their English vocabulary, incorporating culturally relevant materials and utilizing their heritage language whenever feasible. e. Evaluation i. Monitor children’s play activities to observe if they engage in sorting and grouping, which should increase with age and experience. ii. Encourage children to use a variety of descriptors such as color, shape, size, material, pattern, texture, function, association words, and class names during both work and play. iii. Structured evaluation can be conducted using sample assessment tasks provided at the end of the chapter and in Appendix A. IX. Comparison Standards and Description (03.04; PPT Slide 26) i. Children’s development of measurement relationships begins with simple qualitative and quantitative comparisons, as outlined by the CCSSM (2010), where they describe differences like ―I am taller than you‖ or ―I have more marbles than you.‖ ii. By the end of kindergarten, they should be able to identify whether one group of objects has more, less, or an equal number of items compared to another group, using strategies such as number sense, matching, and counting, as well as comparing written numerals between 1 and 10. iii. Comparing involves evaluating relationships between objects based on attributes like size, length, or quantity, forming the foundation for ordering and measurement skills. iv. Examples include statements like ―Father bear is bigger than baby bear‖ for size comparisons and ―I have more blocks than you have‖ for number comparisons. a. The Basic Comparisons i. Children learn various basic comparisons to make sense of differences, including informal measurements such as large/small, big/little, long/short, tall/short, rough/smooth, heavy/light, fast/slow, cold/hot, thick/thin, wide/narrow, near/far, later/sooner, older/newer, and loud/soft (sound). ii. Additionally, they learn number comparisons such as more/less or fewer. iii. They also recognize instances where there’s no discernible difference or when two compared groups have the same amount, aided by concepts like one-to-one correspondence, counting, and classifying. b. Informal Pre-Assessment i. Before initiating instruction, it’s important to assess the children’s current understanding levels, particularly in their ability to make comparisons. ii. During play activities, teachers should observe whether children engage in activities that involve comparing, such as selecting appropriately sized boxes for dolls or building suitable structures for different-sized objects. iii. Additionally, teachers should pay attention to whether children use basic comparison words in their interactions. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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iv. In individual interview tasks, teachers can directly question children to gauge their comprehension and use of basic comparison words. v. Sample tasks involving objects or pictures with varying attributes or quantities are provided for assessment purposes. c. Comparison Activities i. Naturalistic Activities  Young children naturally encounter comparisons in their daily experiences, both at home and at school.  Parents and teachers often use comparison language to provide guidance and instructions, such as encouraging children to eat slowly or select appropriate-sized bowls.  Children also learn through hands-on interactions with materials, noticing differences in size, weight, and space.  For example, infants discover that some objects are easy to hold because they are small and light, while others are too heavy. Similarly, when playing with blocks, children realize they have more small blocks than large ones.  These naturalistic activities help children develop an understanding of various comparisons in their environment. ii. Informal Activities  Young children often express a strong interest in size and number relative to themselves, seeking to be bigger, taller, or to have more things than others. Informal activities naturally arise where adults can assist children in learning the concepts of comparison.  These activities involve concrete experiences in which objects are looked at, felt, lifted, or listened to, and then labeled accordingly.  For instance, a teacher might offer a smaller box of toys to an 18-monthold who struggles with a large box. In another scenario, two 5-year-olds excitedly show their swinging prowess to a teacher, who observes and comments on their height. Similarly, children might compare their heights back-to-back or observe and comment on the differences in size between worms after a rain.  Comparative numbers are also explored concretely, with children matching or counting objects to determine differences in quantity.  Teachers facilitate informal learning by providing materials for exploration and intervening to support children’s discoveries, using comparison words and providing assistance when needed during play and other activities. iii. Adult-Guided Activities  Adult-guided activities provide structured experiences using commercial materials and everyday items to teach comparison skills and vocabulary to children who may not grasp the concept through natural and informal activities. d. Supporting Children with Special Needs i. Comparing groups involves starting with concrete objects and one-to-one correspondence comparisons; progressing to comparing pictorial representations, a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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such as card sets showing various configurations, which may require additional time and practice; utilizing auditory and tactile stimulation; and incorporating terms like ―the same as,‖ ―less than,‖ and ―more.‖ e. Informal Evaluation i. Teachers can assess children’s comparing skills during play and activities by asking questions related to quantity, size, and other attributes without disrupting their engagement, while formal evaluation interviews can utilize tasks from Appendix A.

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X.

Expectations and Characteristics of Shape (03.05; PPT Slide 31) i. By the end of kindergarten, children should be able to recognize, name, build, draw, compare, and sort two- and three-dimensional shapes, integrating geometry with other content areas, with infants learning about shapes through sensorimotor exploration, while preschoolers start developing definitions of shapes through various models and discussions of attributes to generalize to related shapes beyond the obvious. a. Pre-Assessment i. During play, adults should observe whether children group items based on similar shapes or colors, noting instances where children use shape names in conversation, while individual interview tasks focus on discrimination, labeling, matching, sorting, and describing shapes to assess children’s understanding and recognition of different shapes and their characteristics. b. Shape Activities i. Naturalistic activities are crucial for children to learn about shapes, with infants exploring objects through sight and touch, toddlers engaging in sorting and matching activities with various shapes, and older children enjoying exploratory play with objects like buttons and blocks, fostering representational play where shapes are used to symbolize real objects in imaginative scenarios.  Informal Activities (1) Informal activities involving shapes can be integrated seamlessly into daily routines, with teachers acknowledging children’s use of shape concepts through comments and supplying relevant objects, while also incorporating shape labels into regular activities and responding positively when children identify shapes in their environment, fostering their ability to generalize and apply shape knowledge in new situations.  Adult-Guided Activities (1) Adult-guided activities aim to help children understand the critical attributes of shapes by offering diverse models, including variations in orientation and nonexamples for comparison while engaging in activities such as identifying shapes in different settings, sorting shapes based on attributes, and copying and building with shapes using both tactile and visual experiences.

These experiences may involve haptic activities relying on touch, visual activities using sight, and visual-motor activities combining sight and motor coordination that are facilitated through various manipulatives and resources such as puzzles, attribute blocks, and online platforms like the National Library of Virtual Manipulatives, with teachers providing labeling support to reinforce shape vocabulary. c. Supporting Children with Special Needs i. Children facing perceptual-motor challenges can enhance their shape recognition skills by practicing with large shape templates on chalkboards or smartboards, starting with basic shapes like circles and progressing to squares, triangles, rectangles, and diamonds, before transitioning to smaller desktop templates on paper, mastering drawing, tracing, and eventually free drawing as they progress. a

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d. Support for English Language Learners i. The texts by Flores (1995) and Zaslavsky (1996) provide insights into teaching geometry to bilingual students and exploring cultural influences on shape perception. ii. Flores emphasizes using templates and problem-solving in Spanish, while Zaslavsky discusses how cultural beliefs influence the shapes of homes worldwide, illustrating how art reflects geometric shapes and spatial concepts. e. Informal Post-Evaluation i. Teachers can assess children’s understanding of shape concepts by observing their activities during center time and adult-guided experiences, noting their use of shape-related vocabulary and their ability to sort and group materials based on shape. ii. Informal tasks like placing objects on specific shapes or identifying shapes in puzzles are used to gauge comprehension, followed by more structured assessment tasks if needed.

XI.

Summary

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ADDITIONAL RESOURCES PRIMARY SOURCES 

Baumgart, N.A. & Kroll, L.R. (2018). STEAM concepts for infants and toddlers. St. Paul, MN: Redleaf.



Copley, J. V. (Ed.). (2004). Showcasing mathematics for the young child. Reston, VA: National Council of Teachers of Mathematics.



Eichinger, J. (2009). Activities linking science with mathematics. Arlington, VA: NSTA Press.

(Activities 1 & 2).

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Equity for diverse populations. (2009). Teaching Children Mathematics [focus issue], 16(3).

Fantozzi, V.B. (2022). Digital tools for learning, creating, & thinking. Washington, DC: National Association for the Education of Young Children.

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Hildebrandt, M. E., Biglan, B., & Budd, L. (2013), Let’s take a road trip. Teaching Children Mathematics, 19(9), 548–553.

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Manfra, L., Dinehart, L. H. B., & Sembiante, S. F. (2014). Associations between counting ability in preschool and mathematics performance in first grade among a sample of ethnically diverse, low-income children. Journal of Research in Childhood Education, 28(1).



McGuire, P., Kinzie, M. B., & Berch, D. B. (2012). Developing number sense in pre-K with fiveframes. Early Childhood Education Journal, 40(4), 213–222.

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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

National Association for the Education of Young Children (2022). Developmentally appropriate practice in early childhood programs serving children birth through age eight, 4e. Washington, DC: Author.



Novakowski, J. (2009). Classifying classification. Science and Children, 46(7), 25–29.

Schwerdtfeger, J. K., & Chan, A. (2007). Counting collections. Teaching Children Mathematics, 3(7), 356–361.

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Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 4: Prekindergarten and Kindergarten Concepts and Skills: Spatial Sense, Parts and Wholes, and Applications of Fundamental Concepts to Science and Engineering

TABLE OF CONTENTS Purpose and Perspective of the Chapter Chapter Objectives

32

32

What’s New in This Chapter 32 Chapter Outline

33

Additional Resources 37 Primary Sources ...................................................................................................................................... 37

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to equip educators with the necessary skills and knowledge to effectively assess, plan, teach, and evaluate spatial concepts, parts and wholes, and science concepts in alignment with national standards. Through a comprehensive exploration of spatial relationships, parts and wholes, and science principles, participants will learn to develop engaging and rigorous lesson activities that foster students’ conceptual understanding and critical thinking skills. By aligning instruction with national standards, educators will ensure that their teaching addresses key concepts and skills essential for student success in spatial reasoning, understanding of parts and wholes, and scientific inquiry. Through practical strategies and hands-on activities, participants will gain the expertise needed to create dynamic learning experiences that promote active engagement and deeper comprehension of these fundamental concepts.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 4-1

Assess, plan, teach, and evaluate spatial concept lesson activities aligned with national standards.

4-2

Assess, plan, teach, and evaluate parts and wholes concept lesson activities aligned with national standards.

4-3

Assess, plan, teach, and evaluate science concept lesson activities aligned with national standards.

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WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Spatial Sense and Spatial Concepts



Added section: Sample Assessment Tasks



Added section: Sample Activities

[return to top]

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CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic) so that you can see how all the content relates to the topics covered in the text.

XII. Spatial Sense and Spatial Concepts (04.01; PPT Slide 3) i. Spatial intelligence, a component of Howard Gardner’s Theory of Multiple Intelligences, is integral to success in STEM fields, as supported by research emphasizing its connection to creativity and problem-solving. ii. Despite the tendency for children high in spatial talent to be misidentified due to poor performance in traditional subjects, early education standards underscore the importance of spatial understanding and geometry concepts. iii. Through activities like building and construction projects, children naturally develop spatial skills, laying the groundwork for future engineering endeavors. iv. Additionally, spatial intelligence plays a crucial role in proprioception, influencing tasks such as navigating spaces safely and judging distances accurately. f. Pre-Assessment i. Teachers can assess children’s understanding of space by observing their use of spatial language and how they respond to spatial directives, such as placing objects or moving in specific ways. ii. They should observe how children organize and arrange materials during activities like artwork, noting if they demonstrate deliberate design choices and balance in their compositions. iii. Teachers should also pay attention to how children use construction materials and whether they effectively utilize space, such as building structures that accommodate toys or fitting objects into appropriate containers. iv. Additionally, teachers should observe how children navigate physical spaces, noting their ability to find comfortable play areas and move without difficulty. v. Interview tasks focused on spatial relationships and space usage can further inform teachers about children’s spatial understanding. g. Activities i. Naturalistic Activities a) Children learn about space through everyday motor activities, where they develop an understanding of position, direction, and distance relationships. b) They require equipment and environments that allow them to explore various spatial concepts such as going up, down, around, and through. c) Handling objects and engaging in activities like matching and building help children learn about space while also developing other skills. d) Dramatic play, inspired by media or imagination, can further enhance their spatial awareness, as seen in activities like building space vehicles. e) Mapping activities, whether through building structures or playing with commercial toys, help children integrate concepts like position, direction,

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distance, organization, and pattern, laying the groundwork for understanding maps.

ii. Informal Activities a) Teachers can enhance children’s spatial sense through informal activities integrated into daily routines, incorporating spatial words into directions, questions, and comments. b) Children engage in activities like climbing on jungle gyms, navigating packing crates, and swinging on swings, experiencing various spatial relationships and developing proprioceptive skills. c) With large blocks, boxes, and boards, children construct structures like houses and trains, incorporating props to inspire imaginative play. d) They arrange toy animals and objects in spatial patterns and positions, learning to fit structures into available space. e) Art activities, such as collage and painting, offer opportunities for children to organize materials within a given space, fostering spatial understanding and connecting to STEAM concepts. iii. Adult-Guided Activities a) Adult-guided activities play a crucial role in helping children develop their understanding of space and spatial skills. b) These activities cover various aspects of space relations, including position, direction, and distance, as well as the use of space through organization, pattern, and construction using design technology. c) The end of the chapter provides basic activities tailored to each of these space-related concepts, offering structured guidance for educators to facilitate children’s spatial learning effectively. h. Supporting Children with Special Needs i. Many young children acquire spatial understanding through outdoor activities, but those with physical disabilities may miss out. ii. However, efforts to create inclusive playgrounds aim to provide opportunities for all children to play together. iii. Additionally, children with perceptual-motor delays can benefit from activities like working at a chalkboard or engaging in nature-based play, which allows them to express themselves through visual-spatial materials. i. Support for English Language Learners i. Children from diverse cultures benefit from play opportunities, where music and movement facilitate spatial learning, while art projects enable them to construct spatial arrangements reflective of their cultural aesthetics. j. Informal Post-Evaluation i. Informal evaluation through observation entails noting children’s responses to space-related cues, their use of appropriate spatial language, their progress in artwork and block-building organization, their physical coordination in space, and improvements in their use of spatial tools like geoboards and parquetry blocks, followed by further assessment using interview tasks to gauge their overall progress in spatial understanding.

XIII. Standards and Part-Whole Relationships (04.02; PPT Slide 14) a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. Young children possess an innate comprehension of parts and wholes, laying a foundation for understanding fractions included in educational standards. ii. They are expected to grasp the concept of whole numbers and fractions, recognize objects and their bodies as composed of distinct parts, and understand division into smaller parts. iii. Through practical activities like dividing snacks or toys and observing examples like cutting fruit, children gradually comprehend that wholes consist of parts, distinguishing between equal and unequal parts and developing numerical comparisons crucial for later mathematical concepts and STEM understanding. iv. This understanding of parts and wholes serves as a precursor to learning fractions and supports broader comprehension in science, technology, and engineering fields. a. Pre-Assessment i. Teachers should observe children’s use of the terms "part" and "whole" and their understanding of sharing equally, dividing items, and recognizing missing parts during their activities and play, utilizing sample assessment tasks provided for interview questions.

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b. Part-Whole Activities i. Naturalistic Activities  Through naturalistic activities, infants and young children gradually discover the concept of parts and wholes as they explore their bodies and manipulate objects, exemplified by instances such as sharing food portions with pets or recognizing quantities of objects like toy milk bottles and slices of pretend carrots. ii. Informal Activities  Teachers can reinforce children’s understanding of parts and wholes through informal activities throughout the day, incorporating words like "part," "whole," "divide," and "half" into tasks such as sharing food, distributing materials, and identifying body parts, thus providing numerous opportunities for learning about fractions and spatial relationships. iii. Adult-Guided Activities  Children can engage in adult-guided activities focused on three types of part-whole relationships, including becoming aware of special parts of people, animals, and objects, dividing groups into smaller groups, and experiencing the division of wholes into parts. c. Supporting Children with Special Needs i. Preprimary grade children learn about parts and wholes as they develop social skills and mathematical concepts, with opportunities for sharing materials being crucial even for children with behavior problems, who can benefit from activities like distributing materials to a group or sharing what they are using with another child. d. Support for Cultural Differences i. When teaching STEM subjects, it is essential to consider cultural factors, as exemplified by Bonner’s successful approach characterized by "warm demanding" and Md-Yunus’s emphasis on culturally appropriate food practices, highlighting the importance of respecting diverse cultural values, including food, in educational settings. e. Informal Post-Evaluation i. Teachers should observe children’s use of part-whole terminology and their proficiency in related activities, such as dividing groups and wholes, recognizing unique parts of objects, people, and animals, and sharing equitably, with individual evaluations conducted using assessment tasks outlined earlier in the unit.

XIV. Science and Engineering Standards and Connection to Mathematics (04.03; PPT Slide 20) i. The Next Generation Science Standards and the Framework prioritize inquirybased learning for children, stressing the importance of processes like asking questions and analyzing data, which are foundational for investigating science and engineering problems, a perspective that aligns with developmentally appropriate practice for preschool, as described by Moomaw and Davis. ii. While NGSS standards introduce specific areas of study starting from kindergarten, they allow flexibility in instructional methods, covering topics such as motion, energy, life sciences, Earth systems, and human activities, with detailed performance objectives outlined for each area. a. Informal Pre-Assessment

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i. Observation and interviews serve as the primary evaluation methods in science education, with interview questions often referred to as formative assessment probes, designed to uncover children’s existing knowledge on specific topics, akin to their use in mathematics assessment. b. Science and Engineering Activities i. Naturalistic Activities  Young children’s natural curiosity drives them to explore their environment, engaging in activities like examining objects, sorting toys, and observing insects, with teachers fostering their explorations through conversations, documentation, and collaborative projects, following the guidance to start with nature and treat the classroom as a laboratory provided by Frances and David Hawkins. ii. Informal Activities  Informal activities in preschool and kindergarten classrooms often stem from children’s natural interests and explorations, with educators integrating STEM concepts into the curriculum based on topics like bird song patterns, pendulums, inclines, and rocks, fostering long-term investigations supported by teachers, while also recognizing the value of introducing early engineering concepts to toddlers through activities involving ramps, pathways, tracks, and balls. iii. Adult-Guided Activities  Adult-guided activities in early childhood education involve shaping experiences that engage and empower children based on their natural interests, emphasizing interactive and hands-on approaches rather than didactic lecturing or worksheets, aiming to foster meaningful learning experiences while respecting children’s agency and autonomy. c. Informal Post-Evaluation i. Post-evaluation in science education, akin to pre-assessment, predominantly utilizes observation and interviews, with interview questions often referred to as assessment probes, aimed at uncovering children’s learning outcomes following a learning experience, facilitating a deeper understanding of the topic area.

XV. Summary [return to top]

ADDITIONAL RESOURCES PRIMARY SOURCES 

Ashbrook, P. (2011). Sense of place. Science and Children, 49(1), 30–31.



Ashbrook, P. (2014). Shape exploration: Another dimension. Science and Children, 5(5), 30–31.



Clements, D. H., & Sarama, J. (2000). Young children’s ideas about geometric shapes. Teaching Children Mathematics, 6(8), 482–488. a

© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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

Eckhoff, A. & Linder, S.M. (2018). Using observation to build STEAM experiences. In H. Bohart & R. Procopio (Eds.), Spotlight on young children: Observation and assessment (pp. 40–44).

Washington, DC: National Association for the Education of Young Children.



Gavin, M. K., & Moylan, K. G. (2012). 7 steps to high-end learning. Teaching Children Mathematics, 19(3), 184–192.



Hu, W. (2010). Studying engineering before they can spell it. New York Times, June 13, 2010, http://www.nytimes.com/2010/06/14/education/14engineering. html?pagewanted=all&_r=0.



Piccolo, D. L., & Test, J. (2010/2011). Preschoolers thinking during block play. Teaching Children Mathematics, 17(5), 310–315.



Presser, A.L., Kamdar, D., & Dominguez, X. (2021). Navigating spatial learning with preschoolers. Teaching Young Children, 14(2), 16-18.



Taylor-Cox, J. (2009). Teaching with blocks. Teaching Children Mathematics, 15(8), 460–463.

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Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 5: Pre-K-K: Ordering, Measurement, and Data Collection and Analysis

TABLE OF CONTENTS Purpose and Perspective of the Chapter ................................................................................................. 39 Chapter Objectives ................................................................................................................................... 39 What’s New in This Chapter ................................................................................................................... 39 Chapter Outline ........................................................................................................................................ 39 Additional Resources ................................................................................................................................ 48 Primary Sources ...................................................................................................................................... 48

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to equip educators with the skills and knowledge to effectively plan, teach, and evaluate diverse mathematical and scientific concepts aligned with national standards. Through comprehensive exploration of ordering, seriation, and patterning; measurement (volume, weight, length, and temperature); time concepts; data and graph representation; and science concept applications, participants will learn to develop engaging and rigorous lesson activities that promote student understanding and mastery. By aligning instruction with national standards, educators will ensure that their teaching addresses key concepts and skills essential for student success in mathematics and science education. Through hands-on activities and practical strategies, participants will gain the expertise needed to create dynamic learning experiences that foster critical thinking, problem-solving, and scientific inquiry skills in their students.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 5-1

Plan, teach, and evaluate ordering, seriation, and patterning concept lesson activities, aligned with national standards.

5-2

Plan, teach, and evaluate measurement (volume, weight, length, and temperature) concept lesson activities, aligned with national standards.

5-3

Plan, teach, and evaluate time concept lesson activities, aligned with national standards.

5-4

Plan and teach data and graph concept lesson activities, aligned with national standards.

5-5

Plan and teach science concept application lesson activities, aligned with national standards.

[return to top]

WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Sample Assessment Tasks



Added section: Sample Activities

[return to top]

CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

XVI. Standards and Expectations (05.01; PPT Slide 3) a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. The Common Core State Standards for Mathematics (CCSSM) do not directly address ordering, seriation, and patterning but include foundational concepts essential for STEM fields. ii. Ordering involves comparing multiple items or groups and arranging them in a sequence from first to last, termed seriation by Piaget. Patterning, related to ordering, encompasses recognizing and creating auditory, visual, and motor regularities and is essential for algebraic thinking and advanced elementary mathematics. iii. Children begin developing ordering and seriation skills in the sensorimotor stage, progressing from simple nesting toys to more complex sequences, which aids in understanding concepts like one-to-one correspondence and double seriation. iv. Furthermore, ordering and patterning words and ordinal numbers are crucial for understanding and communicating sequences and patterns. k. Pre-Assessment i. While observing children at play, teachers should pay attention to activities that demonstrate their ability to order objects, such as how they use nesting toys or line them up from largest to smallest. ii. Children’s use of words like ―first‖ and ―last‖ independently, as well as their engagement in dramatic play where they organize seating arrangements, can indicate their understanding of seriation. Seriation skills may also be evident in children’s drawings or in tasks where they arrange items in a specific sequence, such as paint chips or sequence stories. iii. Additionally, teachers should look for signs of patterning behavior during play, including in artwork, motor activities, language activities, and with manipulative materials like Unifix® Cubes or building blocks. iv. They can also encourage children to practice ordering through individual interview tasks using various items. l. Activities i. Naturalistic Activities a) Children’s natural development inclines them toward engaging in sorting, ordering, and arranging items in patterns. b) During naturalistic activities, children may sort objects based on size, shape, or color and then line them up in rows or create patterns with them. c) For instance, a child might select blocks of similar characteristics and arrange them in rows, or alternate colors when lining them up. d) As children’s language skills develop, they begin to use order words such as ―first,‖ ―last,‖ ―biggest,‖ and ―middle,‖ indicating their growing understanding of sequencing. e) Additionally, as they start drawing, they often depict family members or objects in a row according to size, demonstrating their comprehension of order. ii. Informal Activities a) Informal teaching opportunities arise frequently during children’s daily play and routines. b) For instance, an 18-month-old playing with mixing bowls and measuring cups learns about size by trying them on their head and stacking them by size with the teacher’s guidance. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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c) Older children engage in informal activities like racing, where they learn about sequencing and comparing sizes and ages. d) Teachers also incorporate informal activities into classroom routines, such as lining up by height or documenting the growth of a bean sprout through daily drawings. e) Adults facilitate learning by asking questions and providing opportunities for children to practice ordering and ordinal numbers. f) Materials like Montessori cylinders and block sets offer hands-on experiences for children to explore and practice ordering skills. iii. Adult-Guided Activities a) Adult-guided activities focusing on ordering and patterning can utilize a variety of materials, which the teacher can either purchase or create. b) Everyday items of different sizes, such as measuring cups, mixing bowls, and clothing, provide tangible resources for children to practice ordering. Additionally, paper and cardboard can be manipulated into various shapes and sizes, while paper-towel rolls can be transformed into graduated cylinders. c) Pre-made materials like Unifix® Cube train patterns and counting boards offer structured opportunities for patterning exercises, facilitating hands-on learning experiences for children. m. Supporting Children with Special Needs i. An understanding of patterns and ordering forms the foundation for comprehending algebraic relationships. Employing a multisensory approach accommodates diverse learners’ needs, such as using large colored beads for children with perceptual-motor challenges, incorporating sequence terms into instructions, and engaging auditory learners with rhymes and kinesthetic learners with movement activities. n. Support for English Language Learners and Cultural Diversity i. Children can explore various cultural patterns, such as those found in Native American fabrics and Bakuba designs, through activities like making stamped repeated patterns and using stencils, ensuring respectful use by accurately attributing specific cultural origins and understanding the cultural contexts in which certain patterns are traditionally used. o. Post-Evaluation i. Monitor and encourage children’s development of ordering and patterning skills during play and routine activities by asking questions or making comments, such as identifying the biggest or smallest items, determining the order of arrival or seating, and acknowledging their success in recognizing, extending, creating, and analyzing patterns.

XVII. Measurement Standards and Expectations (05.02, PPT Slide 12) i. The Common Core State Standards for kindergarten outline expectations for children’s understanding of measurement, including describing measurable attributes like length or weight, comparing and ordering objects based on these attributes, and introducing concepts of temperature and volume, emphasizing the importance of estimation and connecting measurement to geometry and number, a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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a.

b.

c.

d.

with standard units used to assign numbers for comparison across attributes like volume, weight, length, and temperature.

Stages of Development i. The development of the concept of measurement progresses through five stages, beginning with play and imitation where children explore volume, weight, length, and temperature through hands-on activities, advancing to making comparisons during the preoperational stage, followed by learning to use arbitrary units in the transition to concrete operations, realizing the necessity of standard units for effective communication during the concrete operations period, and finally, understanding and using standard units such as inches, meters, pints, liters, grams, and degrees. Prekindergartners are typically in stages 1 and 2, kindergartners move into stage 3, and primary-grade students transition into stages 4 and 5.

How the Young Child Thinks About Measurement i. A review of Piaget’s stages of cognitive development helps elucidate why young children in the sensorimotor and pre-operational stages struggle to understand standard units, as they are primarily focused on appearances and lack the ability to conserve attributes or understand changes in volume or quantity. ii. During the preprimary period, children become acquainted with measurement terminology and learn through observation and experimentation, gradually developing a sense of relative quantity through firsthand experiences and exposure to various measurement tools.

Pre-Assessment i. To assess young children’s measurement skills, teachers observe their use of measurement terms and adult measuring tools during play, noting incidents such as a child scooping flour with a measuring cup while pretending to bake, another child measuring a foot with a ruler for new shoes, or a child estimating weight using a toy scale in a play grocery store. ii. Techniques for assessment include presenting children with real-life measurement tools like a rain gauge to gauge their understanding and observing their discussions during play activities, such as dividing puppets based on quantity or length, as described by Hynes-Berry and Grandau.

Activities i. Naturalistic Activities a) Young children’s understanding of measurement develops through naturalistic activities as they explore their environment and engage in play, observing adults’ actions like baking or shoe fitting, and using play materials such as water, sand, and blocks to experiment and learn about volume, linear measure, weight, and temperature through trial and error, developing concepts like relative units and balance on a teeter-totter as they play and interact with their surroundings. ii. Informal Activities a) Informal activities serve as valuable opportunities for young children to learn about measurement, with adults guiding them by pointing out properties of materials and posing problems that encourage critical thinking and exploration, such as determining the volume of water in a gallon container, assessing body temperature, or a

© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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estimating distance or weight, while the teacher’s role is to create an environment rich in opportunities for children to explore and discover measurement concepts. iii. Adult-Guided Activities a) Adult-guided activities in measurement for young children should be carefully selected to engage their senses, build on their existing knowledge, and demonstrate the relevance of measurement in familiar contexts, providing opportunities for children to use measurement language to solve problems, complementing the naturalistic and informal experiences that form the foundation of their understanding of measurement. e. Supporting Children with Special Needs i. Measurement activities in early education settings are conducive to cooperative learning, where children can work together in buddy groups to compare attributes and measure using nonstandard units, with each child assigned a specific responsibility such as handling the measuring tool or recording measurements, facilitating collaboration among children of different abilities, while ensuring accessibility by providing standardized measurement tools with clear markings or accommodations for children with visual impairments and motor delays. f. Evaluation i. The teacher should carefully observe children’s responses and interactions with the given activities, noting their use of materials, comments, and problemsolving abilities, particularly assessing their proficiency in employing informal measurements like comparisons or nonstandard units to solve everyday problems.

XVIII. Time Measurement Standards and Expectations (05.03; PPT Slide 20) i. The Common Core State Standards for measurement include expectations for measuring objects, while the concept of time measurement is introduced later, typically in first grade, as preschool and kindergarten children focus on understanding attributes of time related to sequence and duration, learning about the order of events and the duration of time intervals such as seconds, minutes, hours, days, and distinguishing between short and long durations. a. Kinds of Time i. Young children learn about time through personal experiences, social activities, and cultural norms, struggling with concepts like past, present, and future based on their own memories and perceptions, finding comfort in routines and sequences of events, and gradually grasping the concept of time as measured by clocks and calendars, learning vocabulary and identifying timekeepers before fully comprehending their significance until later developmental stages. b. Language of Time i. Understanding time relies heavily on language acquisition, encompassing general terms like ―time‖ and ―age,‖ specific descriptors such as ―morning‖ and ―night,‖ relational words like ―soon‖ and ―yesterday,‖ duration markers including ―minutes‖ and ―hours‖ associated with clocks and watches, and recognition of special days such as holidays and birthdays, emphasizing the importance of language in grasping temporal concepts. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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c. Pre-Assessment i. Teachers should monitor children’s usage of time-related vocabulary and assess their ability to situate themselves and events temporally. This involves observing if children can recall the sequence of activities both at school and at home, their capacity to wait for one activity to conclude before proceeding to the next, and their aptitude for arranging events in chronological order. d. Activities i. Naturalistic Activities  From infancy, children begin to grasp the concepts of time and sequence through their daily routines and interactions, gradually developing an understanding of duration and chronological order.  As they grow, toddlers demonstrate comprehension of time-related words through their actions, while older children articulate their temporal experiences, indicating a progression in their time awareness and language skills. ii. Informal Activities  Adults play a crucial role in fostering children’s understanding of time and sequence by engaging in informal instruction and modeling timerelated behavior, utilizing language cues and visual aids such as daily schedules to help children grasp concepts and anticipate events. iii. Adult-Guided Activities  Adult-guided time and sequence activities, including patterns with beads and blocks, story sequencing, calendar work, and clock activities, cater to children’s understanding of time and sequence, with experiences ranging from infancy to over 4 years old. e. Support for English Language Learners and Cultural Diversity i. When working with diverse families, it’s crucial to acknowledge cultural variations in perceptions of time, respecting differing views and collaborating with families accordingly, as Euro-American cultures often prioritize punctuality and time management, while other cultures may conceptualize time more flexibly, necessitating understanding and accommodation without punitive measures in educational settings. f. Informal Post-Evaluation i. Teachers should observe and assess children’s development in using time-related language, understanding sequences, waiting for events to conclude before transitioning to the next, recalling past and future events, and utilizing tools like calendars, clocks, and sequence stories to gauge their maturity level in comprehending time and sequence.

XIX. Data and Graphing Standards and Expectations (05.04; PPT Slide 26) i. The Common Core State Standards expect kindergartners to classify objects and count them in each category, with data collection activities starting early to answer questions posed by children. ii. In one scenario, two children debate over the color of paint for a project, prompting the teacher to guide them in conducting a vote using colored blocks and creating a graph to represent the results. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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a.

b.

c.

d.

iii. Through this hands-on experience, children learn to solve problems by collecting data and creating graphs, which involves fundamental skills like classification, counting, and comparing quantities, enhancing their understanding of data representation. iv. Graphing serves as a visual tool for children to comprehend various quantities and apply mathematical concepts in real-world contexts, fostering critical thinking and communication skills.

Stages of Development for Making and Understanding Graphs i. Stage one, object graphs a) In stage one of graphing, known as object graphs, children utilize real objects like cube blocks to create a graph, typically comparing only two things. b) The primary focus is on establishing one-to-one correspondence and visually understanding length and height as the basis for comparison. ii. Stage two, picture graphs a) In stage two of graphing, known as picture graphs, more than two items are compared, and a more permanent record is created. b) An example involves using a poster board with 12 columns representing each month. Children draw their own heads to mark their birthdays, allowing for comparison of which month has the most birthdays. iii. Stage three, square paper graphs a) In stage three of graphing, referred to as square paper graphs, children advance from using real objects to using cut-out squares of paper to create block charts independently, as depicted in Figure 5-7.

Discussion of a Graph i. As children discuss their graphs and provide descriptions for them, they employ concept words such as ―less than,‖ ―more than,‖ ―fewer than,‖ ―longer,‖ ―shorter,‖ ―the most,‖ and ―the least.‖ Materials for Making Graphs i. Various materials can be used for first-stage graphs, including cube blocks, strings and beads, Unifix® Cubes, and pop beads. Initially, it’s advisable to use stable materials that won’t easily be knocked down by young children. ii. Once they’re comfortable, they can progress to less stable materials like poker chips, bottle caps, and coins for more advanced graph work. iii. Eventually, children can transition to using paper squares, paving the way for squared paper usage. iv. Additionally, numerous graphing materials are available online and as apps and software.

Topics for Graphs i. Students can engage in research on various topics of interest and represent the gathered information graphically, such as investigating school buses, studying trees on campus, or tracking sunlight in a garden. ii. Graphs, a subset of charts, focus specifically on numerical data, prompting students to independently devise problems for exploration, including comparisons like hair color, pet types, or favorite foods, fostering both inquiry and data analysis skills. a

© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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e. Communicating with Graphs i. When children create graphs, they employ fundamental skills like observation, classification, comparison, and visual measurement, transforming data into a communicable format. ii. Graphs serve as tools for displaying information clearly, facilitating predictions, inferences, and conclusions. iii. Clarity in the interpretation of completed graphs is crucial, achieved through questions and discussions that enable graphs to effectively address inquiries, solve problems, and convey data for better understanding. a) Practice Graphs (1) The teacher facilitates kindergarten students’ understanding of graphing by having them stack Unifix® Cubes of different colors to create a bar graph, then replicating the graph using colored poster board squares, reinforcing the concept of one-to-one correspondence. b) Pets Graph (1) Children can utilize graphing skills to compare the types and quantities of pets owned by their peers, engaging in early literacy experiences by creating a graph on a laminated poster board divided into columns representing various pet categories labeled with clothespins, where children can write their names in the corresponding columns. c) Favorite Foods (1) Children can participate in a graphing activity where they divide a poster board into columns representing different food groups, paste or draw pictures of each food group at the top of the columns, and then draw and paste pictures of their favorite foods under the corresponding columns, optionally using Velcro to attach them and writing their names underneath their choices. d) Graphing Attractions: Magnets (1) Children can engage in a hands-on activity exploring magnets of various shapes, where they create a real object graph on ruled poster board or a magnetic whiteboard by tracing the shape of each magnet at the top of columns and attaching a hook below each shape, then experiment with different magnets to see how many paper clips they attract, creating chains of attracted clips under each magnet shape as a visual representation of their observations.

XX. Science Standards and Expectations (05.05; PPT Slide 34) i. The Next Generation Science Standards (NGSS) and the Framework stress the importance of inquiry-based learning and problem-solving skills for children, emphasizing the development of fundamental concepts and skills during the preprimary period as crucial for science, technology, and engineering exploration. ii. Early engineering activities lay the groundwork for later problem-solving abilities and resilience, fostering motivation and the capacity to learn from failure. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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iii. STEM concepts are integrated into developmentally appropriate practices in preschool, allowing children to explore and understand STEM relationships through activities such as ordering, patterning, measurement, and graphing. a. Ordering and Patterning i. The concept of patterning relies on the foundational skills of comparing and ordering. ii. Ordering, a more advanced form of comparing, involves arranging items in a sequence from first to last, known as seriation in Piagetian terms. iii. Children need to develop an understanding of seriation before mastering patterning. iv. Ordering and patterning are built upon the fundamental skill of comparing, and children require prior experience in comparing to effectively order and identify patterns. v. The following examples illustrate using a science emphasis on shape, animals, color, and sound to explore visual, auditory, and motor regularities.  Sun, moon, and stars (1) Children are familiarized with cardboard or plastic figures of the sun, moon, and stars, discussing their shapes in the night sky and arranging them in patterns to reinforce the concept of shapes existing in the sky, which serves as an ideal observational activity for children to recognize natural patterns and changes in the sky from day to night, including the phases of the moon.  Animal patterns (1) Children create patterns using animal shapes that belong to similar groups, such as wild animals like the zebra, tiger, and leopard, or farm animals like the pig, duck, and cow, following the pattern game introduced earlier with tagboard animal shapes.  Sound patterns (1) The teacher introduces sound patterns to kindergarten children by using hand bells with varied tones, prompting them to identify differences and associate each bell’s sound with a colored square, while also engaging them in experimenting with rubber bands to explore sound variations and incorporating rhythmic patterns into activities like marching along with the song ―The Ants Go Marching‖ and adding actions to reflect each verse, fostering early concept development in sound.  Engineering (1) Kindergarten children engage in engineering activities by investigating the effects of different strengths or directions of pushes and pulls on the motion of an object, such as a pendulum, by varying the placement of blocks, the direction of the pendulum, and the force used to push it, recording observations to identify patterns and fulfill a performance expectation. b. Measurement: Volume, Weight, Length, and Temperature a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. The National Science Education Framework and Next Generation Science Standards emphasize the importance of understanding measurement and using measurement tools in investigations, particularly during the early years. ii. Measurement involves active manipulation of objects for comprehension, with water and sand serving as sensory science resources allowing children to explore physical properties and engage in measurement activities. iii. Nine examples are provided to illustrate how sand and water can be effectively utilized for learning measurement concepts through hands-on exploration.  Fill it up.  Squeeze and blow.  A cup is a cup.  Sink or float.  Little snakes.  Outdoors: A big and little hunt.  Body part measures.  How long will it take to sink?  Hot or not.

XXI. Summary [return to top]

ADDITIONAL RESOURCES PRIMARY SOURCES 

Baumgart, N.A. & Kroll, L.R. (2018). STEAM concepts for infants and toddlers. St. Paul, MN: Redleaf.



Copley, J. V. (Ed.). (2004). Showcasing mathematics for the young child. Reston, VA: National Council of Teachers of Mathematics.



Eichinger, J. (2009). Activities linking science with mathematics. Arlington, VA: NSTA Press.

(Activities 1 & 2).



Equity for diverse populations. (2009). Teaching Children Mathematics [focus issue], 16(3).

Fantozzi, V.B. (2022). Digital tools for learning, creating, & thinking. Washington, DC:



National Association for the Education of Young Children.

Hildebrandt, M. E., Biglan, B., & Budd, L. (2013), Let’s take a road trip. Teaching Children Mathematics, 19(9), 548–553.



Manfra, L., Dinehart, L. H. B., & Sembiante, S. F. (2014). Associations between counting ability in preschool and mathematics performance in first grade among a sample of ethnically diverse, low-income children. Journal of Research in Childhood Education, 28(1).



McGuire, P., Kinzie, M. B., & Berch, D. B. (2012). Developing number sense in pre-K with fiveframes. Early Childhood Education Journal, 40(4), 213–222. a

© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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

National Association for the Education of Young Children (2022). Developmentally appropriate practice in early childhood programs serving children birth through age eight, 4e. Washington, DC: Author.



Novakowski, J. (2009). Classifying classification. Science and Children, 46(7), 25–29.

Schwerdtfeger, J. K., & Chan, A. (2007). Counting collections. Teaching Children Mathematics, 3(7), 356–361.

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Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 6: Integrating the Curriculum

TABLE OF CONTENTS Purpose and Perspective of the Chapter Chapter Objectives

50

Chapter Outline

50

50

Additional Resources 55 Primary Sources ...................................................................................................................................... 55

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to provide educators with a comprehensive understanding of how standards, play, emergent curriculum, thematic units, and projects intersect with STEM and STEAM education.

Participants will explore the relationship between these elements and how they can be integrated to promote holistic learning experiences. Additionally, educators will delve into the significance of language and literacy in forming STEM concepts and develop meaningful practices to effectively implement integrated experiences that enhance students’ comprehension and engagement. Through this course, participants will gain the knowledge and skills needed to create dynamic learning environments that foster creativity, critical thinking, and interdisciplinary connections, preparing students for success in STEM and STEAM disciplines.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 6-1

Understand how standards, play, emergent curriculum, and thematic units and projects relate to STEM and STEAM.

6-2

Explain and analyze the importance of language and literacy to STEM concept formation and create meaningful practices to implement integrated experiences.

[return to top]

CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

XXII. Standards and STEM and STEAM (06.01; PPT Slide 3) i. The Common Core Standards for Mathematics, New Generation Science Standards, and the Framework for K–12 Science Education emphasize skills, understandings, and processes applicable across the curriculum, including STEM and STEAM education. ii. Through approaches like dramatic play, thematic units, and project-based learning, children can engage in problem-solving, reasoning, communication, and hands-on experiences. STEM integrates science, technology, engineering, and mathematics, while STEAM incorporates the arts, offering various approaches for interdisciplinary learning. iii. Examples abound where art, math, and science intersect, demonstrating the potential for creative collaboration in education. iv. Teachers are recognizing the potential to integrate Common Core standards into interdisciplinary thematic units and projects, aligning with literacy requirements across subjects. p. Play and Learning a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. Play serves as the primary avenue for children’s learning, allowing them to experiment with adult roles, explore materials, and establish rules for their actions. ii. Curriculum aligned with national standards can be implemented through emergent curriculum, thematic units, and projects integrating STEM with various subjects. iii. An integrated curriculum naturally incorporates mathematics, offering authentic learning experiences through science exploration and outdoor activities. iv. By leveraging dramatic play, emergent curriculum, thematic units, and projects, children can acquire concepts, language, and knowledge across multiple content areas, with opportunities for social learning, science investigations, and mathematical problem-solving. v. Through role-playing and integration with various disciplines, children can apply concepts in meaningful ways, making learning relevant to everyday life. q. Dramatic Role-Playing i. Dramatic role-playing is integral to thematic projects, such as using food as a theme to engage children in STEM investigations and problem-solving while allowing them to explore adult roles and activities. ii. Through activities like growing food, shopping for groceries, and preparing meals, children can apply concepts and engage in imaginative play with props like plastic food and utensils. iii. Teachers can foster social education by providing experiences that mirror adult tasks and cultures, facilitating learning through observation and participation. iv. Various dramatic play centers and props can be set up to support children’s exploration of STEM concepts and skills, including scenarios like grocery stores, service centers, transportation vehicles, and health and medical service centers. v. These activities provide opportunities for applying mathematical concepts, problem-solving, and exploring technologies in a playful and engaging manner across various content areas. r. A Thematic Project Example: Food i. A food-focused project encompasses various curriculum areas and experiences. ii. Children engage as scientists by observing food growth, physical changes during preparation, and effects on humans and animals, while also categorizing tastes, smells, and food types. iii. As mathematicians, they measure, count, divide, and use math in cooking and shopping. iv. They apply engineering skills with cooking tools. v. Food experiences also teach about society and culture, as children make foods from different cultures, learn about food production and marketing, and practice cooperation. vi. They express their experiences through singing, drawing, and movement, incorporating dramatic play, mathematics, and science into food-related activities. a) Food and Dramatic Play.

(1) In food and dramatic play, children engage in purchasing, cooking, serving, and eating food as part of their role-playing activities. A suggested activity involves making dough from a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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flour and salt, which can then be molded into pretend food items for use as props in dramatic play scenarios. b) Food and Math.

(1) Cooking activities provide rich mathematics experiences as children follow recipes, measure ingredients precisely, adjust cooking temperatures and times, divide food into equal portions, and create pictograph recipes, while those with access to gardens or rural environments can engage in real-life math applications by counting days until harvest, measuring plant growth, and participating in farm chores, highlighting the integration of math into everyday activities and nature-based experiences. c) Food and Science.

(1) Food activities also encompass science as children engage in predicting and observing changes during cooking processes, such as mixing ingredients to create playdough biscuits, predicting baking outcomes, and discussing physical changes like those observed in applesauce preparation or stone soup, fostering understanding of concepts like texture, density, and chemical reactions while exploring the origins and transformations of food items. d) Food, Technology, and Engineering.

(1) Food activities inherently involve technology and engineering, as various tools and equipment are utilized by gardeners, farmers, and cooks, including structures like barns and machines such as tractors and mixers, all of which have been designed by structural, mechanical, or electrical engineers. e) Food and Social Studies.

(1) Food activities also integrate social studies, as children engage in trips to farms, orchards, and grocery stores to gather ingredients, collaborate in cooking processes, and participate in group activities like stone soup, fostering cultural awareness and understanding of community needs through emergent curriculum projects like community food drives. f) Food and the Arts.

(1) Food intersects with the arts through paintings featuring various food still lifes, engaging young artists in painting, drawing, and sculpting food items using clay and dough as creative mediums. s. Support for Cultural Diversity i. A culturally responsive curriculum involves exploring the favorite foods of diverse cultures through activities such as cooking ethnic dishes, creating graphs of favorite foods, writing recipes, compiling a class cookbook, studying ethnic groups and customs, incorporating cultural artifacts into dramatic play centers, and providing hands-on experiences beneficial for children with special needs, with active involvement from parents and caregivers. t. Focus on Nature i. The back-to-nature school movement, originating in Scandinavia in the late 1960s and early 1970s and spreading globally, including to the United States, emphasizes a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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children’s benefits from exploring nature, fostering self-regulation, and integrating mathematics with natural patterns, with educators like O’Hara adapting to outdoor classrooms during the COVID-19 pandemic, observing children’s expanded play and increased sense of agency.

XXIII. Language, Literacy, and Concept Formation (06.02; PPT Slide 13) i. The NCTM emphasizes problem-solving, reasoning, communication, connections, and representation as crucial process areas in mathematics, with problem-solving being particularly emphasized for young learners, while literacy skills are essential for understanding science, and children’s language development provides insights into their conceptual understanding in both subjects. ii. Teachers can assess children’s concept development through questions and observations, recognizing that children may imitate adult language use before fully grasping concepts, and technology activities can also aid in vocabulary development. a. Concept Words i. Children can learn and apply various mathematical concepts through vocabulary introduced in Chapters 3, 4, and 5, including terms related to counting, logic, comparison, geometry, spatial sense, parts and wholes, ordering, measurement of volume, length, weight, temperature, time, and practical applications such as money, cooking, and recipes. ii. As children engage in conversation and activities, they become familiar with these words and gradually develop a conceptual understanding of mathematical concepts. b. Mathematics, Science, Engineering, and Literacy i. In the early years of pre-K, kindergarten, and primary education, developing written language skills is crucial, and children’s literature plays a significant role in the curriculum. ii. Pre-reading and pre-writing experiences, such as exploring quality children’s literature, story dictation, and retelling, are essential. Integrating literacy with STEM subjects provides meaningful contexts for communication, reasoning, and making connections. iii. Children can engage with literature relevant to mathematics, science, and engineering, experiment with writing, record data, and write about their explorations, thereby developing their spoken and written language vocabulary in a meaningful way. c. Literature, Reading and Writing, and STEM i. The use of children’s literature as a foundation for integrating mathematics and science into the curriculum has significantly increased, with a growing number of picture books incorporating STEM concepts. ii. STEM and STEAM projects are fostering interdisciplinary learning experiences where students investigate science topics while engaging in reading, writing, and oral communication. iii. Studies have shown that mathematics programs can lead to significant improvements in oral language skills among preschoolers.

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iv. Additionally, picture books serve as effective tools for problem-solving activities, and language plays a crucial role in facilitating discussions and reporting findings in both math and science projects. d. Supporting Children with Special Needs i. Speech, Language, and Communication  Allen and Cowdery (2015) emphasize the significance of speech, language, and communication in child development, highlighting that the purpose of language is communication, with clear speech being crucial for effective verbal communication.  They note that language can also encompass facial expressions, signs, and gestures, particularly beneficial for children with hearing impairments, for whom American Sign Language can be a valuable tool.  In inclusive classrooms, teachers should be attentive to all children’s communication efforts, as math and science activities offer numerous opportunities for communication, while also remaining vigilant for children who may require additional support in speech and language areas. e. Support for English Language Learners and Cultural Diversity i. Whiteford (2009/2010) emphasizes the importance of recognizing cultural diversity in teaching mathematics, noting that each culture has its own approach to mathematical concepts. ii. Children coming from different cultural backgrounds may have learned different numeric systems and problem-solving methods, requiring teachers to be culturally responsive to their students’ needs. iii. Zaslavsky (1996) highlights the role of literature, particularly picture books available in multiple languages, in promoting multicultural understanding and appreciation. These books not only support the heritage languages of children but also expose them to new vocabulary, customs, and geography, fostering respect for different cultures among all students. iv. Many resources in math and science literacy also advocate for a multicultural approach to instruction, further enriching students’ learning experiences. f. Integrating STEM Across the Curriculum i. This chapter illustrates various ways in which STEM concepts and skills can be integrated with other domains like language and literacy, social studies, motor development, and social-emotional interactions, thereby enhancing problemsolving abilities, creativity, and perseverance in children. ii. Integrations may occur spontaneously or be deliberately planned, but it’s essential for teachers to appreciate the value of such integrations in fostering holistic development across different domains. iii. Appendix C provides ―Integration Webs‖ that visually depict the process and benefits of integrating STEM with various content areas and domains.

XXIV. Summary [return to top]

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ADDITIONAL RESOURCES PRIMARY SOURCES 

Ashbrook, P. (2014). Becoming attuned to sound. Science and Children, 51(6), 26–27. Community Playthings. (2010). The wisdom of nature. Ulster Park, NY: Author.

Integration 

Krogh, S., & Morehouse, P. J. (2007). The early childhood curriculum: Inquiry learning through integration. New York: McGraw-Hill.

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Markham, T. (2014). How to reinvent project-based learning to be more meaningful. www.thommarkham.com.

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Miller, A. (2014, April 23). PBL and STEAM education: A natural fit. Edutopia. www.edutopia.org.

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Yagi, S., & Olson, M. (2007). Supermarket math: K–2. Teaching Children Mathematics, 13(7), 376.

Cooking and Food 

Cook, D. (2006). Family fun cooking with kids. Burbank /Glendale, CA: Disney.

Cooking with Kids. A parent helper. www.pbs.org/parents/parenthelpers/cooking.html. Wilburne, J. (2010). Grocery shopping math. Teaching Children Mathematics, 17(1), 20–21.

Literacy 

Ansberry, K., & Morgan, E., (2010). Picture-perfect science lessons using children’s books to guide inquiry, 3–6. and (2012). More picture-perfect science lessons, and (2013) Even more picture-perfect science lessons. Arlington, VA: NSTA Press.

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Bay-Williams, J. M., & Livers, S. (2009). Supporting math vocabulary acquisition. Teaching Children Mathematics, 16(4), 238–245.

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Fulwiler, B. R. (2011). Writing in science in action. Portsmouth, NH: Heinemann.

Royce, C. A., Morgan, E., & Ansberry, K. (2012). Teaching science through trade books.

Arlington, VA: NSTA Press.

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Tyminski, A. M., Richardson, S. L., & Winarski, E. (2010). Enhancing think-pair-share. Teaching Children Mathematics, 16(8), 451–455.

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Wheeler-Toppen, J. (Ed.). (2011). Science the ―write‖ way. Arlington, VA: NSTA Press.

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Wilburne, J. M., Keat, J. B., & Napoli, M. (2011). Cowboys count, monkeys measure, and princesses problem solve: Building early math skills through storybooks. Baltimore, MD: Brookes.

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Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 7: Transitioning from Preschool to Kindergarten to Primary

TABLE OF CONTENTS Purpose and Perspective of the Chapter ................................................................................................. 57 Chapter Objectives ................................................................................................................................... 57 What’s New in This Chapter ................................................................................................................... 58 Chapter Outline ........................................................................................................................................ 58 Additional Resources ................................................................................................................................ 70 Primary Sources ...................................................................................................................................... 70

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to equip educators with a deep understanding of number symbol concepts, groups and number symbols, higher-level mathematical concepts, and science investigations aligned with national standards, focusing on transitional development from pre-operational to concrete operational stages in children. Participants will learn to assess, plan, teach, and evaluate instructional strategies that support this transitional period, ensuring students’ comprehension and mastery of mathematical and scientific concepts. Additionally, educators will explore the use of common artifacts as tools to facilitate this transition, analyzing, creating, and implementing activities that effectively support students’ cognitive development. Through this course, participants will gain the knowledge and skills needed to create enriching learning experiences that promote mathematical and scientific proficiency while supporting students’ cognitive growth during this critical developmental stage.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 7-1

Understand, assess, plan, teach, and evaluate number symbol concepts aligned with national standards that reflect transitional development for children from pre-operational to concrete operations stages.

7-2

Understand, assess, plan, teach, and evaluate groups and number symbols aligned with national standards that reflect transitional development for children from pre-operational to concrete operations stages.

7-3

Understand, assess, plan, and teach nine higher-level concepts aligned with national standards that reflect transitional development for children from pre-operational to concrete operations stages.

7-4

Plan and teach science investigations aligned with national standards that reflect transitional development for children from pre-operational to concrete operations stages.

7-5

Analyze, create, and implement activities using common artifacts as tools to support the transition from pre-operational to concrete operational.

[return to top]

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WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Common Artifacts as Tools to Support the Transition from Pre-Operational to Concrete Operational

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Added section: Sample Assessment Tasks

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Added section: Sample Activities

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CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

XXV. Number Symbols and Concepts: Standards and Explanations (07.01; PPT Slide 4) i. One of the critical developmental transitions for children occurs when moving from pre-operational to concrete operational thinking, typically between ages 4 to 7, with variations among individuals. ii. For instance, a 4.5-year-old might exhibit concrete operational abilities in math while still being pre-operational in literacy skills. iii. Using Vygotsky’s Zone of Proximal Development helps in understanding STEM skill progression, as development is integrated across domains. iv. According to the Common Core State Standards for Mathematics, by the end of kindergarten, children should recognize number names, count sequences, and compare numbers up to 20. v. Children usually begin to understand numerals between ages 4 and 5 but may not grasp their cardinal meanings immediately. vi. Early experiences with numerals should be naturalistic and informal, focusing on play-based learning to develop math skills effectively. u. The Number Symbol Skills i. During the pre-operational period, young children acquire six number symbol skills. ii. They learn to recognize and name each numeral, place numerals in order, associate numerals with groups, and understand the numerical sequence. iii. Additionally, they learn to match numerals to corresponding quantities and reproduce numerals in writing. iv. These skills are covered in two parts of the chapter, with the first four skills discussed early on and the remaining two addressed in the latter half. v. Pre-Assessment i. Teachers should assess children’s interest in numerals by observing whether they repeat numeral names heard on television, identify numerals in their environment, utilize self-correcting materials, and observe their actions when a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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using such materials, along with conducting individual interviews focusing on tasks from the chapter and Appendix A. w. Activities i. Naturalistic Activities a) Young children learn numeral recognition through naturalistic activities as they observe numerals in various settings such as clocks, phones, books, and packaging, hearing number names spoken in everyday contexts, and imitating them in their play, often using numerals before fully understanding their corresponding symbols. ii. Informal Activities a) During the pre-operational period, informal school activities with numerals focus on experimentation and practice in sight and touch perception, facilitated by self-correcting manipulative materials that allow children to solve problems independently through trial and error, while teachers observe children’s organization and persistence in completing tasks, utilizing four basic types of self-correcting manipulative math materials that teach discrimination, sequence, association of symbols with groups, and a combination of association and sequence. iii. Discrimination and Matching a) Teachers can facilitate discrimination and matching skills in young children by using numeral sorting activities and lotto-type games to help children recognize and match numerals, while materials teaching sequence or order, such as number sequencing puzzles or number lines, aid in understanding numerical progression; furthermore, teachers play a supportive role by demonstrating how to use these materials and then allowing children to work independently, intervening with comments and questions as needed. Informal activities like counting the first 100 days of school can also reinforce numeral recognition and sequencing skills in children from kindergarten to grade 3. iv. Adult-Guided Activities a) Adult-guided activities aim to ensure that typically developing kindergarten-aged children can recognize numerals from 0 to 20, place them in order, understand the concept that each numeral represents a group one larger than the previous one, and comprehend that numerals represent quantities; children who struggle with these tasks may benefit from adult-guided scaffolding, and number symbols can be integrated into various content areas, as well. x. Support for English Language Learners i. Cristina Gillanders’ study highlights the importance of developing positive relationships and cultural inclusivity in classrooms with English language learners (ELLs), particularly those who are mono-lingual Spanish speakers, emphasizing the value of incorporating Spanish language and materials to foster a supportive environment. ii. This example underscores the significance of creating an inclusive social and emotional climate in mathematics and science education, where using vocabulary from students’ heritage languages can enhance their comfort and sense of a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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belonging, recognizing that the language of math and science is not universally understood and that incorporating diverse linguistic perspectives enriches learning experiences. y. Post-Evaluation i. Teachers can assess children’s progress with self-correcting materials by questioning them while they work, noting their ability to name numerals and whether they do so in sequence, and conducting individual interviews using assessment questions provided in the chapter and Appendix A. XXVI. Groups and Symbols: Standards and Explanations (07.02; PPT Slide 10) i. The activities in this section build upon various concepts and skills introduced in earlier chapters, focusing on matching, numbers and counting, groups and classifying, comparing, ordering, and symbols, aligning with the Common Core State Standards for Math expectations for kindergarten. ii. Children are expected to have mastered several foundational skills before engaging in these activities, such as recognizing numerals, counting accurately up to 10, understanding the concept of quantity represented by numerals, and attempting to write numbers 0 to 10. iii. As children progress, they transition from working with groups to working with both groups and symbols, ultimately mastering the symbolic representation of numbers in a carefully sequenced manner across different levels of abstraction. a. Informal Pre-Assessment i. Children who have successfully completed the assessment tasks from Chapters 3, 4, and 5 possess the foundational skills required to connect groups and symbols effectively. ii. They may even engage in symbol and grouping activities independently if provided with appropriate materials in the classroom. Individual interview tasks at the end of this chapter can be used to confirm their proficiency in these basic skills and knowledge. b. Activities i. Naturalistic Activities  Children naturally integrate their understanding of groups and symbols into their daily play activities.  For example, two 4-year-olds play a grocery store game, using price tags with written numerals and play money to simulate transactions, demonstrating their understanding of the relationship between numerals and quantities.  Similarly, a 5-year-old incorporates numerals into a drawing of a birthday cake, indicating their age, while another child arranges number cards in order and associates them with corresponding groups, applying skills learned from observing adults. ii. Informal Activities  Children benefit most from informal activities when learning to work with groups and numerals, with each child needing varying amounts of practice.

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Teachers can facilitate this learning by providing a variety of materials for independent exploration, allowing children to choose activities that interest them.

Basic activities for matching symbols to groups and vice versa can be facilitated through materials like counting trays, movable containers with numerals, individual numeral cards, and groups of real or pictured objects. Teachers can introduce new materials to children and offer support as needed to scaffold their learning within their Zone of Proximal Development.

Additionally, informal experiences with writing numerals often arise naturally in children’s curiosity about writing their age, phone number, or address, and teachers should encourage and support these efforts while recognizing that formal writing tasks may not be suitable until fine motor skills are further developed.

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iii. Adult-Guided Activities  Adult-guided activities with symbols and groups for young children are structured as games, such as matching groups and numerals using thematic elements or basic board games focusing on one-to-one correspondence and subitizing.  Teachers can introduce these games and play with the children or allow them to play independently, fostering creativity in devising rules.  Counting books are also valuable resources, with criteria including clear illustrations, emphasis on one-to-one correspondence, and diversity in cultural and linguistic representation.  Teachers can select counting books based on criteria like quantity conservation, skip counting opportunities, cultural diversity, and appropriate use of zero, supporting children’s transition from preoperational to concrete operational thinking. c. Supporting Children with Special Needs i. To support children in making connections between symbols and the groups they represent, teachers can provide a variety of materials and activities that cater to different learning styles and needs. ii. Verbal counting precedes the introduction of written symbols, and some children may require more time to grasp the written number sequence before connecting them with groups. iii. Examples of supportive materials and activities include using cards with numbers for matching games, offering tactile or Braille options for children with visual impairments or learning disabilities, and incorporating kinesthetic activities like hopscotch to reinforce number sequencing. iv. Adaptations such as high-contrast cards or adaptive writing utensils can aid children with dyslexia or fine motor challenges, while tactile or Braille number cards combined with objects for counting support children with visual impairments. d. Informal Post-Evaluation i. For young children, effective evaluation often involves observing their use of materials during informal activities, as well as noting their behaviors during structured games with rules. ii. Before children enter first grade, it is recommended to conduct individual interviews using assessment tools provided at the end of the chapter and in Appendix A. iii. This allows for a more comprehensive assessment of the children’s understanding and readiness for advancing to the next level of learning.

XXVII. Standards and Explanations of Higher-Level Concepts (07.03; PPT Slide 17) i. This section of the chapter builds upon previously learned skills, focusing on more complex problem-solving, reasoning, communication, connections, and representation, as outlined in the Common Core State Standards for Mathematics (CCSSM). These experiences are suitable for students who are developing rapidly and can effortlessly complete higher-level assessment tasks, or for older students who still require concrete experiences during their transition from preoperational to concrete operational thinking. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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ii. The section covers nine areas including algebra, classification, shape, spatial relations, whole number operations and problem-solving, graphs, symbolic level activities, quantities above ten, and estimation. iii. The Common Core State Standards for Mathematics at the end of kindergarten emphasize understanding addition and subtraction within 10, working with numbers 11 to 19 as a foundation for place value, classifying objects, counting objects in categories, identifying and describing shapes, and analyzing and composing shapes. a. Informal Pre-Assessment i. Assessment in early childhood education aims to determine each child’s zone of proximal development, identifying where they can work independently and where they may need support. ii. Activities can be introduced to cater to the varied developmental levels of children, with higher-level peers modeling tasks for those at lower levels. iii. Collaboration between children of different levels facilitates learning, with more advanced peers guiding and assisting those at lower levels. iv. By the end of kindergarten, children should have a solid understanding of number sense, which serves as the foundation for progressing to more abstract mathematical concepts. b. Activities, Skills, and Concepts i. This section of the chapter explores activities and concepts that transcend fundamental skills, spanning various areas such as algebraic thinking, advanced classification, advanced shape concepts, advanced spatial relations, concrete whole number operations and problem-solving, advanced graphs, symbolic level activities, quantities above 10, and estimation.  Algebraic Thinking (1) Algebraic thinking for preprimary-level children involves discovering patterns, solving simple equations with manipulatives, and exploring relationships between quantities using everyday objects, fostering problem-solving skills, and laying the groundwork for more advanced mathematical concepts.  Advance Classification (1) Advanced classification involves multiple classification, class inclusion, and hierarchical classification, where children are tasked with sorting objects in more than one way, solving matrix problems, and understanding subgroup relationships within larger categories, facilitating the transition from pre-operational to concrete operational thinking.  Advanced Shape Concepts (1) Engaging children in activities such as reproducing shapes using materials like geoboards, pipe cleaners, and pattern blocks not only enhances their shape knowledge but also predicts later math performance, highlighting the interconnectedness of spatial and numerical processing areas in the brain.  Advanced Spatial Relations a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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(1) Engage children in spatial learning activities such as creating floor plans and maps of their environment, progressing from the classroom to the neighborhood and town, while incorporating activities like navigating landmarks, using maps, practicing directional concepts, and building spatial vocabulary.

Concrete Whole Number Operations and Problem Solving (1) Children develop problem-solving skills in concrete whole number operations through hands-on experiences with addition, subtraction, division, and multiplication using materials like counters, gradually refining their strategies as they grow, transitioning from counting all to counting on, with teacherguided activities emphasizing drawing solutions.

Advanced Graphs (1) In the fourth level of graphs, children utilize square paper to graph similar items as in previous chapters, using drawn-in squares that can be colored or filled with smaller paper squares, introduced after ample experience with concrete objects and a strong understanding of classification and number sense.

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Symbolic Level Activities (1) Children who have mastered connecting groups and symbols in basic arithmetic operations like addition and subtraction can progress to the symbolic level by solving written addition and subtraction problems, encouraged to communicate their findings through drawing, writing, and using numerals, either through teacher-created problems or problems they create themselves, collaborating with peers to further reinforce their understanding. (a) Addition (b) Subtraction (c) Multiplication (d) Division  Quantities Above 10 (1) Preschoolers transition to counting quantities above 10 by exploring the relationship between groups of 10 and additional amounts, progressing from recognizing numerals 10 to 19 and then extending to 20, 30, and beyond, understanding the place value concept through hands-on activities and games recommended by various educational resources.  Estimation (1) Estimation in young children involves making sensible responses to ―how many‖ or ―how much‖ problems by using known measurements as references, such as comparing their height to estimate the height of a bookcase, aided by techniques like chunking and unitizing, laying the foundation for more advanced math skills. c. Support for English Language Learners i. Bilingual English-Spanish teachers observed that their fourth-grade students were not properly using estimation to check their answers, attributing the issue to a language problem stemming from translation between grades, highlighting the importance of language in students’ mathematical understanding and the need for assessments to be given in a child’s primary language to accurately gauge math skills.

XXVIII. End-0f-Kindergarten Science Standards and Expectations (07.04; PPT Slide 30) i. Children in this transitional stage continue to develop fundamental concepts and are exposed to higher-level experiences, which offer opportunities to build upon ideas from previous sections, while aligning with performance expectations outlined in NGSS and the Framework, emphasizing the eight essential practices for learning science and engineering, ultimately helping students understand the work of scientists and engineers. a. Design Technology/Engineering and Robotics i. Children naturally engage in design technology and engineering during play, such as constructing marble runs or creating art projects with recycled materials, while more advanced transitional children may tackle complex engineering problems, going through steps like problem identification, idea generation, planning, designing, making, testing, and reflecting, with resources like a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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children’s museums and online platforms offering engaging STEM programs and materials for educators to use in the classroom, including robotics activities that can be introduced as early as preschool, fostering skills in coding, sequencing, and integrative learning across multiple domains and content areas. b. Concepts That Crosscut Science and Engineering Content Areas i. The Next Generation Science Standards identify seven basic concepts essential for science and engineering education, including patterns, cause and effect, scale, proportion, systems, energy and matter, structure, and stability. However, for preschool and kindergarten programs, six of these concepts are particularly relevant, focusing on patterns and classification, cause and effect, scale, proportion, systems, groups and symbols, and structure and function.  Patterns and Classification.  Cause and Effect.  Scale, Proportion, and Quantity  Systems and System Models  Structure and Function c. NGSS Performance Expectations in Kindergarten i. The Next Generation Science Standards (NGSS) outline performance expectations for kindergarten, emphasizing inquiry-based learning through questions like how pushing or pulling affects motion, where animals live and why, and understanding weather patterns. ii. Kindergartners are expected to conduct investigations, observe patterns in plant and animal needs, and describe weather patterns over time to develop foundational science understanding.  Physical science  Life science  Earth science

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d. Activities i. Vegetable Time.  ―Vegetable Time‖ involves preparing various vegetables to enhance learning opportunities, categorizing them into leaf and stem, root, and seed vegetables, and engaging in activities with kindergarten or firstgrade students. These activities include describing vegetables, discussing where they grow, digging for them in a sandbox, exploring their insides, matching them to their growth stages, and creating patterns with them, fostering understanding and appreciation for vegetables and their growth cycles. ii. Stone Soup.  ―Stone Soup‖ is an interactive learning activity where children engage with literature and cooking by reading the book and acting out the story.

They learn about vegetables by preparing the soup recipe, which involves washing, peeling, and cutting vegetables. The children follow a sequence of steps in cooking, using picture cards for guidance, and may create an experience chart or graph to reflect on their cooking process and favorite parts of the soup. iii. Animal Groups.  ―Animal Groups‖ activity involves grouping stuffed animals by numbers and having children draw the sets of animals, followed by creating stories about them for early literacy experiences. The drawings are then compiled into books for each table, representing different numbers of animals, which are read together and made available for independent reading in the classroom. iv. More First Mapping Experiences.  ―More First Mapping Experiences‖ introduces mapping activities with the use of symbols, starting with tangible mapping where children create features like roads and villages with clay or at a sand table, progressing to pictorial mapping by drawing what they see from a hilltop or building.

Semipictorial mapping follows, utilizing conventional symbols and colors to represent objects, leading to the creation of a base map outlining key streets and buildings. It’s emphasized to start small and gradually increase the complexity of the mapping tasks while ensuring each map serves a specific purpose without overwhelming the children.

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v. Exploring Pumpkins: October Science  ―Exploring Pumpkins: October Science‖ provides a series of hands-on activities for children to explore pumpkins using their senses and integrating various fundamental concepts. Children examine pumpkins, describing their feel, smell, and appearance, and engage in activities like weighing the pumpkins, measuring their circumference, counting the lines on their surface, and comparing colors and textures. They also explore the inside of the pumpkins, comparing the color and texture of the pulp and seeds. The activities culminate in carving jack-o’-lanterns, making predictions about their weight, and even tasting pumpkin-based snacks like pumpkin bread and roasted seeds, allowing for a comprehensive learning experience centered around pumpkins. vi. Measuring the World Around Us  ―Measuring the World Around Us‖ presents outdoor activities focused on science and measurement, utilizing playgrounds, yards, and sidewalks. Children engage in activities like observing the dispersal of dandelion seeds by the wind, tracking the growth of weeds over time, filling containers with natural objects to compare their capacities, and lining up and comparing the collected objects. They also explore different ways to compare objects, including visual examination and weighing using a balance, fostering a hands-on learning experience that integrates scientific concepts with measurement skills. vii. Popcorn Time  ―Popcorn Time‖ engages children in a sequence activity where they act out the process of popcorn popping, discussing the science behind it and sharing ideas in groups. Children personify popcorn kernels, mimicking their popping process within a designated circle, fostering interactive learning. Additionally, they witness real popcorn popping in a popcorn popper, measuring how far the popcorn flies for a hands-on exploration of distance measurement, encouraging comparison between different popcorn brands. viii. Spatial Relations  The ―Spatial Relations‖ activity aims to enhance children’s understanding of inside and outside concepts by exploring what’s inside their bodies. Children engage in a guessing game with a bag filled with various items, prompting them to identify the contents through touch and sound. They then transition to understanding internal body parts by comparing them to the bag’s contents, discussing bones, muscles, and organs. Children further explore muscle movements, facial expressions, and heartbeat sensations, fostering curiosity about their bodies’ inner workings through interactive and sensory experiences. e. Technology i. Technology can enhance early childhood education by reinforcing math and science concepts learned in the classroom, but it should not replace hands-on experiences.

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ii. When selecting software or online resources, teachers should consider if they are age-appropriate, interactive, culturally diverse, and adaptable to individual learning levels. iii. Internet websites and apps can provide additional opportunities for exploration and learning, such as virtual tours or weather tracking activities, complementing classroom instruction. Fantozzi (2022) provides valuable guidance on effectively integrating technology into early childhood education.

XXIX. Common Artifacts as Tools to Support the Transition from Pre-Operational to Concrete Operational (07.05; PPT Slide 41) i. Transitioning from the pre-operational to the concrete operational stage in children’s development can be effectively supported by utilizing common items and artifacts from their environment, which gain more complex meaning and use as children grow. ii. This can include various categories of artifacts such as picture books, toys and games, and superheroes. iii. These artifacts serve as tools to facilitate cognitive development and understanding as children progress through different stages of learning and reasoning. a. Picture Books i. Children’s book publishing has expanded, offering a wide range of titles covering diverse topics and languages. ii. Picture books, once reserved for preschoolers, now present complex ideas suitable for primary school students, especially in non-fiction genres. iii. Fiction and non-fiction books provide valuable opportunities for exploration and learning across STEM areas. iv. Examples such as ―It’s Okay to Smell Good,‖ ―Count on Me,‖ and ―Red Knit Cap Girl to the Rescue‖ engage children of different developmental stages with entertaining stories while introducing scientific concepts.

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b. Toys and Games i. The expansion of the toy industry has led to a wide array of toys that encourage active, imaginative play and STEM engagement. ii. While commercially produced toys can be beneficial, children also derive play value and STEM learning from common objects and their environment. iii. Terrific Science Press offers titles like ―Exploring Matter with Toys‖ and ―Teaching Chemistry with Toys‖ that highlight the use of toys in teaching science concepts, supporting children’s transition from pre-operational to concrete operational stages through increasingly complex play experiences. iv. Examples include using bamboo lengths for scientific inquiry and exploring physics and math concepts through games and activities. c. Superheroes i. Children’s fascination with superheroes provides a valuable avenue for introducing and exploring STEM concepts. ii. In the pre-operational stage, they focus on observable attributes and imaginative aspects of superheroes’ powers. iii. As they transition to concrete operations, superheroes can serve as a bridge to scientific inquiries, prompting investigations into physics and other STEM topics. iv. By leveraging children’s interests in popular media and culture, educators can create engaging STEM activities that are relevant to their lives and experiences, using a variety of artifacts and objects beyond superheroes, such as sports, arts, media, and food.

XXX. Summary [return to top]

ADDITIONAL RESOURCES PRIMARY SOURCES 

Byrge, L., Smith, L. B. (2014). Beginnings of place value: How preschoolers write three-digit numbers. Child Development, 85(2), 437–443.



Copley, J. V. (2004). Showcasing mathematics for the young child. Reston, VA: National Council of Teachers of Mathematics.



Copley, J. V. (2011). The Young Child and Mathematics, 2nd ed. Washington, DC: National Association for the Education of Young Children and New York: Teachers College Press.



Cwikla, J. (2014). Can kindergartners do fractions? Teaching Children Mathematics, 20(6), 354– 364.



Eisenhardt, S., Fisher, M. H., Thomas, J., Schack, E. O., Tassell, J., & Yoder. M. (2014). Is it counting, or is it adding? Teaching Children Mathematics, 20(8), 498–507.

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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

Greenes, C. E., Cavanagh, M., Dacey, L., Findell, C. R., & Small, M. (2001). Navigating through algebra in prekindergarten–kindergarten. Reston, VA: National Council of Teachers of Mathematics.



Greenes, C. E., Dacey, L., Cavanagh, M., Findell, C. R., Sheffeld, L. J., & Small, M. (2003).

Navigating through problem solving and reasoning in prekindergarten–kindergarten. Reston, VA: National Council of Teachers of Mathematics.



Heroman, C. (2017). Making & tinkering with STEM: Solving design challenges with young children. Washington, DC: National Association for the Education of Young Children.



Kinser, K. (2019). Fresh air, fun, and exploration: Why outdoor play is essential for healthy development. Young Children, 74(2), 90–91.



Konerman, R., Horwitz, J., Clancy, S., & Rietta, C. (2022). Harnessing potential: Integrating technology and media in preschool. Teaching Young Children, 15(2), 6–9.



Outhred, L., & Sarelich, S. (2005). Problem solving by kindergartners. Teaching Children Mathematics, 12(3), 146–154.



Pollman, M. J. (2010). Blocks and beyond. Baltimore, MD: Brookes.

Ritz, W. C. (Ed.). (2007). A head start on science: Encouraging a sense of wonder: grades preK– 2.



Arlington, VA: NSTA Press.



Shillady, A. (Ed.). (2013). Exploring science. Washington, DC: National Association for The Education of Young Children.



Thom, E. E., & Sandhofer, C. M. (2014). How symbolic experience shapes children’s symbolic flexibility. Child Development, 85(2), 738–754.

[return to top]

Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 8: Whole Numbers Operations, Patterns, and Fractions

TABLE OF CONTENTS Purpose and Perspective of the Chapter Chapter Objectives

73

73

What’s New in This Chapter 73 Chapter Outline

73

Additional Resources 80 Primary Sources ...................................................................................................................................... 80 a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to provide educators with the knowledge and skills necessary to assess, plan, teach, and evaluate whole number and algebraic thinking, pattern, and fraction activities and lessons for grades 1–3, all aligned with national standards. Through a comprehensive exploration of instructional strategies and assessment methods, participants will learn how to effectively engage young learners in mathematical concepts essential for their academic development. By aligning instruction with national standards, educators will ensure that their teaching addresses key mathematical skills and competencies required for success in grades 1–3. Through this course, participants will gain the expertise needed to create engaging and rigorous learning experiences that foster mathematical understanding and proficiency among elementary students.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 8-1

Assess, plan, teach, and evaluate grades 1–3 whole number and algebraic thinking activities and lessons aligned with national standards.

8-2

Assess, plan, teach, and evaluate grades 1–3 pattern activities and lessons aligned with national standards.

8-3

Assess, plan, teach, and evaluate grades 1–3 fraction lessons aligned with national standards.

[return to top]

WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Sample Assessment Tasks



Added section: Sample Activities

[return to top]

CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

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XXXI. Background and Basics of Primary Grade Mathematics (08.01; PPT Slide 6) i. This section discusses the evolution of elementary mathematics education, emphasizing the expansion from traditional arithmetic to include algebraic thinking and other concepts like geometry, number sense, and data analysis. It highlights the integration of Common Core State Standards (CCSS) into primary grade planning, alongside the encouragement of mental computation and estimation. ii. While technology aids complex calculations, understanding conventional algorithms remains crucial. However, over-reliance on textbooks and standardized testing can hinder conceptual understanding. iii. The text advocates for a more engaging approach called ―mathematizing,‖ embedding math into daily routines. It stresses the importance of children’s active exploration and social interaction in understanding arithmetic, drawing on Piaget’s and Vygotsky’s theories. iv. The section also cautions against pushing students too fast before they grasp logical reasoning and emphasizes the importance of informal teaching methods and allowing children to progress at their own pace. z. Basic Combinations (Facts) and Algorithms i. Isaacs and Carroll (1999) raise questions regarding the teaching of basic addition facts to first graders and its impact on mathematical thinking. ii. They argue against drill and practice, advocating instead for strategies that build understanding and quick recall. iii. Typically, children enter primary grades with counting skills and an understanding of part-whole relationships, which can be leveraged for learning facts through problem-solving activities. iv. Baroody (2006) contrasts conventional drill methods with a number sense approach, where children progress through phases of learning, from using object counting to mastering facts. v. This approach emphasizes discovering patterns and relationships among facts. vi. Assessment in early grades should focus on understanding and flexible strategies, with mastery expected by third or fourth grade. vii. Finally, Curcio and Schwartz (1998) suggest starting with children’s own strategies before guiding them toward more efficient methods, such as algorithms.

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aa. Computational Fluency i. An essential objective for primary grades is to cultivate computational fluency with whole numbers, as outlined by the National Council of Teachers of Mathematics (NCTM, 2000). ii. Russell (2000) delineates three components of fluency: efficiency, accuracy, and flexibility. iii. Efficiency involves proceeding directly toward the solution without distraction, accuracy entails carefulness and verification of results, while flexibility enables the use of multiple strategies for problem-solving. iv. Fluency extends beyond rote memorization to include the ability to apply knowledge in varied problem-solving contexts. In the early grades (K–2), children should be encouraged to invent their computational methods and problem-solving procedures. v. Heirdsfield (2012) emphasizes the importance of fostering students’ own strategies through exploration, discussion, and justification, signaling a shift in teaching beliefs and practices in primary mathematics. vi. Teachers may require support to navigate this transition effectively. bb. Action and Relational Symbols i. At the primary level, children are introduced to action and relational symbols in mathematics, representing operations and relationships between quantities, respectively. ii. Formal number sentences should be gradually introduced after children engage in extensive exploratory experiences, developing their own notation systems and understanding the symbolic representation of operations. cc. Instructional Strategies i. Fraivillig (2001) proposes instructional strategies under the framework of Advancing Children’s Thinking (ACT), focusing on eliciting, supporting, and extending children’s solution methods in mathematics. ii. Effective teaching involves fostering diverse problem-solving approaches, providing support and encouragement for exploration, and maintaining high standards while creating a safe and respectful learning environment where all students feel comfortable to participate and learn. a) Informal Pre-Assessment (1) Informal pre-assessment of children’s understanding of whole number operations involves observations, interviews, and concrete activities integrated into instruction, emphasizing the inappropriateness of paper-and-pencil tests for primary students and recommending tasks such as conservation of numbers and knowledge of symbols for readiness evaluation. dd. Algebraic Thinking i. Schifter, Russell, Bastable (2010), and Chappell (1997) illustrate the foundation of algebraic thinking in primary grades. Chappell emphasizes that while formal algebraic equations might not be suitable for primary children, they can learn patterns using geometric shapes as variables. This is demonstrated through activities such as the guess-my-rule game and missing addend problems using visual representations like triangles or counters. ee. Addition a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. Constructing the concept of addition entails children comprehending it as the process of combining groups of objects to determine the total, incorporating terms like total, sum, equals, and operation signs (+ and =), and establishing connections between quantities and corresponding symbols, which requires prior understanding of quantity and the outcome of combining quantities. a) Assessment (1) Assessing children’s understanding of addition involves observing their process and questioning them about their actions to reveal their comprehension, utilizing both naturalistic and adult-guided activities, along with interviews, to identify misconceptions and guide their development of accurate arithmetic knowledge. b) Instruction (1) Instruction in mathematics for primary students begins with naturalistic and informal experiences, progressing to adultguided activities and real-life contexts, gradually introducing children to notation and symbolization while emphasizing the understanding of addition concepts beyond mere memorization, and adapting instruction to cater to individual student comprehension levels, including exploration of problem variations and use of concrete materials to solidify understanding. ff. Subtraction i. To conceptualize subtraction, children must understand it as the action of taking away objects or comparing groups to find the difference, learning terms such as minus and difference along with corresponding symbols (- and =), grasping concepts of more than (>), less than (<), and their symbols, and connecting these concepts to symbolic notation, requiring prior comprehension of quantity and the outcomes of subtracting from or comparing groups. a) Assessment (1) Assessing children’s understanding of addition and subtraction involves observing their processes for dealing with quantities, including their use of physical aids like fingers, counters, or mental computation, as well as questioning them to uncover misconceptions and inform their development of accurate arithmetic knowledge, with observations conducted during both naturalistic and adult-guided activities and assessments utilizing interview approaches for a comprehensive evaluation of their understanding. b) Instruction (1) Instruction in subtraction parallels that of addition, beginning with informal experiences and progressing to games, story problems, and gradually introducing subtraction notation, with emphasis on children constructing their own concepts and understanding the relationship between addition and subtraction using a variety of strategies such as games, story problems, and concrete materials to facilitate learning. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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gg. Multiplication i. Conceptualizing multiplication involves understanding equal quantities and recognizing it as a shorthand method for repeated addition, learning terms such as factors and product, and connecting them to action signs, with concrete object manipulation introduced at the primary level and more formal notation typically mastered by fourth grade. a) Assessment (1) Assessment of children’s understanding of multiplication involves observing their process of dealing with quantities, asking questions to uncover their thoughts, and evaluating their ability to work with equal groups, with observations conducted during naturalistic activities and interviews utilizing examples provided at the end of the chapter and in Appendix A. b) Instruction (1) Assessment of children’s understanding of multiplication involves observing their process of dealing with quantities and asking probing questions to uncover their thoughts, while instruction in multiplication, akin to addition and subtraction, begins with naturalistic experiences and gradually introduces formal notation, emphasizing real-life problems and gradual introduction of symbols to solidify understanding. hh. Division i. Division, often encountered in daily activities, involves sharing equally and passing out items so that everyone has the same amount, with formal instruction typically introduced around third grade and proficiency expected by fifth grade, with two main types of problems: grouping, which involves finding the number of subgroups of a particular size in a larger group, and sharing, which involves dividing a larger group into a specific number of groups to determine the quantity in each group, with the children eventually learning division terminology such as dividend, divisor, quotient, and remainder. a) Assessment (1) Assessment of children’s understanding of division centers on evaluating their processes of grouping and sharing, with the task provided at the end of the chapter serving as a tool to assess comprehension in these areas. b) Instruction (1) Instruction in division should commence with naturalistic and informal experiences, providing children with tasks such as sharing items and grouping objects to be shared, followed by concrete problems involving real objects and story scenarios, gradually introducing division notation through modeling and allowing children to act out problems with counters before progressing to written equations and creating their own problems to ensure comprehension of division concepts. ii. Integration with Other Content Areas i. Whole number operations, including addition, subtraction, multiplication, and division, can be integrated into various subjects such as art, science, social a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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studies, and literature, providing students with practical applications and opportunities to apply mathematical concepts in real-world contexts. jj. Technology i. Computers and calculators offer valuable support for exploring whole number operations, with a wide range of software and Internet resources available to help children practice basic addition, subtraction, multiplication, and division facts in engaging ways. ii. These tools provide immediate feedback, allowing children to progress at their own pace, and can also be used for exploring multiples and skip counting, enhancing mathematical understanding. kk. Support for English Language Learners i. In the primary grades, helping English Language Learners (ELLs) understand both language and mathematical concepts presents a challenge, addressed through a problem-based approach that gradually increases in complexity and incorporates familiar vocabulary, leading to improved problem-solving skills and persistence compared to traditional instruction. ll. Supporting Children with Special Needs i. Gifted learners, often overlooked, may achieve below their potential and may benefit from encouragement to explore multiple problem-solving methods and engage in complex, challenging problems. ii. Special education teachers Tabor and Canonica focused on teaching division to their students by emphasizing division as sharing and the inverse of multiplication, allowing students to select comfortable numbers and engage in various tasks to develop understanding. mm.

Post-Evaluation i. Evaluation, akin to assessment, should initially involve concrete tasks and include observation of both process and product. ii. Tasks provided in Appendix A and at the conclusion of this chapter serve as valuable tools for evaluation in addition to initial assessment.

XXXII. Description and Explanation of Patterning (08.02; PPT Slide 27) i. The developmental expectations for patterning for children from prekindergarten through grade 3 encompass ordering objects by various properties, recognizing and extending patterns, and analyzing pattern development. ii. Children transition from simple repetitive rhymes and songs to more complex patterning activities involving numbers and arithmetic patterns by grade 3, with early patterning ability serving as a reliable predictor of later math performance. iii. Patterning is connected to algebra, and by third grade, children are expected to identify and explain arithmetic patterns using properties of operations. iv. The chapter emphasizes extending patterning concepts to more complex patterns, connecting symbols and patterns and exploring patterns in the environment.

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a. Informal Pre-Assessment i. The chapter points readers to Chapter 5 for comprehensive insights into naturalistic and informal patterning behaviors in children’s activities, emphasizing that by the primary grades, children should adeptly copy and extend patterns, develop skills in creating and describing patterns, and recognize patterns in numbers, while also providing sample assessment tasks for evaluating these abilities. b. Activities i. Children in the concrete operations stage of cognitive development are naturally drawn to seeking out rules and regularities in the world and make patterning activities, such as noting number patterns, counting by multiples, arranging paper shapes into quilt patterns, and exploring patterns with calculators, fit their interests and cognitive abilities. Supplementary materials and integration across the curriculum enhance their learning experiences. c. Supporting Children with Special Needs i. Children with severe visual impairments or total blindness rely on their other senses for information, requiring educators to incorporate rhymes, routines, and give-and-take games to facilitate learning, while also utilizing tactile objects, consistent routines, and Braille instruction during the primary grades, with concrete materials and digital tools with speech components being essential adaptations for mathematics instruction. d. Informal Evaluation i. Observe how children engage with pattern activities by noting if they count aloud, apply number sense concepts like subitizing, and if they can explain the pattern when prompted, utilizing the assessment tasks in Appendix A for individual evaluation interviews.

XXXIII. Standards and Descriptions of Fractions (08.03; PPT Slide 29) i. The section emphasizes the importance of children’s understanding of fractions by the end of grade 3, outlining expectations such as recognizing fractions as numbers, understanding their placement on a number line, comprehending equivalence, and comparing fractions by reasoning about their sizes. ii. It stresses the significance of building a strong conceptual foundation for fractions through informal experiences, avoiding the premature introduction of symbols, and providing concrete activities to aid comprehension, with recommendations for effective fraction instruction based on research findings.

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a. Informal Pre-Assessment i. The section suggests transitioning to higher-level assessment tasks for understanding fractions once children demonstrate comprehension of the partwhole concept, including the conservation of wholes when divided and the understanding that part size decreases as the number of divisions increases. b. Activities i. The text emphasizes the importance of continuing naturalistic and informal activities as the foundation for adult-guided experiences, particularly in understanding fractions, and suggests using various materials and number lines to reinforce fraction concepts, with the goal of integrating fractions across the curriculum by the fourth grade. c. Supporting Children with Special Needs i. Children with severe hearing impairment or deafness require special considerations in communication and education, including the use of sign language, direct face-to-face communication, clear gestures, visual aids, and consistent routines, with concrete materials being crucial for conveying mathematical and scientific concepts effectively. d. Informal Evaluation i. Continuously observe whether children apply their understanding of fractions in everyday scenarios, particularly when sharing items equally or during measuring tasks in food preparation and science investigations, and administer the assessment tasks outlined in Appendix A to evaluate their comprehension further.

XXXIV. Summary [return to top]

ADDITIONAL RESOURCES PRIMARY SOURCES 

Billings, E. M., Tiedt, T. L., & Slater, L. H. (2007/2008). Algebraic thinking and pictorial growth patterns. Teaching Children Mathematics, 14(5), 302–308.



Bofferding, L., & Aqazade, M. (2023). ―Where does the square go?‖: Reinterpreting shapes when solving a tangram puzzle. Educational Studies in Mathematics, 112(1), 25–47.



Cadzow-Wardell, L. (2009/2010). White trillium. Teaching Children Mathematics, 16(5), 264– 266.



Cavey, L. O., & Kinzel, M. T. (2014). From whole numbers to invert and multiply. Teaching Children Mathematics, 20(6), 374–383.



Dubon, L. P., & Shafer, K. G. (2010). Storyboards for meaningful patterns. Teaching Children Mathematics, 16(6), 325–329.



Eichinger, J. (2009). Activities linking science with math K–4. Arlington, VA: NSTA press.



Fisher, E. C., Roy, G., & Reeves, C. (2013). The functionator 3000: Transforming numbers and children. Teaching Children Mathematics, 20(4), 254–260. a

© 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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

Jong, C., & Magruder, R. (2014). Beyond cookies: Understanding various division models.

Teaching Children Mathematics, 20(6), 366–371.



Kamii, C. K. (1994). Young children reinvent arithmetic, third grade. New York: Teachers College Press.



Kamii, C. K. (2003). Young children continue to reinvent arithmetic, second grade, 2nd ed. New York: Teachers College Press.



Kidd, J. K., Pasnak, P., Boyer, C. E. & Carleson, A. (2014). Instructing first-grade children on patterning improves reading and mathematics. Early Education and Development, 25(1), 134– 151.



Moss, E. R. (2013). Pattern blocks. Teaching Children Mathematics, 20(3), 136–142.



Murphy, M. S., (2009). Mathematics and social justice in grade 1: How children understand inequality and represent it. Young Children, 64(3), 12–17.



Piasta, S. B., Pelatti, C. Y., & Miller, H. I. (2014). Mathematics and science-learning opportunities in preschool classrooms. Early Education and Development, 25(4), 445–468.



Polly, D., & Ruble, L. (2009). Learning to share equally. Teaching Children Mathematics, 15(9), 558–563.



Rittle-Johnson, B., Hofer, K.G., Fyfe, E.R., & Farran, D.C. (2017). Early math trajectories: LowIncome children’s mathematics knowledge from ages 4–11. Child Development, 88(5), 1727– 1742.



Science for all. [Focus Section]. (2014). Science and Children, 51(5).



Supply, A-S., Wijns, N., Van Dooren, W., & Onghena, P. (2023). It is probably a pattern: does spontaneous focusing on regularities in preschool predict reasoning about randomness four years later? Educational Studies in Mathematics, 112(1), 3–24.



Thomas, J. N., Tabor, P. D., & Wright, R. J. (2010/2011). First graders’ number knowledge.

Teaching Children Mathematics, 17(5), 298–308.



Wu, Z., An, S., King, J., Ramirez, M., & Evans, S. (2009). Second grade ―professors.‖ Teaching Children Mathematics, 16(1), 34–40.

[return to top]

Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 9: Place Value, Geometry, Data Analysis, and Measurement

TABLE OF CONTENTS Purpose and Perspective of the Chapter ................................................................................................. 83 Chapter Objectives ................................................................................................................................... 83 What’s New in This Chapter ................................................................................................................... 83 a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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Chapter Outline ........................................................................................................................................ 84 Additional Resources ................................................................................................................................ 90 Primary Sources ...................................................................................................................................... 90

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to equip educators with the necessary skills to assess, plan, teach, and evaluate primary grade lessons in place-value, geometry, data collection and analysis, and measurement, all aligned with national standards. Through a comprehensive exploration of instructional strategies and assessment methods, participants will learn how to effectively engage young learners in foundational mathematical concepts crucial for their academic development. By aligning instruction with national standards, educators will ensure that their teaching addresses key mathematical skills and competencies required for success in primary grades. Through this course, participants will gain the expertise needed to create dynamic and rigorous learning experiences that foster mathematical understanding and proficiency among elementary students.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 9-1

Assess, plan, teach, and evaluate primary grade place-value lessons aligned with national standards.

9-2

Assess, plan, teach, and evaluate primary grade geometry, data collection, and analysis lessons aligned with national standards.

9-3

Assess, plan, teach, and evaluate primary grade measurement lessons aligned with national standards.

[return to top]

WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Standards and Descriptions of Geometry, Robotics Programming, and Data Analysis and Graphs



Added section: Sample Assessment Tasks



Added section: Sample Activities

[return to top]

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

XXXV. Standards and Description of Place Value and Numbers Above 10 (09.01; PPT Slide 3) iii. The Common Core State Standards outline expectations for primary-grade students to understand place value and perform operations involving it, with specific standards delineated for each grade level. iv. Place value instruction has undergone significant changes over the years due to differing pedagogical approaches, including the ―New Math,‖ ―Back to Basics,‖ and progressivist movements. v. Understanding place value is crucial for students’ grasp of whole number operations and trading rules, which involve regrouping. vi. Developing a strong foundation in place value requires hands-on experiences and conceptual understanding rather than rote memorization, ultimately enabling students to comprehend the significance of numeral placement and perform operations accurately. a. Informal Pre-Assessment i. Understanding place value can be challenging for many young children, who may struggle to grasp the concept consistently, but developing a solid understanding of it is crucial for accessing more complex mathematical concepts and operations later on, necessitating patience and appropriate experiences from teachers, with assessment tasks aiding in tracking children’s progress and ensuring foundational knowledge of one-digit numbers before advancing to more complex numerals. b. Activities i. Young children require ample experiences with place value and manipulations of objects exceeding 10 before engaging in two-digit whole number operations; Disney and Eisenreich stress the importance of starting with groupable models to aid in understanding tens and hundreds before transitioning to pregrouped models like Base-10 blocks. ii. Trading procedures, essential for working with place value, should be introduced gradually, ensuring children are proficient in counting, grouping, and relating numerals before advancing to regrouping and renaming, with hands-on activities and concrete materials laying the groundwork for more abstract concepts. c. Discourse Approach i. The activities in this unit follow a structured sequence while promoting concept construction through exploration, with Kamii and colleagues highlighting the effectiveness of open-ended activities and discourse in deepening understanding, contrasting conventional instruction where students can perform regrouping without comprehending the underlying concepts, emphasizing the importance of discourse in mathematics teaching, as reflected in both the Common Core State Standards for Mathematics and NCTM’s Principles to Actions. d. Calculators a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. Exploring calculators for counting reveals the dynamic changes in place value, especially when inputting numbers like 10 and repeatedly pressing 1, highlighting the significance of each place and reinforcing concepts constructed through manipulatives, while adding or subtracting 1 from numbers aids in understanding place value transitions. e. Supporting Children with Special Needs i. Children with motor delays may struggle with various motor skills tasks, but with appropriate support, including technology tailored to their needs, they can develop cognitive understanding and interact with their environment, while children with perceptual processing issues like dyslexia may require strategies such as lining up numbers vertically or color-coding to perceive commonalities among numbers above nine, emphasizing the importance of early interventions and evidence-based practices in developing their place value skills. f. Support for English Language Learners and Cultural Diversity i. Zaslavsky (1996) discusses various cultural methods of recording and calculating numbers, including finger counting and the use of tally marks or knots on string, highlighting the diverse origins and adaptations of numerical systems, while the Pueblo of Jemez in north-central New Mexico initiated an education program prioritizing the Jemez language and culture in 2000, aiming to integrate the community into the educational experience, especially with the implementation of the Common Core. g. Post-Evaluation i. Kamii (2003) suggests an evaluation technique involving presenting children with a card displaying a two-digit number, asking them to identify the digits and demonstrate their understanding using manipulatives, revealing that children taught through self-constructed methods showed better comprehension of place value compared to those instructed conventionally with workbooks, emphasizing the importance of observing children’s processes closely to ensure genuine understanding rather than rote memorization.

XXXVI. Standards and Descriptions of Geometry, Robotics Programming, and Data Analysis and Graphs (09.02; PPT Slide 11) a. First Grade i. In geometry, students should understand the properties of shapes and be able to explain how specific attributes define each shape, as well as use shapes to create new ones and decompose shapes into smaller parts. ii. In data analysis, students should represent and interpret data with up to three categories, explaining the numbers within each category and comparing which categories have more or fewer data points. b. Second Grade i. In geometry, students should understand and reason about shapes, including triangles, quadrilaterals, pentagons, hexagons, and cubes, identifying their attributes and partitioning shapes into equal shares. ii. In data analysis, they should be able to represent and interpret data using picture graphs and bar graphs with up to four categories, as well as solve simple problems related to the data presented in the graphs. c. Third Grade

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i. In geometry, students should reason with shapes and their attributes, recognizing that shapes in different categories may share attributes, and identify rhombuses, rectangles, and squares as examples of quadrilaterals while also learning to partition shapes into parts with equal areas. In data analysis, they should represent and interpret data, drawing scaled picture graphs and scaled bar graphs with several categories and solving problems using the information in the graphs. ii. This integration of mathematics with real-world applications, such as analyzing weather data, fosters interdisciplinary learning, combining mathematical skills with scientific inquiry, geography, and language arts, and building on foundational concepts covered in previous chapters. d. Informal Pre-Assessment i. Children’s readiness for primary-level activities, including early graphing and spatial relations, should be assessed using the preoperational assessment tasks provided in Appendix A, as it cannot be assumed that all children have had the necessary prerequisite experiences before entering a primary classroom. ii. Teachers in grades 1 to 3 may need to begin with these foundational levels before progressing to the activities outlined in this chapter.

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e. Activities i. Geometry  Primary children can be introduced informally to basic geometry concepts such as points, curves, lines, angles, congruency, and symmetry, often through hands-on activities like story mapping or shape sorting.  While technical terms like congruency and symmetry may not be essential at this stage, activities with inch cubes and geometric manipulatives help develop spatial reasoning.  Materials like tangrams and geoboards are recommended for working with two-dimensional shapes, while three-dimensional explorations can utilize everyday items like coffee stirrers and craft sticks, fostering the groundwork for formal geometry study. ii. The Geography of Robotics Programming  Robotics programming involves a logical progression of commands within a virtual geometric grid, starting from pre-coding games where children give directions to navigate through a grid, to more complex tasks like programming Lego® robots in competitions organized by the First Lego® League.  Children engage in a cycle of creativity and problem-solving as they decide on tasks, design code, test it, evaluate results, refine code, and test again.  Lego® Mindstorms® robotics integrates building with Lego® bricks with STEM education, allowing children to explore physics, technology, and mathematics through programming apps and programmable Lego® bricks, making robotics accessible even to kindergartners. iii. Collecting and Analyzing Data and Constructing Graphs (1) Students are taught to collect data, categorize it, and represent it graphically for analysis, with graphing activities tailored to their interests and current activities to make the data relevant to them.

Picture graphs, bar graphs, line graphs, and circle graphs are the main types taught, with line graphs requiring more advanced thinking as they depict variations over time, such as temperature fluctuations.  Charts and Tables (1) Charts and tables are utilized to organize data before graphing, with simple charts often consisting of tally marks and tables organizing data before constructing graphs.  Estimation (1) Estimation, crucial at the primary level, involves making rational predictions, such as guessing the number of pennies in a jar or cubes in a container, allowing children to develop their estimation skills through hands-on activities and comparisons between their estimates and actual counts.  Probability (1) At the primary level, probability is introduced informally, prompting children to discern likelihoods by answering a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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questions such as whether it’s more probable to snow or rain in certain conditions, and engaging in activities like tallying outcomes of dice throws or disc tosses to observe patterns without delving into formal calculations. b. Support for English Cultural Diversity i. Various cultures have long employed diverse geometric principles in their daily lives and creations, evident in practices like constructing perfect rectangular bases in Mozambique using bamboo sticks and equal lengths of rope, as described by Gerdes (1997), and in other forms such as woven basket designs, beadwork, pottery markings, cloth designs, and monumental constructions like Egyptian and Mayan pyramids, all predating formalized Western geometry. c. Supporting Children with Special Needs i. Children with Down syndrome, or trisomy 21, often require individualized accommodations due to challenges in language development stemming from impaired short-term memory, necessitating repetition of new skills and reviews of previously learned ones, along with simplified instructions and tasks, as highlighted by Lewis (2003) and Gargiulo & Kilgo (2014). d. Informal Post-Evaluation i. Observing children’s ability to follow directions and engage in activities is crucial, noting where breakdowns occur to determine if further practice or guidance is needed or if the activity exceeds their current developmental level, emphasizing the importance of not pushing children beyond their capabilities and allowing more advanced peers to support those who may struggle, as suggested in the text.

XXXVII. Standards and Description of Measurement (09.03; PPT Slide 25) a. Measurement is a fundamental aspect of mathematics, integral to everyday activities, and integrating it with children’s environment enhances their skill development; the primary curriculum emphasizes introducing standard units and applying them to various measurements like length, volume, area, weight, temperature, time, and money, gradually progressing through different stages of development and introducing both English and metric units. b. Informal Pre-Assessment i. Concrete operational thinking is crucial for children to grasp the concept of standard units, with conservation tasks and assessment guidelines helping educators evaluate children’s understanding of measurement across various dimensions like length, weight, volume, temperature, and time, ensuring mastery of nonstandard measurement before progressing to standard measurement methods. c. Instruction i. Measurement concepts are best developed through hands-on, relevant, and meaningful experiences, with a sequenced approach to introducing standard units consisting of comparisons without numbers, using nonstandard arbitrary units, comparing measured objects to the units used, and finally introducing standard units with appropriate measuring instruments, always preceded by comparisons and nonstandard measurements to ensure understanding.  The Concept of Unit a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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(1) The concept of unit is fundamental to children’s ability to measure accurately, and it can be developed through the use of both nonstandard and standard units.

(2) Children learn that units can vary and must be consistent in length or volume when measuring, and they reinforce this concept by comparing measurements made with different arbitrary units.

(3) Accuracy in measurement is emphasized, starting with units that can be easily aligned without gaps, and as children progress, they learn to use units efficiently to measure lengths, capacities, and other quantities.  Measuring Instruments (1) Introducing measuring instruments to children involves starting with simple versions marked only with the unit being used, ensuring children understand how units are marked, and providing ample experiences measuring objects shorter than their ruler before moving on to longer objects.

(2) Scaled instruments like thermometers and balance scales can be challenging, but children can gain understanding by making their own instruments or exploring objects with known weights.

(3) Analog clocks can be particularly difficult to understand due to the circular movement of the hands, but activities and practice with both analog and digital clocks help children develop their understanding of time passage. d. Measurement Activities i. The activities presented at the end of this chapter aim to assist children in understanding and constructing concepts related to measuring length, volume, area, weight, temperature, and time using standard units. It is important to refer to previous units in the text for comparison and arbitrary measurement experiences before introducing standard units, and to focus on both the concepts of the units used for each type of measurement and actual measurement. e. Support for Children with Special Needs i. The number of children diagnosed with autism spectrum disorder (ASD) has increased due to changes in diagnostic criteria, with symptoms varying from social and communication disorders to challenging behaviors. ii. Teaching strategies for ASD children focus on social involvement, with communication and tasks broken down into small steps and a carefully structured environment. Individualized approaches tailored to each child’s unique strengths and challenges are essential, incorporating peer interactions, visual schedules, consistent routines, minimal distractions, and concrete directions. iii. Additionally, Mathematics Recovery (MR) offers one-on-one, problem-based instruction to help struggling first graders with mathematics. f. Evaluation i. Evaluate children’s progress with measurement through concrete tasks, such as providing a list of classroom items to measure using measuring cups and containers, weighing items on a scale with known weights, interpreting a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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temperatures on model thermometers, and telling time using both analog and digital clocks.

XXXVIII. Summary [return to top]

ADDITIONAL RESOURCES PRIMARY SOURCES 

Barker, L. (2009). Ten is the magic number! Teaching Children Mathematics, 15(6), 336–345.

Brickwedde, J. (2023). Place value as a rate of ten. Teaching Children Mathematics, 25(1), 30– 35.

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Burgess, C. R. (2014). Untangling geometric ideas. Teaching Children Mathematics, 20(8), 508– 515.



Castle, K., & Needham, J. (2007). First grader’s understanding of measurement. Early Childhood Education Journal, 35(3), 215–222.



Cengiz, N., Grant, T. J. (2009). Children generate their own representations. Teaching Children Mathematics, 15(7), 438–444.



Christy, D., Lambe, K., Payson, C., Carnevale, P., & Scarpelli, D. (2008). Alice in numberland: Through the standards in wonderland. Teaching Children Mathematics, 14(8), 436–446.



Crawford, H. G. (2010). Economic insights through problem solving. Teaching Children Mathematics, 17(4), 218–219.



Dixon, J. K. (2008). Tracking time: Representing elapsed time on an open timeline. Teaching Children Mathematics, 15(1), 18–24.



Dougherty, B. J., & Venenciano, L. C. H. (2007). Measure up for understanding. Teaching Children Mathematics, 13(9), 452–456.



Eichinger, J. (2009). Activities linking science with math. Arlington, VA: NSTA. (Vertex graphs)



Kieran, C. (2014). Algebraic thinking in arithmetic research brief. National Council of Teachers of Mathematics. Retrieved May 7, 2014, from www.nctm.org/news /content. aspx?id=42315.



Kunze, S. A. (2014). Making tens: Finding addends that sum to ten. Retrieved April 7, 2014, from http://illuminations .nctm.org.



McDuffie, A. R. & Eve, N. (2009). Break the area boundaries. Teaching Children Mathematics, (16)1, 18–27.



Mokros, J., & Wright, T. (2009). Zoos, aquariums, and expanding students’ data literacy.

Teaching Children Mathematics, 15(9), 524–530.



Shultz, G. O. (2008). Making sense of time with A Toad for Tuesday. Teaching Children Mathematics, 15(4), 212–216. a

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

Skinner, A., Louie, N., & Baldinger, E.M. (2019). Learning to see students’ mathematical strengths. Teaching Children Mathematics, 25(6), 339-344.



STEM: Science, engineering, technology, and mathematics. (2010). Science and Children, 47(7).

[Focus issue].



Whitin, D. J., & Whitin, P. (2009). Why are things shaped the way they are? Teaching Children Mathematics, 15(8), 464–472.



Wickett, M. (2009). Tuheen’s thinking about place value. Teaching Children Mathematics, 16(4), 256.

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Yeh, C. (2014). Pattern-block puzzlers. Teaching Children Mathematics, 20(8), 528.

[return to top]

Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 10: Overview of Primary Science: Life Science, and Physical Science

TABLE OF CONTENTS Purpose and Perspective of the Chapter ................................................................................................. 92 Chapter Objectives ................................................................................................................................... 92 What’s New in This Chapter ................................................................................................................... 92 Chapter Outline ........................................................................................................................................ 92 Additional Resources .............................................................................................................................. 102 Primary Sources .................................................................................................................................... 102

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to provide educators with a comprehensive understanding of primary grade science, encompassing both life and physical sciences, aligned with national standards. Through an exploration of key concepts and principles, participants will comprehend and explain an overview of primary grade science education. Additionally, educators will learn to plan, teach, and evaluate engaging and effective lessons and projects in both life and physical sciences, ensuring alignment with national standards and promoting students’ scientific literacy and inquiry skills. By integrating hands-on activities and inquiry-based learning experiences, participants will gain the knowledge and skills needed to create dynamic and engaging science lessons that foster curiosity and understanding among primary grade students.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 10-1

Comprehend and explain an overview of primary grade science.

10-2

Plan, teach, and evaluate primary grade life science lessons and projects aligned with national standards.

10-3

Plan, teach, and evaluate primary grade physical science lessons and projects aligned with national standards.

[return to top]

WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Common Artifacts as Tools to Support the Transition From Pre-Operational to Concrete Operational



Added section: Sample Activities

[return to top]

CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic) so that you can see how all the content relates to the topics covered in the text.

XXXIX. Next Generation Standards and Guidelines for Primary Grade Science (10.01; PPT Slide 3) i. Science teaching requires ongoing professional development and a commitment to expanding knowledge, with the Next Generation Science Standards (NGSS) providing a framework grounded in A Framework for K–12 Science Education. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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ii. Teaching strategies in this field should reflect how science is practiced, encompassing life science, physical science, earth and space science, environmental awareness, and engineering design technology. iii. Children in the primary grades are avid explorers who require ample opportunities for hands-on investigations and experiences with concrete objects. iv. As they transition from the preoperational to concrete operational stage, they can begin to use abstract symbols tied to concrete experiences, fostering industriousness and enjoyment of long-term projects. v. Key instructional strategies include small group work, classification by multiple characteristics, inference drawing, and experimentation. vi. To develop essential science and engineering practices, children need exposure to questioning, modeling, investigation planning, data analysis, mathematical thinking, explanation construction, argumentation, and information communication. vii. STEM experiences in primary education cultivate critical thinking, problemsolving skills, and content learning, laying a foundation for future academic success. nn. Translating NGSS for Classroom Instruction i. Teachers face the challenge of translating the Next Generation Science Standards (NGSS) into effective instruction, as the NGSS serves as a guide rather than a curriculum. Curriculum, instruction, and assessment are responsibilities left to practitioners, with efforts made by educators like Bybee to develop guidelines for integrating NGSS into classroom practices. ii. Bybee emphasizes that assessments, curriculum, and instruction should align with NGSS performance expectations, with curriculum and instruction being developed before assessments. Bybee provides a planning guide table to aid in this process, focusing on Science and Engineering Practice, Disciplinary Core Idea, and Crosscutting Concept. iii. Frequently asked questions about NGSS address topics like the inclusion of engineering and the broader concept of ―practice‖ in science education. a) Classroom Instruction (1) Bybee recommends planning instruction by moving beyond individual lessons to an integrated instructional sequence, starting with an engaging lesson, followed by exploration, explanation, elaboration, and evaluation, incorporating a group of performance expectations into thematic units or projects, and promoting backward design by using performance expectations to design assessments and sequence activities. oo. Conventional Science Instruction i. Collecting a) Encouraging primary children’s natural inclination to collect objects can foster their observation, comparison, sorting, and classification skills, promoting scientific inquiry practices such as critique and evaluation rather than focusing solely on object identification. ii. Getting Started by Using Magnifiers a) Introducing magnifiers to primary students facilitates exploration and observation, fostering scientific inquiry skills. Handheld plastic a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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magnifiers and magnifying boxes are recommended for outdoor explorations and observing small treasures and insects, emphasizing humane observation practices. b) Additionally, jumbo-sized magnifiers on stands allow for hands-free examination of objects, serving as a precursor to microscope use. c) Teachers can facilitate independent exploration with magnifiers, prompting students to describe their observations, compare appearances under different magnification levels, and understand the role of lenses in magnification.

(1) Focusing the Collecting (a) Encourage focused collecting among primary students by suggesting various items to collect, such as leaves, shells, seeds, spider webs, feathers, rocks, rubbings, modeling clay impressions, and plaster molds of footprints, while emphasizing inquiry and observation over identification. Facilitate sorting and classification activities with collected items, fostering scientific thinking and comparison skills. pp. Practices and Design i. The primary focus of science is investigation and empirical inquiry, while engineering involves constructing explanations or designs, and technology develops tools to facilitate investigation and design. ii. Hands-on, manipulative activities support science learning, but some teachers may feel hesitant due to perceived barriers like lack of training or managing materials. iii. However, basic science concepts can be effectively taught with a willingness to learn, guiding children in investigations and fostering curiosity about the natural world. iv. By exploring scientific phenomena, teachers often discover their own understanding of basic concepts and can convey them to students in accessible ways, demonstrating that scientific principles can be grasped through observation and exploration. a) Supporting Science Investigations (1) Supporting science investigations involves encouraging students to ask questions, make predictions, consider factors, keep records of observations and results, and draw conclusions, resembling the conventional scientific method.

(2) It’s important to allow flexibility in the investigation process, as scientists and engineers move back and forth in their analyses.

(3) Hands-on learning is crucial, but it should also foster problemsolving and inquiry skills, exemplified by comparing two approaches to teaching the displacement of water.

(4) The second approach, which encourages students to discover and share their findings, promotes richer inquiry and discourse.

(5) By listening to students’ questions and experiences, teachers can better guide instruction. qq. Managing the Classroom Environment and Experiences a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. A well-thought-out management plan is crucial for instructional success in the classroom, encompassing both organizing children and materials for learning. ii. Children can be organized into teams with designated responsibilities, including material management, recording, moderation, and investigation, with regular rotation of roles to ensure equal participation. iii. Materials can be organized into distribution centers labeled 1 to 4, corresponding to team numbers, with clear instructions and time limits for collection. iv. Clear rules and periodic reviews help maintain focus and behavior during complex activities, fostering a conducive learning environment. rr. Investigation Prompts i. The activities provided in this chapter serve as examples of investigations that allow children to engage in scientific inquiry and processes, fostering their development as young scientists and engineers. ii. Through these activities, students are encouraged to pose questions and design solutions, such as designing a container to prevent ice cube melting, investigating mold growth on different types of bread, exploring magnetism in the classroom, examining seed growth without soil, observing the drying process of wet spots, constructing a bird feeder, determining the appropriate size aquarium for goldfish, and planning a garden layout along with necessary gardening tools. iii. These inquiries stimulate critical thinking and problem-solving skills while nurturing curiosity and creativity in young learners.

XL. Conventional and Next Generation Life Science Instruction (10.02; PPT Slide 8) i. Children, regardless of their environment, demonstrate a keen interest in learning about the world around them, particularly living organisms. ii. The K–12 Framework and NGSS emphasize that during the primary grades, children should engage in firsthand experiences with plants and animals to develop an understanding of biological concepts, life cycles, and habitats. iii. NGSS outlines questions for each grade level, encouraging exploration of topics such as the needs of plants and animals, variations in traits, and the impact of environmental changes on organisms. iv. These early experiences serve as a foundation for further exploration and understanding of key biological concepts in later grades. a. NGSS Life Science Performance Expectations i. First graders should be able to design solutions to human problems by observing how plants and animals use their external parts, recognize patterns in the behavior of parents and offspring, and understand that young plants and animals resemble their parents but are not identical. ii. Second graders are expected to investigate whether plants need sunlight and water to grow, create models mimicking animal functions in seed dispersion or pollination, and compare the diversity of life in different habitats. iii. Third graders should be able to develop models of organisms’ life cycles, argue about the benefits of group formation in animals, analyze inherited traits and variations within a species, explain how traits are influenced by the environment, interpret data from fossils, argue about advantages of variations in characteristics within a species, assess solutions to environmental changes, and evaluate the impact of environmental changes on plant and animal types in specific habitats. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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b.

c.

d.

e.

These expectations are outlined in the NGSS book, which also provides clarification statements and project suggestions related to each performance objective.

Next Generation Instructional Plans i. Herbert Spencer, an English philosopher and scientist, advocated for children to engage in their own investigations and draw their own inferences, emphasizing minimal guidance from teachers. ii. This philosophy influenced the development of the Learning Cycle by Robert Karplus and J. Myron Atkin, who aimed to connect developmental psychology principles to science instruction. iii. The Learning Cycle consists of three phases—exploration, concept introduction, and concept application—aimed at fostering independent thinking and relevance to students’ lives. iv. This approach contrasts with traditional methods focused on rote memorization. v. The NGSS further emphasizes hands-on learning and inquiry-based instruction, encouraging students to conduct their own scientific investigations from an early age, aligning with the shift towards student-centered science education. vi. Activities in this chapter are designed to support this approach, with an emphasis on students actively engaging in scientific inquiry.

Conventional Life Science Instruction i. Life Science Concepts  Through activities in the primary grades, students should gain an understanding of the characteristics of organisms, including their life cycles, environmental dependencies, behavioral adaptations, and impacts on their surroundings, fostering a comprehensive grasp of life science concepts. ii. Conventional Planning for Life Science  Conventional planning for life science involves structuring learning experiences around fundamental life science concepts, such as those related to seeds, as illustrated in Figure 10-2 with a unit planning word web, to facilitate effective teaching of primary-age children. iii. Living Things  Living things, including plants and animals, possess unique features and characteristics that distinguish them from nonliving things, impacting each other, requiring essential elements like water, food, and air for survival, while seeds exhibit various attributes and germinate to form specific plants, which undergo growth and change, responding to environmental stimuli, and animals demonstrate individuality, adaptations, life cycles, and varying care needs, with pets requiring specific attention and aquariums serving as environments for aquatic life.

Planning and Teaching a Seed Project i. The seed project suggestions provided offer hands-on learning experiences tailored to the developmental levels of primary-age children, with activities like the ―Sock walk‖ and ―Egghead hair‖ aimed at engaging students in exploring seed dispersal and plant growth, providing clear objectives, materials needed, and extensions for further exploration and evaluation.

Additional Plant Activities Based on Science Concepts a

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i. The unit on seeds can be extended by exploring additional concepts about plants, such as how they grow from roots and stems, and how molds grow in dark, moist conditions. Activities like creating dish gardens from vegetable cuttings and observing mold growth in a controlled environment provide hands-on experiences for students to learn about plant reproduction and the characteristics of fungi, emphasizing record-keeping, observation, and prediction skills while ensuring safety measures are followed. f. Animals in the Classroom i. Caring for and studying living things in the classroom and outdoors fosters respect and understanding for various forms of life, instilling a sense of responsibility and sensitivity in children towards living organisms’ daily requirements. ii. Precautions should be taken to ensure that animals do not suffer from inappropriate care, and preparations should involve the entire class to understand the specific needs of each species. Before introducing an animal into the classroom, considerations regarding its habitat, temperature, diet, care during weekends and vacations, ethical considerations, and long-term commitment should be carefully evaluated to ensure the well-being of the animal and avoid future problems.  Tips for Keeping Animals in the Classroom (1) When keeping animals in the classroom, it’s essential to prioritize the safety and well-being of both the children and the animals.

(2) Proper handling techniques for different types of animals should be followed, including avoiding disturbing pets while eating and washing hands after handling reptiles to prevent bacterial transmission.

(3) Additional precautions include checking local regulations, cautioning students against teasing or sticking objects into cages, purchasing fish from reputable suppliers, and refraining from bringing personal pets to school to prevent overwhelming the animals and ensuring a respectful interaction with therapy animals if necessary.  Teaching with Animals (1) Teaching with animals offers a rich opportunity for students to observe, categorize, and communicate their experiences, integrating science concepts naturally into their learning.

(2) Projects can be designed around questions such as how animals move, eat, behave during the day and night, react to different objects, make sounds, and drink, with technology like digital cameras aiding in data collection.

(3) Additionally, researching the care requirements for animals like earthworms and comparing different animals’ body coverings can deepen students’ understanding, while organizing their findings using word webs helps reinforce their learning and highlight project connections. g. A Trip to the Zoo a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. A well-planned trip to an accredited zoo provides children with engaging opportunities to learn about animals and their habitats, fostering an understanding of species preservation and rehabilitation. ii. Before, during, and after the visit, teachers can plan learning experiences to maximize the educational impact, such as focusing on comparing reptiles and amphibians, as exemplified by a scenario involving observations and discussions about turtles in a third-grade class.  Before the zoo visit, the teacher sets up learning stations to prepare the children, including tactile experiences with simulated body coverings, exploring camouflage, understanding how animals sense vibrations, drawing turtles and their habitats, and comparing historical and modern zoo enclosures.  At the zoo, the teacher organizes small groups with chaperones and assigns each group a turtle task card, prompting the children to observe and answer questions about the turtles’ behavior, environment, food, and companions, and later make comparisons with amphibians, ensuring they read exhibit signs and gather additional information.  After the zoo visit, the teacher reinforces learning by organizing activities including a turtle-themed play and shoebox dioramas of turtle habitats, prompting children to compare their pre- and post-visit understanding of turtles, while providing storybooks and reference materials for further exploration; before, during, and after zoo trips, the teacher engages students with questions and activities focusing on animal characteristics, behaviors, and adaptations to enhance the learning experience. h. Strategies for Teaching About the Human Body i. Understanding the internal anatomy of the human body is challenging for young children, but activities like exploring body awareness, identifying major bones, observing X-ray films, and discovering the workings of joints through movement exercises can help develop their understanding, along with activities such as making paper bodies to locate joints and exploring different muscles in the body through movements and facial expressions.

XLI. Physical Science for the Next Generation and Conventional Physical Science Instruction (10.03; PPT Slide 29) i. Physical science experiences are engaging for primary-age children due to the abundance of opportunities for hands-on exploration, the availability of instantly repeatable experiments, and the use of discrepant events that provoke curiosity and readiness for learning. ii. The NGSS emphasizes understanding matter, motion, forces, and energy, suggesting questions such as how materials vibrate, the properties of materials, and the effects of forces on objects, which serve as starting points for investigations in the primary grades. a. NGSS Performance Expectations i. The NGSS outlines specific performance expectations for first, second, and thirdgrade students.

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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b.

c.

d.

e.

f.

ii. These expectations include conducting investigations on the relationship between vibrating materials and sound production, classifying materials based on observable properties, and exploring the effects of balanced and unbalanced forces on object motion. iii. Each expectation is supported by clarification statements suggesting potential projects and additional information on science and engineering practices, disciplinary core ideas, and crosscutting concepts.

Examples of Instructional Progressions i. The following experiences are designed with a focus on physical science to encourage students to engage in independent thinking and hands-on scientific inquiry, aligning with the principles outlined in the new standards.

Conventional Physical Science Instruction i. This section outlines fundamental physical science concepts relevant to primary grade learning, including properties of air, changes in matter, gravity, light, and energy. It provides a comprehensive list of concepts such as air taking up space, matter changing states, and the principles of motion and energy, offering a foundation for integrating these ideas into lesson planning and activities.

Planning and Teaching About Air: Bubbles i. The learning activities provided in this chapter follow a structured format, similar to the seed project introduced earlier in the Life Science section. ii. The focus is on exploring the concept of air through engaging lessons involving bubbles and sound. Investigation questions prompt inquiry into various aspects of bubbles, such as their formation, strength, and shape, while practical experiences, like making whipped milk topping, provide hands-on opportunities to observe the presence of air bubbles in food.

Concept: Air Can Move Things and Slow Things Down i. The suggestions extend science concepts involving air by providing various hands-on activities for children to explore air movement and properties. These activities include moving bubbles with paper fans, designing gliders, straw painting, making pinwheels, observing air-driven objects outdoors, experimenting with parachutes, observing seed dispersal by wind, testing different objects’ effectiveness in moving bubbles, and creating a straw and ball obstacle course for blowing exercises.

Exploring Vibrating Air: Sound i. Voice  The process of vibration as sound can be experienced by children through activities involving their voice. They can observe the vibrations of their vocal cords by gently resting their fingers over them while speaking different sounds, feel vibrations by placing their fingertips against their lips while blowing and humming, experiment with the intensity of vibration by adjusting the volume of their speech, and create a humming cup by covering the bottom of a paper cup with waxed paper to feel sound vibrations. ii. Percussion Instruments  Children can recognize vibrating air as sound through percussion instruments, both ―real‖ and ―found‖ ones. Percussion instruments create sound by striking some part of the instrument, and examples include a

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iii.

iv.

v.

vi.

drums made from coffee cans or oatmeal containers, homemade drumsticks from tennis balls and dowels, tambourines made from decorated paper or plastic plates, and shakers made from cardboard tubes filled with beans or rice. These activities allow children to explore the concept of sound production through vibration.

Percussion Experiment: The Pitch of Sound  Pitch, defined as the highness or lowness of a sound, can be explored through a hands-on activity using eight bottles filled with varying amounts of water to create a musical scale. Second and third-grade students can assist with the math involved in tuning the bottles, dividing the volume of water among them to produce different notes. Once prepared, children can experiment with different utensils to create simple melodies, and multiple sets of bottles with different substances can be compared to explore differences in sound quality. This activity provides an engaging way for students to understand the concept of pitch and its relationship to the amount of water in the bottles.

Wind Instruments  Wind instruments produce sound through vibrating columns of air, with longer columns producing lower pitches and shorter columns producing higher pitches. While incorporating wind instruments in classrooms presents challenges due to hygiene concerns, strategies to overcome this include creating homemade horns using flexible tubing or PVC pipes, using inexpensive plastic whistles, recorders, and flutes that can be personalized, and utilizing real instruments with metal mouthpieces that can be sanitized between uses, such as trumpets, trombones, or French horns. These approaches provide opportunities for children to explore the concept of pitch and sound production while addressing health precautions.

String Instruments  String instruments offer effective demonstrations of vibration, with students able to both see and feel the vibrations produced by the strings.

Unlike wind instruments, string instruments do not pose hygiene concerns, but they may present challenges in maintaining tuning and durability. Strategies for introducing string instruments in the classroom include creating box guitars using rubber bands stretched around a small box, utilizing autoharps for their ease of tuning and simplicity, and introducing ukuleles, parlor guitars, and child-size violins, which offer accessible options for young learners to engage with string instruments and develop musical skills.

Electronic/Digital Instruments  Electronic and digital instruments offer a diverse range of musical experiences for children, including electric guitars, keyboards, and unique instruments like the theremin. While these instruments may not overtly demonstrate the vibrating air aspect of sound production, connecting them to external speakers can help visualize the vibrations.

Incorporating instruments into the classroom provides a powerful way for students to explore sound properties, combining formal activities with a

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informal exploration opportunities, such as forming a ―Science Rocks‖ band. g. Properties of Matter i. The NGSS emphasizes that young children should understand that matter can be classified based on observable characteristics like size, shape, color, weight, temperature, and reactivity with other substances. ii. Children develop these concepts by engaging in experiences where they observe, describe, compare, and sort objects. For instance, activities involving feely socks or scent jars, temperature comparisons, and ordering objects by weight help children explore these properties through hands-on experiences. iii. These activities lay the groundwork for understanding states of matter and introduce concepts of chemical and physical changes.  Shape and size  Smell  Temperature  Weight iv. Matter experiment: Chemical changes  This experiment aims to explore chemical changes using glue and borax solutions. Students mix equal parts of glue and distilled water in one container and a borax solution in another. They then combine the solutions in pairs, observing the resulting mixture and discussing whether it resembles either original solution and whether it represents a new substance, prompting an understanding of chemical changes. v. Matter experiment: Physical changes.  This experiment focuses on exploring physical changes using water and sand.

Students pour water and sand into bowls and place them in the sun. Later, they observe any changes to the sand and water, prompting discussions about whether a new substance has formed and whether the observed changes represent physical or chemical changes. h. Exploring Light i. This section proposes various learning experiences to help children understand the Next Generation Science Standard for light. ii. It suggests using light tables with plastic shapes and animal x-rays, playing light beam tag with mirror tiles to demonstrate light traveling in straight lines, and utilizing instructional technology such as light meters to measure light intensity. iii. The light meter can be used to measure light levels in different areas and objects, and children can create graphs to compare the comparative light intensity. iv. Further explorations with light meters include investigating the effect of different fabrics on light intensity and the reflectivity of various hard materials. i. Assessment Strategies i. The NGSS standards offer performance expectations that can be tailored to evaluation criteria, emphasizing the need for evidence. Assessment tools such as models, drawings, diagrams, and tables/charts are crucial for gathering evidence. ii. Due to many primary children being early readers, assessments should focus on process skills and anecdotal records to gauge understanding. iii. When recording oral explanations, emphasis should be placed on the child’s ability to communicate ideas rather than on specific terminology. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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iv. Snippets of informal conversation related to the task can also be noted during children’s activities for assessment purposes.

IV.

Summary

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ADDITIONAL RESOURCES PRIMARY SOURCES 

Ansberry, K., & Morgan, E. (2007). More picture perfect science lessons: Using children’s books to guide inquiry. Arlington, VA: NSTA Press.



Early childhood life science. (2013). [Focus Issue]. Science and Children, 50(6).



Instructor. (2014, Spring). Articles focusing on NGSS.



Keeley, P. (2013). Uncovering student ideas in primary science. Arlington, VA: NSTA Press.



Keeley, P., & Harrington, R. (2014). Uncovering student ideas in physical science, vol. 2.

Arlington, VA: NSTA Press.



Konicek-Moran, R. (2011). Series Yet more everyday science mysteries (2010); Even more everyday science mysteries (2009); More everyday science mysteries (2008); Everyday science mysteries. Arlington, VA: NSTA Press.



Krajcik, J. (2013). The next generation science standards: A focus on physical science. Science and Children, 50(7), 7–15.



Lange, A.A., Robertson, L., Price, J., & Perry (Craven), A. (2021). Teaching Early and Elementary STEM. Johnson City: East Tennessee State University. https://dc.etsu.edu/etsu-oer/8



NIH (2014). BRAIN initiative. Retrieved February 2, 2014, from http://www.nih.gov/ science/brain



Ohana, C. (2007). Creative integration [Theme issue]. Science and Children, 44(6), 6.



Sound [focus issue]. (2014). Science and Children, 51(6).



Willard, T. (2013). A look at the Next Generation Science Standards. Science and Children, 50(7), 16–17.

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Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 11: Earth and Space Sciences, Environmental Awareness, Engineering, Technology, and Science Applications a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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TABLE OF CONTENTS Purpose and Perspective of the Chapter ............................................................................................... 104 Chapter Objectives ................................................................................................................................. 104 What’s New in This Chapter ................................................................................................................. 104 Chapter Outline ...................................................................................................................................... 104 Additional Resources .............................................................................................................................. 112 Primary Sources .................................................................................................................................... 112

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to empower educators with the knowledge and skills to effectively plan, teach, and evaluate primary grade lessons and projects in Earth and space science, environmental awareness, and engineering, technology, and science applications, all aligned with national standards.

Participants will delve into key concepts and principles in each area, exploring hands-on activities and inquiry-based learning experiences to engage young learners in meaningful scientific exploration.

Through this course, educators will develop the expertise needed to create dynamic and rigorous learning experiences that foster curiosity, critical thinking, and problem-solving skills among primary grade students, preparing them for success in the ever-evolving fields of science, engineering, and technology.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 11-1

Plan, teach, and evaluate primary grade Earth and space science lessons and projects aligned with national standards.

11-2

Plan, teach, and evaluate primary grade environmental awareness lessons and projects aligned with national standards.

11-3

Plan, teach, and evaluate primary grade engineering, technology, and science application lessons and projects aligned with national standards.

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WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Sample Activities

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CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

XLII. Standards and Guidelines for Earth and Space Sciences (11.01; PPT Slide 3) i. Earth and Space Sciences (ESS) encompass the study of Earth’s processes and its relationship with the solar system and galaxy. ii. It integrates various disciplines like astrophysics, geophysics, and geobiology, with traditional geology as a cornerstone. iii. ESS explores interconnected systems such as the atmosphere, hydrosphere, geosphere, and biosphere, which influence each other. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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iv. As our understanding of astronomy and Earth’s structure advances, ESS becomes increasingly important, particularly in addressing the impacts of human activity and natural hazards. v. In primary education, children are introduced to ESS through questions about celestial objects, land changes, weather patterns, and methods to reduce weatherrelated hazards, laying the foundation for understanding Earth’s systems and their relevance to human life. ss. NGSS ESS Performance Expectations i. Students who demonstrate understanding in Earth and Space Sciences can predict celestial patterns, correlate daylight duration with seasonal changes, gather evidence to understand the pace of Earth events, compare solutions for land shape alterations, construct models of terrain and water bodies, identify water states on Earth, describe weather conditions and climates globally, and evaluate design solutions for minimizing weather-related hazards. tt. The Constructivist Approach to the Next Generation Science Standards in Primary Earth and Space Science i. The Next Generation Science Standards advocate for more in-depth teaching focused on critical thinking, and NASA’s educational website offers abundant resources for K–12 teachers to support investigations in Earth and space science, aligning with a constructivist approach where students are encouraged to validate or revise their own understanding rather than simply receive factual information. uu. Conventional Earth and Space Science Instruction i. In primary Earth and space science education, the focus is on fostering observational skills as children explore and record information about Earth materials and natural changes, guided by teachers to observe cyclical phenomena like the movement of the sun and moon, variable changes such as weather, and the properties and uses of Earth materials like rocks, soils, and water, all of which lay the groundwork for understanding environmental impacts of human activity. vv. Planning and Teaching a Unit on Rocks i. Children develop understanding of Earth materials through hands-on experiences, such as observing rocks to discern their composition and grouping them based on properties like color or pattern, with assessments focusing on their ability to classify rocks according to specific characteristics, while basic geology activities at the chapter’s conclusion aim to instill fundamental concepts and stimulate curiosity about rocks and minerals in a manner that is interactive and captivating for primary-age learners. ww.

How Rocks Are Formed i. Primary students often hold misconceptions about rocks and soil, perceiving the ground primarily as soil and rocks as only what they can carry; educators can use visuals and discussions about mountains, cliffs, and deserts to illustrate the diverse, extensive presence of rocks in Earth’s crust, which is predominantly solid rock made of various minerals. While the processes forming major rock types may be too complex for younger students, educators can introduce upperlevel children to simplified examples of rock formation, such as igneous rocks formed from magma or lava cooling, sedimentary rocks formed from compressed a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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and cemented sediments, and metamorphic rocks resulting from pressure and heat altering existing rocks. xx. Fossils i. Typically developing early elementary students may struggle with grasping the vast time spans involved in lessons about fossils and dinosaurs, but they are often intrigued by the idea of an ancient Earth and large prehistoric creatures; educators should help them understand that dinosaurs lived long before humans, debunking inaccurate depictions of coexisting cave dwellers and dinosaurs, while emphasizing that movies portraying Jurassic creatures in modern times are largely fantasy despite some scientific accuracy; students can explore various types of fossils, including shells, bones, and imprints, and learn about their formation by making imprints themselves and examining sedimentary rock, which often contains fossils, with hands-on activities like pressing leaves into clay to create imprints. yy. Soil Samples i. Regular visits to an outdoor study site enable children to observe changes in Earth materials and vegetation, fostering awareness of soil variation in texture, color, and fertility, while hands-on activities such as collecting soil samples, observing with magnifiers, and conducting soil composition experiments deepen their understanding of soil properties and their importance for plant growth and human uses. zz. Weather i. Lessons on weather and seasons are well-suited for primary-age children.

Incorporating discussions of daily weather alongside hands-on activities, such as field trips to observe weather equipment or setting up a school weather station to measure and record various parameters, foster familiarity with weather instruments and encourage recording of changes in weather and seasons through graphing, storybooks, and integrated learning experiences. Investigations into temperature and sunlight enable children to correlate daily temperature changes with seasonal variations. a) An Investigation of Temperature (1) Initiate a discussion on temperature by prompting children to explain how they determine if it’s hot or cold outside, introduce the concept of using thermometers for measurement, engage them in hands-on activities such as examining thermometers and conducting experiments with hot and cold water, encourage recording observations to articulate their understanding, and facilitate ongoing temperature readings at different times to observe patterns and relate them to changing seasons, incorporating sensory experiences and visual aids to enhance learning. b) Extending the Concept (1) To extend the concept further, encourage children to explore how shadows affect temperature and test their hypotheses, investigate factors influencing temperature, such as color, by comparing thermometer readings in dark and light envelopes, or challenge them to identify the hottest and coldest spots in their environment and devise experiments to test various ideas while also recording a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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and discussing changes in daylight and seasons through observations of a chosen tree throughout the year, fostering a deeper understanding of the relationship between temperature, sunlight, and seasonal variations. c) A Thermometer Table (1) Create a thermometer table for children to explore by collecting various types of thermometers, including oven, indoor-outdoor, and body thermometers, allowing them to compare and investigate their differences and uses. aaa. Water i. Children should be provided with numerous opportunities to explore evaporation and condensation phenomena, starting with simple investigations like observing the gradual disappearance of water spots on construction paper and progressing to activities like creating ―puddle pictures‖ on the sidewalk to track the process of evaporation; they can further investigate factors affecting evaporation, such as temperature and time of day, and explore condensation by observing what happens when hot and cold air collide, fostering an understanding of changes in matter and the role of heat in these processes. bbb.

Space Science i. Young children are intrigued by space exploration, the sun, moon, and stars, and while they may not grasp the vastness of space, they can observe aspects of space science, such as the sun’s movement throughout the day and the changing phases of the moon; engaging in activities like shadow play and creating lunar landscapes fosters understanding and curiosity, introducing them to binoculars allows them to explore features of the moon, and observation of the night sky, including constellations and celestial objects, stimulates their natural curiosity about space.

XLIII. Standards and Guidelines for Environmental Awareness (11.02; PPT Slide 23) i. Environmental awareness is integrated into kindergarten and fourth-grade expectations of NGSS, focusing on communicating solutions to reduce human impact on the environment and understanding the relationship between energy use and environmental effects. ii. The K–12 Framework emphasizes the interconnectedness of living organisms and Earth’s systems, addressing topics such as the global carbon cycle, greenhouse gases, natural hazards, and human alteration of the environment. iii. Students are encouraged to make choices that reduce their impact on the environment, and E-STEM curriculum integration allows for interdisciplinary learning experiences. iv. Teachers play a crucial role in guiding students to understand the characteristics and changes within their local environment and the impact of human decisions on resources. a. Next Generation Environmental Awareness Instructional Plans i. Environmental awareness encompasses understanding the environment and its preservation and mitigating its destruction, including global, regional, local, and individual impacts, with a focus on air, water, land, plants, animals, and human habitats. Despite debates on issues like climate change, there’s a consensus on a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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the need for environmental protection, emphasizing the importance of understanding the environment’s role for all living beings, including humans.

The section aims to guide primary-grade discussions on environmental topics and offers investigative models.  Earth and Human Activity (1) The Earth and Human Activity section focuses on two main disciplinary core ideas: natural resources and natural hazards.

(2) In kindergarten, children learn that living things require resources like water, air, and land, while in fourth grade, they understand that energy and fuels are derived from natural sources and that their use affects the environment.

(3) Additionally, kindergarten students grasp that severe weather patterns vary by region and can be forecasted, whereas fourth graders learn about various natural hazards like earthquakes, tsunamis, and hurricanes, and how to mitigate their impacts.  Performance Expectations (1) In kindergarten, performance expectations include using a model to understand the relationship between the needs of plants and animals and their habitats, asking questions about weather forecasting for severe weather preparation and response, and communicating solutions to minimize human impact on the environment.

(2) For fourth graders, the expectations involve gathering and synthesizing information to explain how energy and fuels come from natural resources and their environmental impacts, as well as generating and comparing solutions to mitigate the effects of natural Earth processes on humans. b. The Constructivist Approach to the Next Generation Science Standards in Primary Grades Environmental Awareness i. The conventional instruction section includes inquiry projects focused on environmental awareness, such as Water Changes the Earth, Trash and Litter, and Recycling. These investigations are designed to empower students to think independently and engage in scientific inquiry aligned with the new standards. c. Conventional Environmental Awareness Instruction i. Concepts and approaches in environmental education include understanding environments as spaces and conditions affecting survival, recognizing resources like coal and water, and grasping recycling as the reuse of materials.  Environmental investigations allow children to explore their surroundings actively, fostering cooperation and understanding.  Three common approaches to environmental education are awareness, environmental concept, and conservation, each focusing on feelings, learning, or action.  Lessons should yield observable results, fostering direct understanding of actions’ impacts, and can begin with brainstorming sessions to build awareness and understanding of the environment. d. Water a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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i. The importance of water is highlighted through its presence in various forms on Earth’s surface, including rivers, lakes, and oceans. ii. Children can explore how water shapes the Earth’s surface through erosion and investigate its vital role for living organisms. Activities such as identifying water usage, detecting and addressing water wastage, and measuring personal water consumption foster awareness and responsibility towards water conservation. iii. Furthermore, children can delve into the issue of water pollution and the importance of clean drinking water, engaging in investigations to understand the impact of pollutants and explore methods of water purification, potentially through visits to water treatment facilities. e. Trash and Litter i. The activity ―How Much Trash?‖ encourages students to explore the amount and types of garbage they generate, emphasizing the importance of waste management and recycling. ii. Students sort their garbage into categories and weigh them to understand the distribution of waste materials. iii. They also research global environmental issues like the ―great Pacific garbage patch‖ to grasp the broader impact of human waste. iv. Additionally, activities like the ―Litter Collage‖ and ―Recycling Survey‖ engage students in hands-on learning and promote environmental awareness and responsibility. v. The ―Class Landfill‖ activity allows students to witness firsthand the degradation of biodegradable and non-biodegradable materials, highlighting the consequences of improper waste disposal.

XLIV. Description and Standards for Engineering Design, Technology, and Applications of Science (11.03; PPT Slide 32) i. The 2012 Framework for K–12 Science Education expands the traditional science curriculum to include engineering and technology, emphasizing their practical applications. ii. Engineering is defined as the systematic design process to address human needs, while technology encompasses any human-made modification of the natural world. iii. The integration of engineering practices in classrooms enhances students’ understanding and application of scientific knowledge. iv. The Next Generation Science Standards (NGSS) incorporate engineering design practices, guiding students through problem definition, solution development, and solution comparison processes. v. By second grade, students are expected to engage in more complex problemsolving tasks and analyze data to evaluate different solutions. vi. This integration fosters creativity, critical thinking, and practical problem-solving skills in students from an early age. a. Engineering i. Engineers use practices like problem definition, model development, and data analysis to solve problems, emphasizing the importance of setting criteria for success. ii. By second grade, students understand that various situations can be tackled as engineering problems, with multiple solutions possible. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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iii. The engineering design process involves brainstorming, model creation, testing, and refinement, fostering critical thinking and creativity. iv. Students integrate scientific knowledge into design challenges by third grade, addressing real-world problems such as overcrowding in classrooms. v. The American Society for Engineering Education advocates for comprehensive engineering programs to cultivate capable problem solvers adept in engineering concepts and practices.  Engineering Habits of Mind (1) Engineering Habits of Mind encompass optimism, emphasizing the belief in continuous improvement and the potential for novel solutions from anyone.

(2) Persistence is valued, with failure seen as part of the iterative process inherent in engineering design.

(3) Collaboration is essential, with teamwork and effective communication playing key roles in engineering successes.

(4) Creativity is prized for its ability to identify new patterns and solutions, fostering innovation and novel approaches to problemsolving.

(5) Conscientiousness is crucial, as engineers must consider the ethical implications of their work and its impact on society.

(6) Systems thinking is highlighted, emphasizing the interconnectedness of various systems and the importance of considering these relationships when addressing complex problems.  Engineering Practice (1) Engineering Practice involves several key components.

(2) Engineering Design is a systematic process used to develop solutions to problems, considering clients’ objectives and specified constraints.

(3) Material Processing entails transforming raw materials into valued products through efficient application of tools and processes.

(4) Quantitative Analysis supports problem resolution by collecting and interpreting quantitative information using data analytic tools and mathematical models.

(5) Professionalism emphasizes maintaining integrity and honesty to make ethical design decisions that prioritize the public’s wellbeing and environmental protection.  Engineering Knowledge (1) Engineering Knowledge encompasses three main components.

Engineering Sciences involve fundamental principles and laws of the natural world used by engineering professionals to accomplish tasks.

(2) Engineering Mathematics consists of practical mathematical techniques applied within industry and research to solve problems predictively.

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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(3) Engineering Technical Applications comprise interdisciplinary principles necessary to realize ideas, operate tangible engineering outputs, and conduct technical analyses.

(4) These elements form the foundation of engineering learning and practice. b. Links Among Engineering, Technology, Science, and Society i. The interconnectedness of science, engineering, and technology is evident in how new scientific knowledge leads to technological advancements, which in turn drive engineering design. ii. Conversely, emerging technologies enable new scientific investigations, showcasing the reciprocal relationship between these fields. iii. This synergy influences various aspects of society, including agriculture, energy, and communication, highlighting the profound impact of science, engineering, and technology on people’s lives and the environment.

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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c. Next Generation Instructional Plans i. Engineering is increasingly integrated into science education through various student projects, such as designing a community of homes in Italy, building a house access ramp by third and fourth graders, creating food containers, designing parachutes, and constructing a hamster habitat, all of which incorporate elements of engineering design, technology, and scientific inquiry to engage students in hands-on learning experiences. ii. Additionally, schools like Harrisburg City Public Schools in Virginia implement integrative STEM programs spanning kindergarten to fifth grade, culminating in projects like designing and testing kinetic cars in fourth grade, emphasizing the importance of progression and continuity in engineering education. iii. Lastly, project plans are provided to support Next Generation Science Standards, aiming to foster independent thinking and hands-on scientific inquiry aligned with the new standards.

XLV. Summary [return to top]

ADDITIONAL RESOURCES PRIMARY SOURCES 

Cianca, S. (2020). Teaching elementary STEM education: Unpacking standards and implementing practice-based pedagogy. Oxfordshire, UK: Taylor and Francis.

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Crismond, D., Soonyiah, M., & Cain, R. (2013). Taking engineering design out for a spin.

Science and Children, 50(5), 52–57.



Graca, R. M. (2012). It’s no problem to invent a solution. Science and Children, 50(4), 34–39.

High, V., & VanHorn, L. (2012). Soil science in the digital age. Science and Children, 50(3), 37– 45.

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Masters, H., Plants, K., Sutton, E., & Mitchell, R. (2023). Using force and motion concepts to achieve a hole in one. Science and Children, 60(6), 54–59.

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National Academy of Engineering (2017). Engineering technology education in the United States. Washington, DC: National Academies. http;//nap.nationalacademies.org/23402



Powell, S. (2014). The cardboard box book. New York: St. Martin’s Press.



Sibley, A., & Kurz, T. L. (2014). iSTEM: Celebrating Earth Day with sustainability. Teaching Children Mathematics, 20(8), 516–518.



Science and Children. (2013). The history of our planet [Focus issue on Earth Science]. 50(8).

Spring, P., & Harr, N. (2014). Our world without decomposers: How scary! Science and Children, 51(7), 28–37.



Truesdell, P. (2014). Engineering essentials for STEM instruction. Arlington. VA: NSTA Press & ASCD. a

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Instructor Manual Howard, Rebecca and Charlesworth, Rosalind, Math and Science for Young Children, 9e, 2025, 9780357636565; Chapter 12: Materials and Resources for Supporting STEM in the Classroom and the Home

TABLE OF CONTENTS Purpose and Perspective of the Chapter ............................................................................................... 114 Chapter Objectives ................................................................................................................................. 114 What’s New in This Chapter ................................................................................................................. 114 Chapter Outline ...................................................................................................................................... 114 Additional Resources .............................................................................................................................. 123 Primary Sources .................................................................................................................................... 123

a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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PURPOSE AND PERSPECTIVE OF THE CHAPTER The purpose of this course is to equip educators with the knowledge and skills necessary to create effective and engaging STEM learning spaces aligned with national standards. Through a comprehensive exploration of materials and strategies, participants will learn to select appropriate materials and design learning environments that promote inquiry, creativity, and critical thinking. Additionally, educators will plan and implement STEM experiences using a variety of materials, including blocks, woodworking, games, outdoor activities, technology, and manipulatives, ensuring alignment with national standards and fostering interdisciplinary connections. Furthermore, participants will gain the tools to provide families with strategies and activities that support STEM experiences at home, fostering collaboration between home and school environments to enrich students’ STEM learning experiences and promote lifelong curiosity and engagement in STEM disciplines.

CHAPTER OBJECTIVES The following objectives are addressed in this chapter: 12-1

Select appropriate materials and create effective and engaging STEM learning space aligned with national standards.

12-2

Plan and provide STEM experiences using blocks, woodworking, games, outdoor activities, technology, manipulatives, and other materials, aligned with national standards.

12-3

Provide families with strategies and activities that support STEM experiences at home.

[return to top]

WHAT’S NEW IN THIS CHAPTER The following elements are improvements in this chapter from the previous edition: 

Added section: Family Involvement in STEM

[return to top]

CHAPTER OUTLINE The following outline organizes activities (including any existing discussion questions in PowerPoints or other supplements) and assessments by chapter (and therefore by topic), so that you can see how all the content relates to the topics covered in the text.

XLVI. Overview of Materials and Environment (12.01; PPT Slide 3) i. This chapter stresses the importance of hands-on STEM activities in early childhood education, advocating for various approaches like informal exploration and adult guidance. ii. These activities require materials for children to interact with, reducing the need for extensive teacher preparation once organized. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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iii. It emphasizes the significance of concrete and pictorial manipulative materials, along with children’s picture books, in enriching STEM education by teaching math vocabulary and illustrating real-world applications. iv. Teachers are encouraged to select quality picture books that align with STEM topics to deepen students’ understanding through engaging discussions. v. Online resources and provided titles of relevant picture books are suggested to aid educators in effectively integrating STEM concepts into their curriculum. ccc. Basic STEM Materials i. Teachers rely on miscellaneous materials collected from various sources, utilizing ―junk boxes‖ filled with items such as glass containers, aluminum foil, hardware supplies, and recyclable objects for educational activities, fostering creativity and resourcefulness in students while promoting recycling and reuse practices. ii. Commercial curriculum and textbook products often come with supplemental materials designed for hands-on implementation of suggested activities, facilitating the practical component of a textbook-based science program; additionally, STEM-focused kits of various sizes, available from both retail and online sources, cater to a growing interest in STEM activities for home use, but they may require continuous reordering of consumable supplies for sustained classroom use. iii. To be an effective science teacher, acquiring essential equipment such as magnifiers, eyedroppers, plastic tubing, mirrors, and a rock and mineral set is crucial, with magnifiers being highlighted as the most useful tool for early childhood science classrooms; similarly, for mathematics education, a wide range of commercially available materials, including unit blocks, Unifix Cubes, Lego, and various other manipulatives, offer versatility and aid in the development of multiple mathematical concepts. iv. To ensure organization and accessibility of STEM materials, utilizing labeled containers such as shoe boxes or commercial kits is essential, with clear marking and visible materials lists facilitating easy retrieval; furthermore, storing materials related to specific topics in centrally located spaces promotes convenience, and involving primary-age children in inventorying and organizing tasks can be both enjoyable and beneficial. v. The ―outdoor classroom‖ concept, which has gained renewed interest in recent years, provides children with opportunities to play, explore, and engage in childinitiated activities in the natural environment, fostering learning through gardening, insect exploration, rock collection, and sensory experiences with sand and dirt. ddd.

Powerful Math Learning Spaces i. Neatly organized and labeled math materials, readily accessible to students, should be displayed in specialized spaces to enhance learning experiences, allowing for exploration and engagement with manipulatives before incorporating them into adult-guided activities, fostering enthusiasm and peer tutoring opportunities within a comfortable and inviting math environment. eee. Powerful Science Learning Spaces i. Children’s interests are influenced by the availability of learning materials and experiences, and one effective way to foster exploration is by creating topicfocused spaces where individual or small groups of children can engage in selfa © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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directed learning, allowing for personalized instruction and ample time for hands-on exploration; different types of science learning spaces, such as discovery spaces characterized by active engagement with materials and discussions, serve varying purposes and modes of operation, emphasizing the importance of providing environments conducive to exploration and discovery. a) Discovery spaces, where active engagement with materials and discussions occur, should be located away from quiet activities like listening or literacy, and can be set up on large tables, desks, or as mobile setups using trays, boxes, or baskets, ensuring flexibility in accommodating different ages and space requirements for effective exploration. b) In an open learning space within a STEM classroom, children are encouraged to explore their creativity using abundant manipulatives and recycled materials, with minimal guidance, fostering invention and exploration through open-ended activities like sink-and-float experiments, while teacher evaluation focuses on informal observation of children’s interactions with the materials. c) Inquiry learning spaces within a STEM classroom are designed to engage children in problem-solving beyond existing knowledge by providing materials, directions, and open-ended questions to explore scientific concepts, requiring adequate preparation and clear guidance to ensure successful completion of tasks and achievement of desired learning outcomes. d) Science interest spaces in schools aim to reinforce and supplement ongoing programs by providing stimulating materials to cultivate children’s curiosity and motivation to learn more about scientific subjects, often repeating lesson explorations and offering resources such as videos, storybooks, and hands-on activities to further engage students in scientific inquiry and exploration. e) When planning learning spaces, clearly state learning objectives aligned with children’s developmental levels, ensuring activities are engaging and independent while regularly evaluating space effectiveness and potential improvements to enhance learning outcomes. fff. Selecting Math Materials i. In a classroom setting, it’s essential to cater to each child’s individual and ageappropriate mathematical needs by providing a diverse range of math materials and ample time for free exploration, while selecting materials based on criteria such as sturdiness, versatility, safety, and inclusivity, considering factors like cultural representation and family donations to supplement resources and ensure a well-rounded learning environment. ggg.

Selecting Science, Technology, and Engineering Materials i. The responsibility of the teacher is to provide materials that encourage children to investigate and explore, ensuring that materials are selected and arranged based on criteria such as open-endedness, action-oriented design, and promotion of communication among children while incorporating a variety of materials and considering individual differences, cultural inclusivity, and process skill a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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development, exemplified through sensory learning spaces featuring tasks to engage children’s senses and promote scientific exploration and understanding.

Digital Technology i. The integration of digital technology resources, including computers, tablets, and Smartboards, alongside software, apps, and online platforms, provides students with opportunities for exploration, collaboration, and communication, enhancing learning experiences beyond the classroom and schoolyard, with numerous software programs and internet resources available to support critical thinking, problem-solving, and global interaction.

XLVII. Standards and Action Overview (12.02; PPT Slide 16) i. In early childhood classrooms, action in STEM involves hands-on problemsolving and inquiry, encompassing activities such as observation, data collection, and analysis, while emphasizing essential mathematics process standards like problem-solving, reasoning, communication, connections, and representations. ii. Children engage in active learning both indoors and outdoors through block building, woodworking, songs, action games, problem-solving tasks, outdoor activities, technology use, and culturally relevant activities, fostering affective, cognitive, and psychomotor learning needs. iii. As children progress into primary grades, active learning opportunities should continue to be emphasized, allowing them to construct their understanding of the world through exploration and investigation, with STEM projects emerging from children’s interests and questions and utilizing problem-solving approaches like the K-W-L-D model to guide their inquiry and reflection processes. a. Blocks: Science and Engineering in Action i. Blocks, particularly unit blocks, are crucial play materials for young children’s development, yet they are often underutilized in classrooms beyond kindergarten despite their potential to enhance mathematics achievement. ii. Children explore mathematical and scientific concepts as they manipulate unit blocks, progressing through stages of cognitive and motor development, from basic handling to creating complex structures. Block play fosters skills in art, literacy, physical development, social studies, and socioemotional development while promoting problem-solving and inquiry. iii. Organizing block areas with labeled shelves or bins facilitates children’s access and organization, supporting their exploration and learning. iv. Through block building, children engage in scientific and engineering processes, stimulating scientific thinking and encouraging them to distinguish, classify, and sort objects, promoting creativity, problem-solving, and collaboration. v. Guiding questions can prompt children to focus on specific aspects of construction, fostering verbal expression of problem-solving strategies and providing insights into their thought processes.  In the Block Village project, first-grade students integrated their study of their neighborhood with block building, choosing buildings to recreate and incorporating roads and streetlights using blocks and black electrical tape, providing opportunities for measuring, writing, and decisionmaking, fostering detailed construction and collaborative problem-

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solving, and sparking curiosity and research as they explored geographical features and considered the needs of their community.

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In block building, children explore interactions within systems by maintaining equilibrium through balance, predicting stress, and observing cause-and-effect relationships, which is reinforced through activities like arranging dominoes, bowling with blocks, playing with pendulums, experimenting with inclines, and creating marble mazes to foster spatial reasoning and understanding of physical phenomena.

Children engage in hands-on exploration by creating ramps and pathways using cove molding, paper towel rolls, and wooden strips to manipulate speed, direction, and obstacles for marbles or toy cars, fostering an understanding of physics and engineering principles such as gravity, friction, acceleration, and momentum.

Children learn about spatial conditions and limitations through straw construction, using large straws connected by string, pipe cleaners, or paper clips to create rigid structures, fostering problem-solving and experimentation as they explore concepts of stability and strength.

b. Woodworking i. Woodworking offers practical learning opportunities in measurement, balance, and spatial relationships, with children progressing from informal to standard measurement as they engage in projects such as building birdhouses, requiring supervision, real tools, and safety gear like safety glasses and gloves. c. Math Games i. Board games are valuable for young children as they promote counting, social skills, and creativity, with older children often enjoying the flexibility of creating their own games; various math concepts, from basic counting to multiplication and money, can be reinforced through board games like UNO® and Yahtzee®; outdoor activities such as running and throwing beanbags allow for physical engagement while practicing measurement and estimation skills; during the primary years, children’s interest in competitive activities should be balanced with individual achievement to prevent feelings of inferiority, with games providing opportunities to develop math skills through observation and problemsolving puzzles. d. Math in Action: Outdoors i. The outdoors offers numerous opportunities for children to apply mathematics, including counting windows, informal measurements of playground equipment and distances, measuring shadows, and creating math trails, as demonstrated in a rainforest-themed first-grade unit which involved activities like journaling, graphing, and estimating space. e. Science in Action: Outdoors i. Engaging children in outdoor exploration provides numerous opportunities for hands-on science experiences and learning about the natural world, regardless of the setting, with activities ranging from building structures to studying animal habitats, conducting scavenger hunts, and integrating outdoor observations with writing and art exercises, all requiring careful planning, preparation, and management to ensure a successful and enriching experience. f. Culturally Relevant STEM i. The NCTM (2000) principle of equity emphasizes the importance of high expectations and strong support for all students in mathematics education, a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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highlighting the need for respect for and accommodation of differences, including cultural diversity. Ethnomathematics, the natural mathematics learned in different cultures, underscores the significance of discovering and leveraging the mathematics children bring to school, utilizing culturally relevant materials and activities. Culturally relevant STEM education can seamlessly integrate with social studies, offering opportunities to learn about diverse cultures while acquiring science and mathematics knowledge, with examples including comparing mathematical systems and calendars from various cultures.

XLVIII. Family Involvement in STEM (12.03; PPT Slide 30) i. Children’s interest in math and science begins at home, where learning occurs through daily activities such as cooking, sorting laundry, and observing nature, providing ample opportunities for exploration and discovery. ii. Teachers can support families in recognizing these opportunities by encouraging them to incorporate STEM into everyday routines and activities, emphasizing that expensive materials are not necessary. iii. Crawford, Heaton, Heslop, and Kixmiller (2013) offer guidelines and resources for engaging in science-related activities at home across various science domains. a. Getting Families Involved i. Family structures have evolved significantly, emphasizing the need for educators to acknowledge diverse family compositions and recognize that not all children come from traditional nuclear families. ii. Teachers should be sensitive to the varied family dynamics, including those with single parents, same-sex parents, adoptive parents, foster parents, grandparents, or other relatives, while also being aware that not all children have stable or supportive home environments. iii. To foster family involvement in education, communication channels should be expanded to include all family members and caregivers, with a focus on opening lines of communication and providing home learning tasks that integrate seamlessly into everyday life. iv. Suggestions for engaging families include sending home newsletters, organizing family meetings and events like Family Math or Science Fun Day, encouraging volunteering and classroom assistance, facilitating one-to-one conferences, offering take-home activity kits, and providing resources available on the internet and through museums and STEM organizations. b. Guidelines for Families as Teachers

i. Families seeking to provide STEM learning experiences at home should embrace naturalistic and informal learning opportunities, recognizing that play is the primary vehicle for learning during early childhood. ii. Parents can support their children’s math education by maintaining a positive attitude, linking math with daily life, making it enjoyable, exploring math-related careers, setting high expectations, and providing support for homework without doing it for them. iii. Close relationships at home can foster exploration and conversation, enriching STEM language development. a © 2025 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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iv. Adults should be patient and allow children to explore, reflect, and construct concepts through repetition and concrete experiences, using simple household items for learning. v. Naturalistic experiences involve applying concepts in everyday activities, while informal experiences involve involving children in various tasks like setting the table or measuring ingredients. vi. Adult-guided activities should be introduced carefully, ensuring that children are ready and interested, with adults providing support without pressure and allowing children time to explore materials before presenting planned questions or problems. vii. Daily learning opportunities can be integrated into activities like art, cooking, bath time, playing with blocks, chores, games, and reading, with adults offering hints and asking open-ended questions to support children’s problem-solving skills.

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c. STEM in the Home, Yard, Neighborhood, and Park

i. STEM activities can be integrated into everyday routines and experiences at home, in the backyard, neighborhood, or even during vacation trips. ii. Families can encourage STEM skills through various daily activities and routines. For instance, while sorting laundry, children can learn about classification by discussing the differences and similarities in clothing articles. They can also compare human body parts to animals and explore their functions, such as toes. iii. Additionally, activities like organizing kitchen utensils or starting collections of bottle caps or buttons can promote sorting, counting, and classification skills. iv. Engaging children in woodworking projects or letting them assist with basic repairs can introduce them to tools and engineering concepts. v. Cooking together provides opportunities to practice measurement and observation skills, while also exploring scientific concepts like changes in state.

vi. Furthermore, families can incorporate STEM activities into outings, such as finding numerals while shopping or playing observation games while traveling. These activities not only promote STEM learning but also encourage family bonding and fun. d. Family STEM Outdoors

i. Families can engage in STEM activities outdoors, utilizing their backyard, local parks, or even during vacation trips. ii. One such activity involves observing ant behavior during a backyard picnic. iii. By providing food items such as peanut butter, honey, and fruit, families can observe which foods ants prefer and how they interact with the food. iv. They can also create scent trails using extracts to understand how ants locate food. v. This activity provides insights into ant behavior, such as their role within the colony and unique habits like farming aphids for honeydew. vi. Another outdoor STEM activity involves bird watching and feeding. vii. Families can create bird feeders using peanut butter mixtures and various natural materials like pinecones or coconut shells. viii. Additionally, a family bird walk can help children and adults alike develop observational skills by identifying different bird behaviors and characteristics. ix. These outdoor STEM activities not only foster curiosity and learning but also encourage appreciation for nature and wildlife.

XLIX. Summary [return to top]

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