Issuu

Issue 1, Fall 2026

Editor: Karen Zwanch, Ph.D. Student Editors: Blane Burge & Kareem Salim

Editor-in-Chief Karen Zwanch, Oklahoma State University, Stillwater, OK

Editorial Board Blane Burge, Student Editor, Oklahoma State University, Stillwater, OK Kareem Salim, Student Editor, Oklahoma State University, Stillwater, OK Jessica Farquhar, Connors State University, Warner, OK Amanda Wilson, Perry Public Schools, Perry, OK

Reviewers Dr. Bridget Broome, Oklahoma State University, Stillwater, OK Dr. Kansas Cole, Oklahoma State University, Stillwater, OK Dr. Jennifer Cribbs, Oklahoma State University, Stillwater, OK Dr. Jennifer Hofeld, Oklahoma State University, Stillwater, OK Dr. Toni Ivey, Oklahoma State University, Stillwater, OK Mike Millard, Anadarko Public Schools, Anadarko, OK Cara O’Daniel, Union Public Schools, Tulsa, OK De’Ira Taylor, Tulsa Public Schools, Tulsa, OK Jill Taylor, Tulsa Community College, Tulsa, OK Dr. John Weaver, Oklahoma State University, Stillwater, OK All correspondence should be addressed to The Oklahoma State STEM Teacher, Attn: Karen Zwanch, 235 Willard Hall, Stillwater, OK 74078 or electronic communication can be sent to karen.zwanch@okstate.edu. Permission to photocopy or print materials from The Oklahoma State STEM Teacher is granted to persons who wish to distribute items individually (not in combination with other articles or works), for educational purposes, in limited quantities, and free of charge or at no cost; to librarians who wish to place a limited number of copies on reserve; to authors of scholarly papers; and to any party wishing to make one copy for personal use. The Oklahoma State STEM Teacher, copyright © 2026 by the Center for Research on STEM Teaching and Learning at Oklahoma State University, is a peer-reviewed journal, published annually.

The Oklahoma State STEM Teacher (2026) 1

Letter from the Editor

Helping Oklahoma’s Teachers do More with More Welcome to The Oklahoma State STEM Teacher – A journal for Oklahoma’s teachers by Oklahoma State University! This journal was conceptualized as a way of helping Oklahoma’s teachers do more with more. Teachers are constantly asked to do more with less – teach more students, work more hours, give more resources. They are asked to do more with less time, less money, and fewer resources. We designed this journal to change that narrative by providing teachers with more resources to do more with in their classrooms. The journal is also an extension of the STEM Teacher Conference held on Oklahoma State University’s Stillwater campus every June. In 2026, the conference hosted more than 200 STEM teachers representing PK-12 from across the state. We asked some of the presenters at the conference to submit articles that reflected the ideas they presented at the conference, so that more of Oklahoma’s teachers could learn from them and so that teachers who attended the conference could have a written record of the presentation’s main ideas. The journal is divided into three sections. Classroom-to-Classroom articles include “big ideas” that span grade-levels or courses. The second section of the is called “My Favorite Lesson” and features STEM lesson plans. Finally, Problems (mathematics) or Phenomenon (science) for Productive Struggle offer a single problem or phenomenon that teachers can use to introduce dissonance as a learning opportunity in their lessons. We hope you find these resources help you do more with more this school year.

Sincerely,

Karen Zwanch, Editor

The Oklahoma State STEM Teacher (2026) 1: i

Contents Classroom-to-Classroom: Stellar ideas that transcend courses or grade-levels

1 The AI Inquiry Implementation Template (AIIT): A Framework for Integrating AI as a Tool for STEM Learning, Jolie Hicks, Kansas Cole, and Maria Stewart 7 Using 3D Printed Manipulatives in the Secondary Mathematics Classroom to Expand Students’ Conceptual Understanding, Angela Just and Hailey Brydie 14 Bridging Disciplines: Best Practices for Integrating Science and Mathematics in the Classroom through STEM Concepts, Adam Welsh

My Favorite Lesson: A lesson plan ready for more classrooms

19 Seeing Science in Your Hands: Using Merge Cubes and the 5E Model to Support InquiryBased Learning, Sarah McDowell and Kirtika Panwar 37 Using Area Models to Develop a Doubling and Halving Strategy for Multiplication, Bridget Broome

Problem for Productive Struggle: A mathematics problem to open a lesson

Exploring Radians and Pi in Grades 6-12, Myka Collett

Phenomenon for Productive Struggle: A science phenomenon to open a lesson

Exploring Energy Sources in Physical Science, Staci Thomas

The Oklahoma State STEM Teacher (2026) 1: ii

The Oklahoma STEM Teacher (2026) 1: pp. 1-6

The AI Inquiry Implementation Template (AIIT): A Framework for Integrating Artificial Intelligence as a Tool for STEM Learning Jolie Hicks1, Kansas Cole2, Maria Stewart2 The 2026 K–12 Science, Technology, Engineering, and Mathematics (STEM) Teacher Conference brought together Oklahoma educators committed to fostering curiosity and preparing students to navigate an increasingly complex and rapidly changing world. As part of this collaborative community, we facilitated a session that explored practical approaches for integrating Artificial Intelligence (AI) into STEM learning. To better understand educators' perspectives on integrating artificial intelligence into STEM instruction, we invited session participants to respond to the following questions: How are students already interacting with AI? What excites or concerns you most about AI in STEM education? Our Oklahoma educators’ responses mirror the dichotomy of opinions similar to a good versus evil debate, citing “academic misuse,” “efficiency/shortcut use,” and “appropriate academic support” as noted in Figure 1. STEM educators agree that they want to prepare students for success in the modern world yet remain divided on how to address the rapid advances in AI. STEM education focuses on critical thinking, problem solving, innovation, and creativity, all important aspects in our technologydriven society to engage in scientific knowledge in solving real-world issues, such as Oklahoma fish deaths, climate change, and sustainable energy problems. However, many STEM programs lack the resources to provide the transition from theory to practice when applying STEM education frameworks (Zhai & Krajcik, 2024). AI offers educators “a unique set of tools” to address a lack of resources and provides instructional content in a specialized learning environment (Zhai & Krajcik, 2024, p. 4). Latif et al. (2024) note how “[AI] technology could help education systems…improve educational equity and quality” (p. 10). Rather than serving as a substitute for student thinking, AI can function as a cognitive tool that extends inquiry and problem-solving. AI can assist STEM educators in designing inquiry-based learning (IBL) experiences, which include student-centered approaches that engage learners in authentic tasks, such as projects, research, and case studies, to promote problem-solving, collaboration, and research skills (Gholam, 2019). When strategically integrated into inquiry-based instruction, AI can support students in asking questions, investigating phenomena, analyzing data, and explaining their findings, fostering curiosity and deeper conceptual understanding of STEM content. This article presents the AI Inquiry Implementation Template (AIIT), a design template for AI-supported STEM instruction that helps educators align AI use with disciplinary practices, evidence-based reasoning, and ethical classroom implementation.

Jolie.hicks@okstate.edu, Oklahoma State University, School of Teaching, Learning and Educational Studies, Stillwater, OK 2 Oklahoma State University, School of Teaching, Learning and Educational Studies, Stillwater, OK

Hicks et al. The AI Inquiry Implementation Template (AIIT) Figure 1 Oklahoma K-12 STEM Educators’ Perceptions of AI in STEM

Planning STEM Inquiry Through Lesson Design Templates The planning process for STEM educators includes time-consuming efforts to prepare for what actually takes place in the classroom. While lesson plans serve as a roadmap to assist teachers in designing learning opportunities for student skill development (McLeskey et al., 2023), a variety of lesson formats and/or planning practices can cause decision fatigue and stifle the process. McLeskey et al. (2023) assert that effective instruction begins with a well-designed lesson plan, identifiable student objectives, and engaging learning activities with scaffolded practices for all students to participate at their individual level. Çelik (2022) highlights how using a lesson template serves as a guiding framework for effective inquiry-based planning processes and helps teachers organize how they integrate skills-based instruction. As educators gain experience, many instructional routines become second nature. However, AI challenges us to revisit and rethink some of those routines. Implementing AI in the classroom often feels like exploring new territory. Therefore, our AIIT provides a structure for capturing the new considerations, challenges, and opportunities educators encounter as they navigate the "wild west" of AI implementation in instructional practice.

Hicks et al. The AI Inquiry Implementation Template (AIIT)

Introducing the Sample Inquiry Lesson When considering how to craft the AIIT, we needed to drill down on the STEM connection components. These included things like standards, real-world problem/solutions, AI’s role, students’ learning objectives, ethical guardrails, and reflection. Utilizing AI as a thinking tool offers teachers the autonomy to scaffold inquiry-based instruction without spending a ton of money on resources. For our session example, we implemented a backward design in lesson planning: beginning with the end in mind (Wiggins & McTighe, 2005). Step 1: Determine the Standards-Based Learning Goal. First, we had to determine what skills we wanted our participants to learn during this session before completing the AIIT. This STEM session objective includes, “At the end of this session, STEM teachers will be able to design an AI-supported inquiry activity that strategically uses AI to generate questions, analyze data trends, brainstorm solution ideas, revise explanations, and reflect on reasoning while preserving student ownership of evidence-based decision-making and incorporating at least two ethical guardrails for responsible AI use.” According to Hammack and Ivey (2019), the Oklahoma Academic Standards (OAS) mirror the National Next Generation Science Standards (NGSS) in Science and Engineering; therefore, we previewed NGSS and created the Crosswalk handout (OpenAi, 2026), noting how the standards complement one another well. The crosswalk provides Oklahoma teachers with an overview of shared objectives for multiple content areas in STEM learning lesson design. While the NGSS framework emphasizes inquiry-based learning (Morris, 2025), the OAS similarly incorporate inquiry-based approaches (OSDE, 2025). Together, these standards support the development of learning experiences that integrate content knowledge, scientific practices, critical thinking, and evidence-based reasoning, enabling educators to address multiple learning goals while fostering student exploration and problem solving. Step 2: Real-World Problem. Thinking about Oklahoma’s summer context, we crafted an authentic issue for participants to investigate. The scenario includes, “Over the last two summers, a pond near a local Oklahoma community has experienced increasing fish deaths. Community members are concerned about water quality and environmental conditions. Your task: Use data, inquiry-based strategies, and AI as a thinking tool to investigate possible causes.” We asked Open AI to generate realistic datasets for students to analyze based on the given scenario. We took the dataset and designed an easy-toread handout, using Canva. Step 3: Role of AI. We developed prompts that help students use AI as a starting point for inquiry while maintaining ownership of the questions they asked and the reasoning they used. This step invites students to engage with AI as a tool for sparking curiosity and generating ideas, not as a substitute for their own thinking. See teacher resources for “Prompts for AI Inquiry Handout.” We also provided a “good prompt versus weak prompt” handout as a guide for teachers and students. Step 4: Student Thinking. Through a series of steps, participants evaluated AI-generated responses to determine which claims required evidence, verification, or additional explanation. We concluded this phase with the following discussion questions: Where did human thinking matter most? How did AI support inquiry? How could AI be misused? What guidance might students need to use AI responsibly? The accompanying “Evaluation Tool” handout provides a framework for helping students critically examine their thinking throughout the inquiry process.

Hicks et al. The AI Inquiry Implementation Template (AIIT) Step 5: Ethical AI Use. This step points out a teacher’s expectations of how they want students to engage with AI in ethical ways and what this practice entails. In our “Ethical AI Use” handout, we cover AI hallucinations, AI biases, overreliance issues, verification strategies, transparency, and more. Our session participants acknowledged the benefits of covering these guidelines in class before, during, and after the assignment. Step 6: Reflection. As an important element of inquiry-based learning, reflection helps students make sense of what they learned and evaluate the extent to which they met the learning objective(s). Using their notes from the “Evaluation Tool,” students examine their decision-making, reasoning, and use of evidence throughout the inquiry process. The reflection questions provide insight into students’ understanding of the STEM content they learned, their evaluation of the effectiveness of AI in supporting that learning, and how they used AI ethically and in ways that aligned with the expectations established for the activity.

Providing Classroom Task Examples During our session, we provided classroom task examples for varying classroom grade levels from 3rd to 12th grade (slides 24-27). In each example, teachers integrate AI use in the STEM classroom with scaffolded steps. Educators model how to use AI as a tool and how to move beyond a copy/paste practice with real-world scenarios. Students in each grade level evaluate data, draw conclusions, and explain their thinking. The AIIT helps teachers plan guided lessons and provides students the opportunity to demonstrate their learning growth.

Highlighting 3rd and 4th Grade We crafted a lesson geared toward 3rd and 4th grade and included McCann’s (2021) children’s book If the World were 100 People. In the lesson titled “The People of Oklahoma,” teachers read a portion of the children’s book. Then, teachers ask AI for Oklahoma demographic data and to create a visual representation of the data. Student thinking requires them to interpret the data, use fractions to represent selected demographic data, and identify the best representation.

Investigating in 5th and 6th Grade In a lesson titled “Weather Pattern Investigation,” we guide teachers and students to examine Oklahoma weather data, to ask AI to summarize patterns, and to compare AI summaries to their own observations. Students are required to verify data accuracy, interpret causes of the patterns, and explain weather pattern impacts.

Analyzing in 7th–9th Grade In this lesson titled “School Energy Consumption,” students will analyze school electricity usage, use AI to suggest conservation ideas, and evaluate which are realistic. Throughout this guided lesson, students move beyond identifying possible solutions to conservation to engaging in data analysis with evidence-based reasoning.

Constructing Explanations in 10th–12th Grade Looking at water quality and community health, high school students will interpret real water quality data, use AI to identify variables, and construct scientific explanations supported by

Hicks et al. The AI Inquiry Implementation Template (AIIT) evidence. To accomplish these tasks, students will verify the quality of the data analysis with evidence-based reasoning and explain their thinking with potential solutions.

Acknowledging Why AI Literacy Matters The internet has transformed our relationship with gaining knowledge, giving us unfettered access to information, some of it reliable, most of it unreliable (Bowen & Watson, 2023). Educators recognize the growing reality of how 21st-century literacies and our educational landscapes have quickly evolved with advances in technology, including the introduction to artificial intelligence (AI) and large language models (LLMs) (Zhai & Krajcik, 2024). While the internet changed how we gain access to large bodies of information, AI will “change our relationship with thinking” (Bowen & Watson, 2023, p. 2). Yim and Su (2025) assert how AI literacy will soon be as crucial as reading and writing literacy. Consequently, educators should consider how this burgeoning technology continues to influence their students’ abilities to navigate a world saturated with AI integrations (Yim & Su, 2025) and how we can prepare students for the future with an education that “mirrors [technological] advancements” (Zhai & Krajcik, 2024, p. 182).

Wrapping It Up To conclude the session, we invited educators to reflect on their learning by identifying one AI-related strategy they planned to implement and one concern they still had about using AI in the classroom. Their responses revealed both enthusiasm and thoughtful caution.

Utilizing One Strategy from the Session Analysis of teacher responses revealed three primary themes: (1) developing AI literacy and responsible use, (2) using AI as a tool for student thinking and inquiry, and (3) integrating AI into teaching practice. The strongest emphasis included helping students use AI effectively and ethically while also leveraging AI to support inquiry, brainstorming, and problem-solving. Teachers additionally expressed interest in applying AI to lesson planning and classroom implementation.

Expressing Continued Concern Analysis of teacher concerns also revealed three primary themes: (1) student misuse and overreliance on AI, (2) concerns about the accuracy and trustworthiness of AI-generated information, and (3) implementation barriers, including district policies, time constraints, and teacher readiness. The most prevalent concern centered on maintaining student critical thinking and preventing AI from becoming a substitute for authentic learning.

Conclusion These reflections underscore the importance of ongoing conversations and professional learning opportunities around AI integration, ensuring that educators feel prepared to leverage AI as a thinking tool while addressing the complexities it introduces into teaching and learning.

Hicks et al. The AI Inquiry Implementation Template (AIIT)

References Bowen, J.A. & Watson, C. E. (2024). Teaching with AI: A practical guide to a new era of human learning. Johns Hopkins University Press. Çelik, A. Y. (2022). Determination of the effectiveness of a template for lesson planning based on inquiry. International Journal of Education Technology and Scientific Research, 7(20), 2402-2416. http://dx.doi.org/10.35826/ijetsar.547 Gholam, A. P. (2019). Inquiry-based learning: Student teachers’ challenges and perceptions. Journal of Inquiry and Action in Education, 10(2), 6. https://digitalcommons.buffalostate.edu/cgi/viewcontent.cgi?article=1165&contex t=jiae Hammack, R., & Ivey, T. (2019). Elementary teachers’ perceptions of K-5 engineering education and perceived barriers to implementation. Journal of Engineering Education, 108(4), 503–522. https://doi.org/10.1002/jee.20289 Latif, E., Mai, G., Nyaaba, M., Wu, X., Liu, N., Lu, G., Li, S., Liu, T., & Zhai, X. (2024). AGI: Artificial General Intelligence for education. https://arxiv.org/abs/2304.12479 M365 Copilot (basic). (2026, June. 17). Oklahoma K-12 STEM educators’ perceptions of student AI use. (AI-generated figure based on user-provided data and prompts). https://copilot.microsoft.com/ McCann, J. (2021). If the world were 100 people: A visual guide to our global Village (A. Cushley, illus.). Crown Books for Young Readers. McLeskey, J., Maheady, L., Billingsley, B. S., Brownell, M. T., & Lewis, T. J. (2023). High leverage practices for intensive interventions. Routledge. Morris, D. L. (2025). Rethinking science education practices: Shifting from investigationcentric to comprehensive inquiry-based instruction. Education Sciences, 15(1), 73. https://doi.org/10.3390/educsci15010073 OpenAI. (2026). ChatGPT (GPT-5.5). [Large language model]. https://chatgpt.com/c/6a0dd4f8-cfc0-83ea-a4ca-827c309ec0f8 Wiggins, & McTighe, J. (2005). Understanding by design (Expanded 2nd ed.). Association for Supervision and Curriculum Development. Yim, I. H. Y., & Su, J. (2025). Artificial intelligence literacy education in primary schools: A review. International Journal of Technology and Design Education, 35(5), 2175-2204. https://doi.org/10.1007/s10798-025-09979-w Zhai, X. & Krajcik, J. (Eds). (2024). Uses of artificial intelligence in STEM education. Oxford University Press.

The Oklahoma State STEM Teacher (2026) 1: pp. 7-13

Using 3D Printed Manipulatives in the Secondary Mathematics Classroom to Expand Students’ Conceptual Understanding Angela Just1, Hailey Brydie2 Secondary mathematics curricula and instruction in the United States generally prioritizes students’ acquisition of procedural skills (Carlson et. al., 2022; Stigler & Hiebert, 1999). However, conceptual and procedural knowledge are critically interdependent. To fully find balance between procedural and conceptual understanding, they must be recognized as valuable and complementary while still honoring their distinct and separate contribution (Bahr & Bossé, 2008). The National Council of Teachers of Mathematics (NCTM) (2023) made four declarations which they believe, if followed, would ensure every student is supported in developing their procedural fluency. The first declaration is “Conceptual understanding must precede and coincide with instruction on procedures” (NCTM, 2023, p. 2). They explain that including conceptual foundations when providing instruction will facilitate critical reasoning strategies that are not available when students are focused only on memorizing algorithms (NCTM, 2023). This declaration has not only drawn attention to the value of both conceptual and procedural instruction, but it also highlights the interdependence of the two when planning for effective mathematics instruction. There are pitfalls for students when procedures are emphasized before or without conceptual knowledge. Many years prior to the 2023 positional statements release, the NCTM (2000) recognized “Students who memorize facts or procedures without understanding often are not sure when or how to use what they know, and such learning is often quite fragile” (p. 20). It is valuable for mathematics educators to acknowledge that when students make a mistake using a procedure, it is often because they do not understand the underlying concept that necessitates the procedure. If educators are to heed the suggestion that conceptual understanding should precede or coincide with procedures (NCTM, 2023), they must identify best practices for incorporating conceptual learning into mathematics instruction. Research suggests students obtain flexible mental models and the ability to solve more conceptually challenging problems when they first engage with, discuss, and make connections between multiple representations of mathematical concepts (NCTM, 2014). By examining and re-examining mathematical concepts in a variety of ways, the possibility of making connections conceptually increases tremendously (Dick & Edwards, 2008). Thus, to develop appropriately complex concept images, learning environments must provide students with the opportunity to work with different representations. Representations can take many forms and may possess attributes that dictate which concepts they are best suited to represent. Studies investigating the use of technology to incorporate representations in mathematics, including 3D modeling tools, have shown an increase in not just student understanding, but enjoyment and achievement (Abdullah et al., 2014; Sung et al., 2015). One purpose of 3D printed manipulatives is to provide a physical representation that

1 2

Just.angelak@gmail.com, Owasso Public Schools, Owasso, OK Sperry Public Schools, Sperry, OK

Just et al. Using 3D Printed Manipulatives in the Secondary Mathematics Classroom to Expand Students’ Conceptual Understanding can be touched, thus creating concrete experience with the mechanics of how it works, how it looks, and any variations that will assist learners as they internalize the concept. By combining conceptual and procedural instruction, educators can assist their students in developing a more robust understanding of the concepts included in their curriculum. The ideas presented in this article highlight opportunities to build conceptual understanding prior to, or coinciding with, procedural understanding while facilitating stronger reasoning skills and a deeper, more defined understanding of the concept. The medium we will suggest for encouraging conceptual understanding will be representations created on a 3D printer.

Choosing Concepts for Enrichment with 3D Printing As part of our work with secondary mathematics students, we have identified dozens of concepts within the curriculum where typical instruction lacks conceptual foundation. By this, we mean that students are generally not provided with opportunities to work with multiple representations. We chose to incorporate 3D printed representations for three main reasons: they are tangible representations that students can easily touch, observe, and manipulate for a full 3D experience, studies have shown that students’ understanding, enjoyment, and achievement increase when working with 3D models (Sung et al., 2015), and 3D models are easily printed due to the increase of 3D printer availability in schools. For this article we will report on three concepts we attempted to enrich with 3D printed representations: conic sections, distance between two points, and parent functions. After researching each concept, we found patterns for 3D manipulatives that provided a hands-on and visual experience we felt would be beneficial to students. We outlined questions, experiences, and intended outcomes (See Table 1) for each of the concepts we chose to explore. The QR codes to the files we used for prints are provided (See Figure 1). Once the topic was chosen, our questions and intended outcomes were defined, and our 3D models were created; we presented the 3D representation to our students. Our students’ overwhelming reaction to the 3D manipulatives was positive. They not only enjoyed using the 3D prints, but also asked to use them even after instruction ended. They engaged in conversations about the relationships and characteristics they identified visually. They extended their conceptual understanding when we pivoted to paper-and-pencil tasks. The following sections share our inclass experiences with the 3D prints. Figure 1 Links to Files for 3D Printing Projects

Link to Conic Sections Print

Link to Pythagorean Theorem Print

Link to Parent Function Print

Just et al. Using 3D Printed Manipulatives in the Secondary Mathematics Classroom to Expand Students’ Conceptual Understanding Table 1 Outline of Instructional Plan for Three Concepts Using 3D Manipulatives Lesson Driving Suggested Experience Contribution to Conceptual Question Understanding What is a conic • Students are asked how many shapes. • Hands-on exploration of section? they can make by slicing a cone. each conic section • Students dissect the 3D cones. • Students connect the section • Students are asked to explain sections with its placement on a created and how they might vary. based cone. on placement within the cone. • Students build a conceptual • Students are tasked with creating a table understanding of conic to describe conic sections and diagram sections that lay the how each is created from a cone. foundation for future work Students will use correct names for each with conics and conic section. formulas. How does the • Students are shown two points on a • Kinetic experience proving Pythagorean Cartesian Plane and asked to find the the Pythagorean Theorem Theorem help us distance between them. • Students build their own find the distance • Students given 3D Pythagorean proof. connection between distance between two • Students are asked if they know the and Pythagorean Theorem. points? length of the two legs, would they be • Students’ conceptual able to find the hypotenuse. understanding is extended beyond typical textbook examples. What are the • Students are shown parent functions and • Dynamic experience with characteristics of labels as normal. functions parent • Students are given a 3D Cartesian Plane • Students learn to create functions? with moving points. parent functions based on • Students are asked to create a graph that characteristics unique to matches a given parent function label. each function. • Students are asked to create a graph that • Students extend their matches a transformed parent. function understanding by applying equations or create a graph and identify characteristics under the appropriate equation transformation.

Conic Sections Typical instruction for conic sections includes a picture of two cones with slices marked to indicate how the sections are created. Students move immediately to the equations and invest their attention in learning to manipulate them to identify vertices, asymptotes, etc. Although students view the picture, we have not felt like students truly grasped or internalized a visual understanding of the sections’ relationships to the cone. To address the lack of conceptual understanding, we 3D printed two cones that could be disassembled into conic sections. The 3D print was placed out for students to view as they entered the classroom (See Figure 2). Students immediately gathered around, asking questions, and pulling the pieces apart. Questions asked included: what the object was, what the pieces were, and when we would start learning about the sections. The interest spanned across Precalculus classes as well as Algebra II 9

Just et al. Using 3D Printed Manipulatives in the Secondary Mathematics Classroom to Expand Students’ Conceptual Understanding (which provided an opportunity to encourage them to take Precalculus next year). Students continued to play with the 3D print for weeks. They even created some very interesting reconfigurations of the pieces (See Figure 3). Figure 2 3D model of Conics

Figure 3 Students’ Interesting Reconfigurations of Conic Sections

Our Takeaways Interest and engagement in conic sections increased across all classes. Conics became something they wanted to talk about instead of a boring math topic for the week. Students’ active thinking about relationships between the sections and the cone was evident by their inquiries and interactions with the model.

Distance Between Two Points - Pythagorean Theorem When finding the distance between two points, students are generally given the distance formula to accomplish the task. Typical textbook instruction involves a brief connection to the Pythagorean Theorem, but no lasting conceptual foundation is formed. As a result, students do not remember the distance formula for long. When asked to find distance in subsequent courses, we often hear them say something like, “There’s a formula for that, but I don’t remember it.” We felt students were not making any conceptual connection between the Pythagorean Theorem and tasks that involved finding the distance between two points. To address the lack of conceptual understanding, we 3D printed a demo to prove the Pythagorean Theorem with moving pieces for students to manipulate as they considered finding the length of a hypotenuse. Students in Algebra II were asked if they could find the distance between two points on a Cartesian Plane. Students were allowed several minutes to work on the problem before the 3D print was introduced. Students showed great interest when introduced to the 3D print. We told 10

Just et al. Using 3D Printed Manipulatives in the Secondary Mathematics Classroom to Expand Students’ Conceptual Understanding them it was a proof of the Pythagorean Theorem. They began playing with the tiles as we asked them questions such as: what kind of triangle is in the middle, what do the tiles represent, and could you find the length of the hypotenuse if given the distance of the two legs? Most students arranged tiles in the square connected to the hypotenuse first (the big square). We had them restart, explaining that they were given the leg measurements and asked to find the hypotenuse (See Figure 4). Most students discovered that when the tiles from the two smaller squares were added together, their total equaled the number of tiles in the square constructed on the hypotenuse. Students also recognized that the value represented the square of the hypotenuse rather than the length of the hypotenuse itself. Figure 4 Students’ Attempts at Proving the Pythagorean Theorem

Our Takeaways Discussion of and flexible thinking about the Pythagorean Theorem increased. Students actively worked with the 3D models and shared how to apply Pythagorean relationships in other contexts like on a Cartesian Plane. Several students commented that they finally understood the Pythagorean Theorem. Overall, time with the 3D model helped students to focus on the concept of distance between two points in a way that just learning a formula had never provided in our experience.

Parent Functions Parent Functions are often introduced to students using a series of pre-drawn graphs with labels. There are great activities where students match graphs with labels, but we wanted to go a step further and have students interact with the characteristics of the parent function graphs. We used a 3D print of a Cartesian Plane with movable points. This print included points that were separate from the board. Each point could be placed on a vertical groove and then moved up and down. It was perfect for emphasizing the definition of a function by highlighting that only one “point” can be on each vertical line. We tried a few tasks in Algebra II and Precalculus but felt this would be beneficial in earlier courses as well. First, each group was provided with a Cartesian Plane board. We then displayed the name of a parent function on the front board, and each group used their movable points to graph the corresponding function (See Figure 5). The students engaged in meaningful conversations and took great pains to be as precise as possible with their graphs.

Just et al. Using 3D Printed Manipulatives in the Secondary Mathematics Classroom to Expand Students’ Conceptual Understanding Figure 5 Students’ examples of Parent Functions

In later renditions, we asked students to represent various transformations of parent functions (See Figure 6). They were again invested and appeared to ingest far more conceptual details than we had seen with previous instruction on translations. In Algebra II, this led students to challenge each other within their groups. One student would create a graph of a transformed parent function, and the other group members would each write down an equation for the graphed function. Then the group discussed the answers using their understanding to reach an agreement on the correct equation. Figure 6 Students’ examples of Transformed Parent Functions

Our Takeaways Students increased their understanding of the characteristics of parent functions and were able to apply their understanding to a variety of transformations. Students were engaged and eager to demonstrate their understanding by using the 3D Cartesian Plane. We felt that working in groups helped all students to reach a higher level of conceptual understanding, including students who were struggling at the beginning.

Conclusion Our experience using 3D representations with our students was overwhelmingly positive. Students enjoyed working with the models and actively engaged more than in past instruction. We believe that conceptual knowledge grew beyond anything we have witnessed in past instruction. As a result, their procedural knowledge was not based on memorizing formulae. Instead, they grasped why procedures worked and how to use them correctly. We look forward to using 3D representations with many more mathematical concepts!

Just et al. Using 3D Printed Manipulatives in the Secondary Mathematics Classroom to Expand Students’ Conceptual Understanding

References Abdullah, N., Halim, L. & Zakaria, E. (2014). VStops: A thinking strategy and visual representation approach in mathematical word problem solving toward enhancing STEM literacy. Eurasia Journal of Mathematics, Science & Technology Education, 10(3), 165174. https://doi.org/10.12973/eurasia.2014.1073a Bahr, D. L. & Bossé, M. J. (2008). The state of balance between procedural knowledge and conceptual understanding in mathematics teacher education. International Journal of Mathematics Teaching and Learning. https://scholarsarchive.byu.edu/facpub/924 Carlson, M.P., O’Bryan, A., & Rocha, A. (2022). Instructional conventions for conceptualizing, graphing and symbolizing quantitative relationships. In K. Akar, G., Zembat, İ.Ö., Arslan, S., Thompson, P.W. (Eds.), Quantitative Reasoning in Mathematics and Science Education. Mathematics Education in the Digital Era, vol 21 (pp. 221-259). Springer. Dick, T.P & Edwards, B.S. (2008). Multiple representations and local linearity-research influences on the use of technology in calculus curriculum reform. In G.W. Blume and M K. Heid (Eds.), Research on Technology and the Teaching and Learning of Mathematics: Volume 2 Cases and Perspectives (pp. 131-156). Information Age. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. NCTM National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. (2023). Procedural fluency: Reasoning and decision-making, not rote application of procedures position. NCTM National Council of Teachers of Mathematics. Stigler, J. W. & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. Free Press. Sung, Y-T., Shih, P-C., & Chang, K-E. (2015). The effects of 3D-representation instruction on composite-solid surface-area learning for elementary school students. Instructional Science, 43(1), 115-145. https://www.jstor.org/stable/435757278

The Oklahoma State STEM Teacher (2026) 1: pp. 14-18

Bridging Disciplines: Best Practices for Integrating Science and Mathematics in the Classroom Through STEM Concepts Adam J. Welsh1 As technology and scientific innovation become more widespread in the shaping of our world’s ecosystem, the demand for graduates proficient in STEM continues to increase. Meaningful integration of science and mathematics into the K–12 classroom is key to the advancement and supporting of the critical thinking, problem-solving, and analytical skills students need to thrive in today’s environment. STEM education, by design, promotes interdisciplinary teaching, aligning naturally with national standards such as the Next Generation Science Standards (NGSS) and realworld applications (NGSS, 2026). Science and mathematics integration within STEM contexts enhances student engagement, fosters deeper conceptual understanding, and reflects how these subjects interact outside of the classroom (National Academy of Engineering and National Research Council of the National Academies, 2014). This paper explores best practices for effective integration, supported by peer-reviewed research, and offers actionable strategies for classroom educators.

Why Integrate Science and Mathematics? Science and mathematics are inherently interconnected. Often, scientific inquiry relies on mathematical tools for data analysis, modeling, and interpretation. Likewise, context and relevance are increased with mathematics when applied to real-world scientific challenges. Despite this natural overlap, traditional classroom instruction often treats them as separate disciplines. Integration encourages the transfer of knowledge between domains and better understanding of complex phenomena by students. When activities that require students to apply both scientific and mathematical reasoning are undertaken, they develop more robust conceptual frameworks. This interdisciplinary learning also aligns with NGSS (2026) and Common Core State Standards for Mathematics (Common Core State Standards Initiative, 2026) which emphasize application, modeling, and reasoning.

Best Practices Best Practice #1: Problem-Based and Project-Based Learning Problem-Based Learning (PBL) and Project-Based Learning are recognized as high-impact strategies for integrating science and mathematics. These approaches, which are inquiry-driven, engage students in solving complex, authentic problems that require interdisciplinary thinking (Columbia Center for Teaching and Learning, 2022; Cornell University Center for Teaching Innovation, 2026).

Adam.welsh@okstate.edu, Oklahoma State University, Oklahoma Aerospace Institute for Research and Education, Stillwater, OK

Welsh Bridging Disciplines For example, a unit on climate change may ask students to explore ways in which their school can reduce its carbon footprint while increasing campus comfort during hot seasons. Tasks could include: • collecting and analyzing temperature and CO₂ data (science and statistics) • creating linear or exponential models (mathematics) • proposing solutions through engineering design (engineering) • communicating findings through graphs and presentations (technology and literacy) Capraro et al. (2013) note that students who are engaged in integrated STEM PBL demonstrated improved understanding of mathematical concepts and had an increased interest in science. PBL promotes prioritizing a thorough and in-depth understanding of concepts versus a broad overview, allowing students to connect abstract concepts to realworld applications. Implementation Tip. Start with smaller interdisciplinary challenges that align with current curriculum goals. Gradually scale up to full units as confidence and student autonomy grow.

Best Practice #2: Use of Real-World Contexts and Phenomena The inclusion of real-world phenomena provides relevance, aiding in the students understanding of why the content that they are learning matters. According to Rivet and Krajcik (2008), anchoring instruction in meaningful, real-life contexts leads to greater student motivation and deeper learning. A powerful phenomenon that students could apply STEM principles to is the urban heat island effect; which could involve: • scientific principles (e.g., solar radiation, heat transfer, climate change and extreme heat) • mathematical concepts (e.g., graphing temperature differences, estimating carbon emissions, comparing cost to implement versus return on investment) • engineering challenges (e.g., reflective pavement, rain gardens, green roofs) • technological tools (e.g., thermal cameras or infrared thermometers, spreadsheets for analysis, GIS mapping software) Real-world integration strengthens students’ ability to transfer skills and apply knowledge creatively. It also supports equity by showing students, regardless of their backgrounds, how STEM is relevant in their lives and communities. Implementation Tip. Teachers should encourage students to identify and investigate STEM issues in their communities and, when possible, use local data to increase relevance and accessibility.

Best Practice #3: Leveraging Technology for Integration The use of digital tools and simulations can make abstract mathematics and science concepts more engaging and accessible. Research indicates that well-designed technological interventions can enhance conceptual understanding and student achievement (Li & Ma, 2010). Examples of technology-supported integration when exploring climate change include: 15

Welsh Bridging Disciplines infrared thermometers, digital weather stations, and thermal cameras to collect data digital assets such as Google Earth, ArcGIS, etc... to create a visual representation of their data • Excel or Google Sheets for data collection and statistical analysis • simulation or modeling to propose how changes could have an impact on temperature, electricity use, and carbon emissions These tools support exploration, experimentation, and immediate feedback, key elements in integrated learning environments. Implementation Tip. Focus on tools that encourage inquiry and exploration rather than passive consumption. Provide scaffolding to help students interpret outputs and connect them to conceptual models. • •

Best Practice #4: Interdisciplinary Collaboration and Co-Teaching Cross-departmental collaboration among science and mathematics is an underutilized but powerful strategy. The implementation of integrated units designed by interdisciplinary teams can align learning objectives and assessment across courses. Research by Stohlmann et al. (2012) highlights that schools implementing interdisciplinary STEM teaching saw increased teacher confidence, improved curriculum coherence, and positive student outcomes. Co-teaching or collaborative planning also promotes professional growth and a united instructional vision. An example of interdisciplinary collaboration on climate change includes: • science teacher guiding students in understanding heat transfer and climate science while collecting the field data, • math teacher leading statistical analysis, graphing, and interpretation of energy and temperature data, • engineering or technology teacher leading the use of GIS software, CAD tools, and the engineering design process so the students can develop solutions, • English-Language Arts teacher addressing the student’s communication of finding through reports, presentations, and proposals, • social studies teacher facilitating discussions about environmental justice, community planning, and how state and local governments address climate resilience. Taking this approach helps students apply knowledge from various disciplines to solve a meaningful real-world problem, experience collaboration, increase critical thinking, communication, and teamwork skills, and create a connection between the classroom and the local community. Implementation Tip. Begin with shared planning periods or professional learning communities focused on integration. Identify natural overlaps in curriculum pacing guides or standards.

Best Practice #5: Assessment Strategies that Reflect Integration Traditional assessments generally fail to capture students' interdisciplinary thinking. Integrated science and mathematics instruction requires assessments that measure not only content knowledge but also application, reasoning, and problem-solving.

Welsh Bridging Disciplines Effective assessment strategies for a lesson on climate change could include students: • explaining the scientific principles that led to their solution, • presenting and analyzing environmental data, use technology such as GIS and spreadsheets to support their conclusions, • providing justification using cost, sustainability, and feasibility, • communicating recommendations to an audience such as school administration or community partners. According to Pellegrino, Chudowsky, & Glaser (2001), assessments aligned with learning goals provide more precise and unbiased measures of student understanding and support formative feedback. Implementation Tip. Involve students in developing rubric or success criteria. This promotes metacognition and ownership of learning.

Best Practice #6: Finding Formal and Informal Opportunities for STEM STEM integration occurs well beyond the classroom. Informal learning environments such as museums, after-school programs, maker spaces, and STEM camps, play a vital role in supporting formal instruction. Formal STEM learning is structured, standards-based instruction that is led by credentialed educators within an institutional setting. It focuses on defined learning goals, scope and sequence, and assessment. Informal STEM learning is voluntary, interest-driven, and very likely exploratory. It promotes curiosity, experimentation, and self-directed learning in low-stakes environments. Bevan et al. (2010) argue that integrating informal learning experiences into the classroom can increase accessibility and engagement. For example, inviting a guest engineer from a local university to discuss green engineering principles, analyzing data from a local community project centered around emission reduction, or participating in a national STEM challenge can extend formal learning while maintaining academic rigor. Implementation Tip. Create partnerships with local organizations or leverage free national programs (e.g., National Aeronautics and Space Administration, National Oceanic and Atmospheric Administration, Department of Defense Science, Technology, Engineering, and Mathematics) to bring informal experiences into the classroom.

Conclusion The integration of science and mathematics through STEM is more than simply an instructional method, it’s a revolutionary change in how we prepare students for the world they will soon be a vital part of. By solidifying learning in real-world problems, promoting interdisciplinary collaboration, leveraging technology, and designing authentic assessments, teachers can aid students in building the skills and mindsets needed for college, careers, and citizenship. The effective integration of science and mathematics through STEM requires creativity, collaboration, and an inclination to rethink traditional boundaries between subjects. With perseverance and strategic support, educators can fabricate classrooms where science and mathematics come alive in harmony.

Welsh Bridging Disciplines

References Bevan, B., & Dillon, J. (2010). Broadening views of learning: Developing educators for the 21st century through an international research partnership at the Exploratorium and King's College London. The New Educator, 6(3-4), 167180. https://doi.org/10.1080/1547688x.2010.10399599 Capraro, R. M., Capraro, M. M., & Morgan, J. R. (2013). Interdisciplinary STEM Project-Based Standards. In STEM project-based learning: An integrated science, technology, engineering, and mathematics (STEM) approach (2nd ed., p. 51). Springer Science & Business Media Columbia Center for Teaching and Learning. (2022). Getting started with project-based learning. https://ctl.columbia.edu/resources-and-technology/resources/projectbased-learning/ Common Core State Standards Initiative. (2026). Common Core State Standards for Mathematics. Common Core State Standards Initiative – Preparing America's Students for College & Career. https://corestandards.org/wpcontent/uploads/2023/09/Math_Standards1.pdf Cornell University Center for Teaching Innovation. (2026). Problem-based learning. Welcome | Center for Teaching Innovation. https://teaching.cornell.edu/teachingresources/active-collaborative-learning/problem-based-learning Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22(3), 215243. https://doi.org/10.1007/s10648-010-9125-8 National Academy of Engineering and National Research Council of the National Academies. (2014). Integrated STEM education experiences: Reviewing the research. In STEM integration in K-12 education (pp. 51-76). Author. https://doi.org/10.17226/18612 Next Generation Science Standards. (2026). Three Dimensional L earning. https://www.nextgenscience.org/three-dimensional-learning Pellegrino, J. W., Chudowsky, N., & Glaser, R. (2001). Knowing what students know: The science and design of educational assessment. National Academies Press. Rivet, A. E., & Krajcik, J. S. (2008). Contextualizing instruction: Leveraging students' prior knowledge and experiences to foster understanding of middle school science. Journal of Research in Science Teaching, 45(1), 79100. https://doi.org/10.1002/tea.20203 Stohlmann, M., Moore, T. J., & Roehrig, G. H. (2012). Considerations for teaching integrated STEM education. Journal of Pre-College Engineering Education Research, 2(1), 28-34. https://doi.org/10.5703/1288284314653

McDowell et al. Seeing Science in Your Hands

Seeing Science in Your Hands: Using Merge Cubes and the 5E Model to Support Inquiry-Based Learning Sarah McDowell1, Kirtika Panwar2 Teaching fourth-grade life science concepts about structure and function can easily become abstract for some students. Oklahoma Academic Standards 4.LS.1.1 (Oklahoma State Department of Education, 2020; NGSS Lead States, 2013) asks students to construct an argument that plants’ and animals’ internal and external structures function to support survival, growth, behavior, and reproduction. A core challenge is that some structures are invisible to the naked eye, making it difficult for students to construct a meaningful argument about how those structures help the organism survive. This lesson addresses this challenge by integrating augmented reality through Merge Cubes into the 5E instructional model, making complex, invisible biological structures visible and interactive. Merge Cubes are foam cubes in different sizes, printed with unique patterns that link to augmented reality experiences when you scan them with a camera through the Merge Explorer app. The 3D object superimposes directly onto the cube, blending digital content with the real world in your hand. Building on Bybee's (2015) constructivist approach, this lesson positions students as active learners who construct their knowledge by manipulating interactive 3D models of internal and external biological structures, integrated into a 5E instructional model, and by constructing their arguments using a Claim-Evidence-Reasoning (CER) framework.

5E (Engage, Explore, Explain, Elaborate, Evaluate) Using Merge Cubes Engage One of the things I like about this lesson is that the focus (the structures and functions highlighted) can easily change based on students' and teachers' interests. I begin this lesson by using a Merge Cube and a laptop to project a beating heart on a projection screen. Merge Cubes enable students to observe a three-dimensional beating heart, pulsing in real time. Students are immediately drawn in, reacting with curiosity. After a pause, I ask the students to share what they notice and wonder. Typically, some students focus on the movement itself, while others focus on why the movement is happening. This initial introduction creates space for students to share prior knowledge and misconceptions to surface, while anchoring the lesson in a shared phenomenon. Projecting the beating heart and associated notice/wondering serve as the starting point, where students consider the guiding question: How do structures inside and outside of living things help them survive?

Explore During the explore phase of this lesson, students transition to small groups, each using their own Merge Cube, with each student assigned a task (investigator, explainer, or recorder). By interacting with Merge models of structures such as the lungs, skeleton, muscles, and the circulatory system, students can rotate, zoom, and closely observe various features. Instead of providing direct explanations, I usually circulate and ask each group open-ended questions to encourage deeper student thinking, for example, “What do you think this part does?” or “How is 1 2

Sarah.mcdowell@maryvillecollege.edu, Maryville College, Education Division, Maryville, TN Oklahoma State University, College of Education and Human Sciences, Stillwater, OK

McDowell et al. Seeing Science in Your Hands this structure similar to or different from another one you observed?” Students talk through ideas within their groups and record observations and possible functions, building initial understandings through discussion and shared inquiry. This phase allows students to take the lead in making sense of what they are seeing.

Explain After exploring, the students create initial models (sketch models) to represent the structure and its function. Then have the students come back together as a class to share their models and make sense of their observations. During this time, each group should have the opportunity to share what they discovered, using their own words to describe what different structures appear to do. I typically use this discussion time to introduce academic vocabulary (structure, function, organ, system), which helps students connect their informal ideas to scientific concepts. As students explain their thinking to their peers, it might be helpful to project the structure using a Merge Cube; this allows students to point out features that support their reasoning. After the whole group discussion is complete, allow students to revise their models by adding details or using accurate vocabulary.

Elaborate To extend learning, students apply their understanding of structures in new contexts. For example, I have them explore how plant structures like roots, stems, and leaves also support survival. A design task can also provide an opportunity for deeper thinking, where students create their own organism and determine what structures it would need to survive, grow, behave, or reproduce. As students develop their ideas, they might be prompted to justify their choices with questions like, “How does that structure help your organism survive?” or “What problem does it solve?”

Evaluate To bring the lesson together, students can demonstrate their understanding by constructing an argument that connects structure, function, and survival. Using the organism they created, the students explain how a specific structure supports the organism's ability to grow and survive, using evidence from their observations. Sometimes I will revisit the beating heart to provide a throughline and reflection point.

In Practice The approach to 4.LS.1.1 in this lesson is effective because it provides multiple entry points for diverse learners and makes abstract scientific ideas more accessible. The use of Merge Cubes allows students to interact with three-dimensional models, offering a hands-on experience that supports all types of learners (Panwar & McDowell, 2026). Students are not limited to static images; they can rotate, zoom, and manipulate structures, helping them better understand concepts that can otherwise be difficult to visualize. Opportunities for students to talk, draw, model, and explain their thinking give teachers multiple ways to “see” and assess student understanding in real time. The multi-modal approach helps surface misconceptions and support deeper conceptual development. The organization of this lesson strengthens learning by promoting student collaboration and purposeful engagement. Opportunities to work in small groups with defined participant roles, such as investigator, explainer, and recorder, ensure that all students participate meaningfully. 20

McDowell et al. Seeing Science in Your Hands Structured exploration tasks guide inquiry without limiting student thinking and allow learners to take ownership of their discoveries. Over the course of the lesson, students move from simply naming structures to explaining how those structures function and support survival. When students can see, manipulate, and explain structures, they are more likely to develop a deeper and more lasting understanding of how living systems work.

McDowell et al. Seeing Science in Your Hands

References Bybee, R. W. (2015). The BSCS 5E instructional model: Creating teachable moments. Arlington, TX: NSTA Press, National Science Teachers Association. Oklahoma State Department of Education. (2020). Oklahoma Academic Standards for Science. https://sde.ok.gov/science NGSS Lead States. (2013). Next Generation Science Standards: For States, By States. Washington, DC: The National Academies Press. Panwar & McDowell (2026). Seeing Science Come Alive: Integrating Augmented Reality for Inquiry-Based Learning in Elementary Classrooms. Innovate to Illuminate: Rethinking Elementary Science Instruction. Association for the Advancement of Computing in Education (AACE). https://www.learntechlib.org/primary/p/2128798/

McDowell et al. Seeing Science in Your Hands

Lesson Plan: Structure and Function Using Augmented Reality Download all lesson resources using this link. Oklahoma Academic Standard 4.LS1.1 Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behavior, and reproduction. CCC: Structure and Function Phenomenon: Beating Heart (teacher projected Merge Cube) Guiding Question: How do structures inside and outside of living things help them survive?

From Molecules to Organisms: Structure and Processes 4.LS1.1 Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behavior, and reproduction. Clarification Statement: Examples of structures could include thorns, stems, roots, colored petals, heart, stomach, lung, brain, and skin. Assessment Boundary: Assessment is limited to macroscopic structures within plant and animal systems.

Science and Engineering Practices Engaging in Argument from Evidence: Construct an argument with evidence, data, and/or a model.

Disciplinary Core Ideas Structure and Function: Plants and animals have both internal and external structures that serve various functions in growth, survival, behavior, and reproduction.

Crosscutting Concepts Structure and Function: Substructures have shapes and parts that serve functions. Timeline: 3 Class periods of 40-60 minutes Learning Objectives: • Students will identify internal and external structures of plants and animals. • Students will explain structures that support survival, growth, behavior, and reproduction. • Students will cite evidence from observations to construct an argument about the function of structures. Materials: • Merge Cubes and device with app (one per group/pair) o Directions for paper Merge Cubes can be found at https://support.mergeedu.com/hc/en-us/articles/360052933492-Making-a-MergePaper-Cube • Observation recording sheet (Explore) • Chart Paper (Engage and Explain) 23

McDowell et al. Seeing Science in Your Hands •

Organism sheet (Elaborate and Evaluate)

Prior to the lesson, the Merge Explorer App needs to be downloaded and installed on all devices that will connect to the cubes. The cubes can connect to tablets, computers, and phones. Most cubes come with three free months, and free trials are available along with educator and classroom discounts for extended use.

Academic Vocabulary • • • • • • • • •

Structure: Something (as an anatomical part) arranged in a definite pattern of organization Function: The action for which a thing is specially fitted or used or for which a thing exists: purpose Internal Structures: The inner parts of a plant or animal that are not visible from the outside External Structures: The outer parts of a plant or animal that are visible Organ: A structure that is performing some specific function in an organism System: A group of organs that work together to perform a specific task (i.e., moving, breathing) Adaptation: Adjustments to environmental conditions Organism: Any living thing, including plants, animals, bacteria, and fungi Reproduction: The biological process by which living things produce new individuals (offspring)

Overview of the Lesson Plan This lesson engages fourth-grade students in constructing an understanding of structure and function through an inquiry-based, technology-enhanced approach aligned to Oklahoma Standard 4.LS1.1. Using Merge Cubes, students interact with three-dimensional models of animal and plant structures, allowing the students to observe, manipulate, and make sense of structures that are often difficult to visualize. The integration of augmented reality provides a powerful entry point for diverse learners by making abstract concepts visible and accessible. Refer to Table 1 about what students and teachers are expected to do in each 5E phase, along with the opportunities for discourse and evidence of student learning. Figure 1 presents a visual storyline of the 5E instructional model aligned with the lesson plan's context. Table 1 5E Lesson Table for teaching “Structure and Function Using Augmented Reality.” 5E Phase

What Students are doing

What Teachers are doing

Opportunities for discourse

Evidence of Student Learning

Engage

- Students observe a beating heart projected using the Merge Cube.

- The teacher introduces the lesson phenomenon (Beating Heart).

- Think-PairShare, then whole-group

- Student questions and observations Initial explanations (preconceptions)

McDowell et al. Seeing Science in Your Hands - Record notice/wonder statements. - Share initial ideas about what the structure does.

- Prompt observation with questions: What do you notice? What do you wonder? - Activates prior knowledge

discussion of notice/wonder.

- Participation in discussion

- Students build on each other’s ideas.

-Identifies misconceptions, leads students to the guiding question: How do structures inside and outside of living things help them survive? Explore

- In small groups, manipulate Merge Cubes to investigate structures (internal: heart, lungs, skeleton, muscles; external: wings, feathers, webbing, fur). - Rotate, zoom, compare structures. - Record observations and possible functions on the Observation Page.

Explain

- Each group will explain to the class: what structures are doing using evidence. - Each student will create a model (drawing/diagram) of a structure and its function. - Share explanations with peers, then revise

- The teacher facilitates exploration without direct instruction. - Circulates and asks probing questions (i.e., What do you think is happening? How does XXX help the animal? Is this the same in all animals? How do you know?)

- Small-group discussion.

- Completed Observation Pages.

- Students justify ideas (“I think this because…”).

- Student-generated ideas about structure/function.

- Collaborative observation sharing within the small group.

- Evidence of curiosity and questioning.

- Encourages careful observation and comparison.

- The teacher introduces academic vocabulary (structure, function, organ, system.) - The teacher highlights connections between students' ideas and scientific concepts. - Guides students in refining explanations.

- Partner or small-group explanation, then students present and defend their explanatory model to the class. - Sentence stems should be available for support (“This

- Student models with labeled structures and functions. - Use of scientific vocabulary. - Then, revised models with clearer, more accurate explanations.

McDowell et al. Seeing Science in Your Hands thinking using new vocabulary. Elaborate

- Students compare plant and animal structures. - Individually, students will design an organism with structures that support survival. - Explain how each structure functions.

structure helps….”). - The teacher facilitates learning through new challenges (e.g., comparing plant and animal structures). - Prompts deeper thinking (How does this help survival?).

- Peer feedback on designs. - Discussion of similarities/ differences across organisms after all students share.

- Designed an organism with labeled structures/ functions. - Written or oral explanations connecting structure to survival.

- Then, collectively with students, create guidelines for the creation of “new” organisms (i.e., be able to live in the desert or the Arctic; live in groups). -Encourages connections across organisms.

Evaluate

- Construct an argument connecting structure to function, then to survival. - Students use their designed organism or a studied example.

- The teacher will use a rubric to assess understanding. - Facilitates student reflection on learning.

- Students justify claims with evidence.

- Student CER (Claim-EvidenceReasoning) responses include accurate explanations of structure/function on revised models. - Demonstration of understanding aligned to 4.LS1.1.

- Present (oral, written, or recorded) explanation.

McDowell et al. Seeing Science in Your Hands

5E Narrative Engage The lesson begins with a projected Merge Cube showing a beating heart, immediately capturing students’ attention and curiosity. After several minutes, have a student hold the Merge Cube (so it will continue to project) and ask the class to share what they notice and wonder about the heart. This discussion can be facilitated by asking: • What do you notice? • What makes you say that? • What are you wondering about how this structure works? These talk moves help position student ideas as central to the learning process while also surfacing prior knowledge and misconceptions. While students are engaging in their observations and wonderings, lead them to the guiding question: How do structures inside and outside of living things help them survive? A helpful tip at this stage is to resist explaining the phenomenon too early; instead, allow students’ curiosity and questions to create the desire for further investigation. Figure 1 A beating heart captured using Merge Cube through the Merge Explorer app

Explore During the Explore phase, students work in small groups to investigate a range of internal and external structures using Merge Cubes. Assigning student roles such as investigator, explainer, and recorder can help ensure active student participation. Students should rotate, zoom, and compare models, and record their observations on their Observation Recording Sheet and propose possible functions for each observed structure. During the group observation time, the teacher should circulate and ask probing questions such as: • What do you think is happening here?

McDowell et al. Seeing Science in Your Hands How might this structure help the organism? Is this the same across different organisms? How do you know? Can you show us what you mean? Does the whole group agree or disagree, and why? The goal in this phase is to support student-driven discovery, so the teacher acts primarily as a facilitator, encouraging careful observation and discussion rather than providing direct explanations. Before the Explore part of this lesson, please note that getting multiple groups logged in to Merge may take several minutes; in theory, it works quickly, but in a classroom of 4th graders, it will take several minutes. Students should also be given some time to simply explore the technology at the beginning of this phase. This pays off by keeping students on task once the lesson has started. • • • •

Figure 2 Complex model of beating heart captured using Merge Cube through the Merge Explorer app

Explain In the Explain phase, students begin to solidify their understanding by sharing what they discovered in their small groups and creating sketch models that represent a structure and its

McDowell et al. Seeing Science in Your Hands function. When students present their ideas, they introduce academic vocabulary such as structure, function, organ, and system to help them connect observations to scientific concepts. Students’ models should be labeled with movement notations and words to help describe the function of the structure. As students explain their initial models, some questions that might be asked are: • Can you explain your reasoning? • What evidence supports your idea? • Can someone restate what was just shared? Sentence stems (e.g., “This structure helps…”) can support students in articulating their thinking. After time for all students to share, allow students to revise their models using updated vocabulary and clarifying new points of understanding.

Elaborate The Elaborate phase extends student thinking by asking them to apply their understanding in new contexts. Students compare plant and animal structures and then design their own organism, selecting and justifying structures that support survival in a specific environment. Students are challenged to think about the environment (terrestrial vs. aquatic, ideal climate, and the organism's role) and then identify three structures the organism will need to survive, grow, or reproduce. Encourage students to be creative while they focus on three specific structures their organism will have. Before the design task, it might be easier to either assign or decide, as a class, the environment in which the organism will live. This helps students understand what structures may be unique to organisms thriving in different ecosystems and what structures similar organisms might have in common. Students sketch and describe the structures and functions belonging to their organism on the Organism Sheet. Students should identify and label at least three structures, as outlined in the directions on the sheet. This process can be supported by posing questions such as: • How does this structure help your organism survive? • What would happen if this structure were missing? • How is your organism like or different from others? Students should be encouraged to share their organisms with their groups to receive peer feedback and refine their ideas. This phase promotes the transfer of knowledge of a specific function of a structure, and the application of that understanding broadly across living systems.

McDowell et al. Seeing Science in Your Hands Figure 3. Life cycle of a frog captured using Merge Cube through the Merge Explorer app

Evaluate In the Evaluate phase, students demonstrate their understanding by constructing an argument that connects structure, function, and survival. Students use the CER (Claim, Evidence, Reasoning) framework to demonstrate their understanding of how specific structures help an 30

McDowell et al. Seeing Science in Your Hands organism survive. If this framework is new to students, or they need a refresher, take the time to model this process in a whole-class activity using structures identified during the elaborate. Using their designed organism, students present their explanations orally, in writing, or through recorded responses. Assessment is done using a rubric. If students are presenting their final product, some questions that might be asked to facilitate reflection and demonstrate understanding are: • What is your claim? • What evidence supports your idea? • How does your evidence show that this structure supports survival? • Can you add on to that idea? • What might someone else say about this? Revisiting the beating heart (lesson phenomenon) provides a powerful opportunity for reflection, as students can now explain it more accurately and confidently. Revisit the initial wonderings: have these changed? By this stage, students demonstrate a clear progression from initial observations to evidence-based explanations aligned to the standard.

McDowell et al. Seeing Science in Your Hands

Appendix A Teacher Resources

Lesson tips Before the Lesson • • • • •

Test the technology ahead of time, open the Merge Explorer app, and preload models. Choose a limited number of models, select a few to focus on that clearly connect structure to function (lungs, skeletal, wings, leaves, stem, flowers). Prepare and assign student roles in advance. Print student recording sheets. Print and create paper Merge Cubes if necessary (https://support.mergeedu.com/hc/enus/articles/360052933492-Making-a-Merge-Paper-Cube)

Engage • •

Allow students to “sit” with the phenomenon, do not provide any explanations, and allow students to be curious. Record student observations on chart paper so students can see them throughout the lesson.

Explore • • • •

Encourage students to manipulate the models slowly; this allows them to make more observations. Focus on student thinking; do not provide answers to questions. Walk around and listen for misconceptions. Encourage students to compare structures.

Explain • • •

Use sentence stems for support “The structure I observed is ______.” “Its function is ______.” “This helps the organism survive because ______.” “My evidence is ______.” Have students revise models at the end of sharing. Have students connect their explanations to the guiding question: How do structures inside and outside of living things help them survive?

Elaborate • • •

Encourage students to explain why their organism has certain structures, not just create something imaginative. Connect back to real organisms, where are similar structures found in nature? Promote sharing and peer feedback.

Evaluate • • •

Assess explanations, focus on whether students can connect structure to function and survival. Offer multiple ways for students to show understanding. Revisit the beating heart.

Additional resources • • •

What are Storylines? All about Merge Cubes Merge Explorer App

McDowell et al. Seeing Science in Your Hands

Appendix B Student Observation Recording Sheet Structure name

Describe what is happening?

What evidence supports that observation?

Structure name

Describe what is happening?

What evidence supports that observation?

McDowell et al. Seeing Science in Your Hands

Appendix C Organism Sheet Name__________________ Step 1: Sketch your organism A. B. C.

Label three structures that help the organism survive. Provide details of the function for each structure. Label any movements of the structure.

My organism:

McDowell et al. Seeing Science in Your Hands Step 2: Build Your Argument Write about three structures that you labeled in Step 1. For each one, explain: • Claim: How does this structure help your organism survive? • Evidence: What observations, facts, or data support your claim? • Reasoning: How does your evidence prove your claim? Structure #1:_______________________ Claim (How does this structure help your organism survive?) Evidence (What observations, facts, or data support your claim?) Reasoning (How does your evidence prove your claim?) Structure #2:_______________________ Claim (How does this structure help your organism survive?) Evidence (What observations, facts, or data support your claim?) Reasoning (How does your evidence prove your claim?) Structure #3:_______________________ Claim (How does this structure help your organism survive?) Evidence (What observations, facts, or data support your claim?) Reasoning (How does your evidence prove your claim?)

McDowell et al. Seeing Science in Your Hands

Appendix D Rubric Organism Design and CER Rubric Criteria

Exceeds Expectations (5 points)

Meets Expectations (4 points)

Approaching Expectations (3 points)

Beginning Expectations (2 Points)

Structures Identified and Labeled

The organism includes 3 or more clearly labeled structures with detailed and accurate labels.

The organism includes 3 labeled structures, most of which are accurate.

The organism includes fewer than 3 structures; OR labels are incomplete/confusing.

Structures are missing, unclear, or not labeled.

Explanation of Structure and Function

Thoroughly explains how each structure supports survival, growth, behavior, or reproduction using clear reasoning.

Explains how each structure helps the organism survive with generally accurate reasoning.

Provides partial or unclear explanations of how structures help survival.

Explanations are missing or scientifically inaccurate.

Claim

Makes a strong and specific claim about how each structure supports survival.

Makes an accurate claim about how each structure supports survival.

Claims are vague, incomplete, or partially connected to survival.

Claims are missing or unrelated to the structure.

Evidence

Uses multiple observations, facts, or details from investigations/models to support claims.

Uses observations or facts to support claims.

Uses limited or unclear evidence.

Evidence is missing or unrelated.

Reasoning

Clearly explains why the evidence supports the claim using accurate structurefunction connections.

Explains how evidence supports the claim.

Reasoning is incomplete or somewhat unclear.

Reasoning is missing or inaccurate.

Scientific Vocabulary

Correctly and consistently use academic vocabulary.

Uses appropriate scientific vocabulary correctly most of the time.

Uses limited or sometimes inaccurate scientific vocabulary.

Rarely uses scientific vocabulary or uses terms incorrectly.

Creativity and Application (Related to science content)

The organism's design is creative, detailed, and closely aligned with the chosen environment.

The organism's design is well suited to the environment.

The organism shows a limited connection to the environment.

The organism does not connect to the environment or task.

Communication and Presentation

Ideas are exceptionally clear, organized, and easy to understand through speaking, writing, or visuals.

Ideas are organized and understandable.

The presentation is somewhat unclear or incomplete.

The presentation is difficult to follow or incomplete.

Total Points _____________

The Oklahoma State STEM Teacher (2026) 1: pp. 37-43

Using Area Models to Develop a Doubling and Halving Strategy for Multiplication Bridget Broome1 Fluency with multiplication facts is prevalent across grades three and four and is essential to students’ understanding of whole number multiplication and division. According to the National Council for Teachers of Mathematics (NCTM) (2014), students are considered fluent when they solve problems efficiently, flexibly, and accurately. Part of students being considered fluent is their use of strategies. The strategies that students learn support not only their whole number multiplication and division, but also their understanding of decimal and fraction operations. According to the Oklahoma Academic Standards for Mathematics, third grade students represent multiplication facts through models (3.N.2.1) and demonstrate fluency with multiplication facts using factors up to 10 (3.N.2.2). By fourth grade, students should demonstrate fluency with multiplication and division facts using factors up to 12 (4.N.2.1) (Oklahoma State Department of Education, 2022). Teachers can increase conceptual understanding of fluency in a way that is consistent with the Oklahoma math framework as well as introduce strategies through the use of area models. Area models are an appropriate model for students in third and fourth grade because in third grade students analyze why the length and width are multiplied together when finding area (3.GM.2.2) and in fourth grade this objective is extended to include finding the area of polygons by determining if they can be decomposed into rectangles (4.GM.2.2). For this reason, using area models to develop strategies for multiplication not only addresses fluency objectives, but also supports these two objectives from the geometry and measurement strand. Multiplication is essential in understanding area, and area models can benefit students when they are learning their multiplication facts, so it makes sense to merge these two objectives when teaching. This article will present a lesson called Multiplying with Area Models that can be used with third or fourth grade students in order to increase their conceptual understanding of multiplication facts through the doubling and halving strategy, while also increasing their understanding of how to find the area of a rectangle. This activity offers students an opportunity to exhibit efficiency and flexibility with numbers by allowing them an opportunity to explore why the doubling and halving strategy works with multiplication. Before beginning this activity, it is assumed that students have a basic understanding of how to find area of a rectangle by counting the total number of square tiles in an array or multiplying the length times the width.

Lesson Preparation The materials needed for Multiplying with Area Models are one-inch square tiles, along with a recording sheet (Appendix A). Each group of students should be given enough square tiles to build multiple rectangles using numbers such as 24, 32, 36 and 48. It is important to determine the number of tiles student groups will be assigned before beginning. Numbers such as 24, 32, 36 and 48 lend themselves well to students being able to build multiple rectangles because of their

Bridget.Broome@okstate.edu, Oklahoma State University, School of Teaching, Learning & Educational Sciences, Stillwater, OK

Broome Using Area Models to Develop a Halving and Doubling Strategy for Multiplication many factor pairs. This allows students more than one opportunity to demonstrate the doubling and halving strategy.

Engaging Students To begin Multiplying with Area Models, students will participate in a Which One Doesn’t Belong (WODB) (Danielson, 2019). WODB promotes a respectful learning community that values students as thinkers by offering them an opportunity to explain their thinking and justify their reasoning. Students are shown the image in Figure 1 and asked, “Which one doesn’t belong?”. They are encouraged to tell the class why they think one of the images does not belong and justify their answer. A possible response for the WODB might be that the image of the white array in the bottom right corner does not belong because it is a 2 × 6 and the other images are rectangles with dimensions that include a three and a four which matches the number sentence in the top right image. Another possible response might be that the 3 × 4 does not belong because it is a number sentence and the other images are rectangles. Students might also say that the top left image does not belong because it is an empty rectangle with no squares. Finally, students might say that the image of the dark grey rectangle does not belong because the other images with rectangles are white. Once students have shared their ideas about what they think does not belong, the teacher will ask whether the images have anything in common. A possible response might be that each rectangle has an area of 12 square units and 3 × 4 equals 12. The teacher should ask the students how they know each rectangle has an area of 12 square units. Students might respond that they counted the squares or that they knew there were three rows and four columns, and then they multiplied 3 × 4 to get 12. A teacher-led discussion should take place so that all students have an understanding of how to determine the area of a rectangle through multiplication. Figure 1 Which One Doesn’t Belong Image

Explore The explore portion of the lesson allows students to explore the topic of multiplication through area models. Students are given a set of square tiles at their table so they can work in groups. Each group is assigned one of the following numbers as the area of their rectangle: 24, 32, 36, or 48. Give students ample time to build rectangles with their tiles. An example of the rectangles students could build with an area of 24 square units is shown in Figure 2. As they build the rectangles, they sketch each rectangle on the recording sheet (Appendix A) along with the dimensions and area. Students usually have no trouble getting started with this activity, but often times get stuck and say there are no more rectangles to build. The one rectangle they usually forget 38

Broome Using Area Models to Develop a Halving and Doubling Strategy for Multiplication is the one with the length or width of one. It is important during the explore portion of the lesson that the teacher asks questions to guide students’ thinking but does not offer them answers. Figure 2 Rectangles Students Might Build with an Area of 24 Units 1 × 24 2 × 12

3×8

4×6 Note. Students could also rotate these area models and build a 24 × 1, 12 × 2, 8 × 3, and 6 × 4. After the students have built as many rectangles as they can, the teacher should guide student groups to think more deeply about how the area models are related. Asking questions such as, “I notice you have a 2 × 12 rectangle and a 4 × 6 rectangle. Is there a way for you to take the 4 × 6 and build the 2 × 12 without completely taking the 4 × 6 apart?” Questions like this allow students to begin thinking flexibly about multiplication as they begin to notice that they can break the tiles used to create the 4 × 6 in half horizontally and move the portion they broke off to the side to create the 2 × 12. This allows them to begin to notice that two is half of four and 12 is double six. Students might begin to notice that if they break the tiles used to build the 2 × 12 in half horizontally and move the pieces to the side, they will end up with the 1 × 24. They realize that one is half of two and 24 is double 12. Once they see that this idea of cutting the area models in half works, they often want to try it with other numbers to see if it continues to work. It is important to note that doubling and halving reflects the associative property of multiplication because factors are regrouped without changing the product. For example, 3 × 8 = 3 × (2 × 4) = (3 × 2) × 4 = 6 × 4. Moving the two from the 2 × 4 to the 3 × 2, halves one factor and doubles the other. An example of how students could break their tiles apart is included in Figure 3.

Broome Using Area Models to Develop a Halving and Doubling Strategy for Multiplication Figure 3 Example of Doubling and Halving Area Models

Wrapping It Up Students from each group will share their rectangles with the class and discuss if they were able to use the doubling and halving strategy to help build more rectangles. This opens the door for more discussion about whether this works for other area models, and it is a good time to allow other groups to share what they discovered with their tiles. Through this activity, students have discovered the strategy of doubling and halving in order to solve multiplication problems, and they have a visual in their minds of why this strategy works. Doubling and halving is a strategy that is both efficient and flexible and allows students to solve multiplication facts quickly.

Evaluation To evaluate the effectiveness of this activity and ensure students have an understanding of this strategy, students will be given an exit ticket (Appendix B). The exit ticket has a rectangle with dimensions of 4 × 7. Students will be asked to demonstrate the idea of doubling and halving by drawing another area model and explaining how they created the new area model through doubling and halving.

Extension Multiplying with Area Models provides an engaging way to help students develop a conceptual understanding of multiplication and allows them to learn a new strategy through exploration. An extension of this activity would be to give students different numbers of tiles such as 15, 17, or 21 and ask them to build as many rectangles as possible. Then ask them whether they can use the doubling and halving strategy with the rectangles they built. This will help students understand that while the doubling and halving strategy is efficient and flexible, it does not work for every multiplication problem. Having students build an area model with 17 tiles also opens up the opportunity to begin a discussion of prime numbers. Building area models is a powerful way to promote students’ multiplicative reasoning and engages students in the mathematics they are participating in.

Broome Using Area Models to Develop a Halving and Doubling Strategy for Multiplication

References Danielson, C. (2019). Which one doesn’t belong?: Playing with shapes. Charlesbridge. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Author. Oklahoma State Department of Education (2022). Oklahoma academic standards. https://sde.ok.gov/oklahoma-academic-standards

Broome Using Area Models to Develop a Halving and Doubling Strategy for Multiplication

Appendix A Download all lesson resources using this link. Name _________________________ Draw a sketch of each rectangle as you build it. Include the dimensions and area. Rectangles

Dimensions

Area

Broome Using Area Models to Develop a Halving and Doubling Strategy for Multiplication

Appendix B Name _________________________ What is the area of the 7 x 4 rectangle? ________________________ Show how you could create another rectangle with the same area using a doubling and halving strategy.

The Oklahoma State STEM Teacher (2026) 1: pp. 44-45

A Problem for Productive Struggle – Grades 6-12 Mathematics Myka Collett1 This problem includes an exploration of circles that can introduce the idea of pi in middle school or the idea of radians in high school. This problem and activity structure were adapted from Sarah Carter’s blog, Math Equals Love (mathequalslove.net), from the lesson exploring the fundamental question, “What is a radian?”

What’s the problem? Students are given a variety of circular objects of completely different sizes and a pipe cleaner. They trace and cut out their circle, measure its diameter (middle school) or radius (high school) using a pipe cleaner, and wrap the exact radius length repeatedly around the circle’s outer edge (i.e., the circumference). Regardless of whether a student has a tiny coffee canister lid or a massive garbage can top, every single student discovers the exact same geometric anomaly: the diameter fits along the circumference of the circle 3 times, with a specific “little bit” left over (middle school) or the radius fits along the circumference of the circle 6 times, with a specific “little bit” left over (high school). This creates an immediate discrepant event, in which students wonder why the size of the circle does not change the outcome, and why the radius or diameter does not fit around the circumference a whole number of times.

Teacher Reflection In mathematics, students are routinely handed formulas to memorize, which strips away their natural curiosity and breeds anxiety. Pi is notoriously difficult, as it is typically a student’s first experience with an irrational number. Radians are similarly feared when first introduced in trigonometry. Both pi and radians may be treated as confusing labels. To shatter this anxiety, teachers can use the “3 and a bit” (middle school) or “6 and a bit” (high school) mystery to anchor a unit, shifting the classroom dynamic from passive learning to active geometric reasoning. When students first realize that everyone in the room, despite having vastly different circles, is stuck with the exact same result, the room buzzes with productive struggle. They want to know why this phenomenon occurs. I use this moment of high curiosity to orchestrate a whole-class science and math discussion. In a high school trigonometry class, we first tackle the math they think they know. I ask, “What is the formula for the circumference of a circle?” They (hopefully) echo back, “circumference equals two pi r.” Then, I challenge them to look at their models and translate the formula into plain English. Through guided discussion, they realize that 2𝜋 is just a number that is roughly equivalent to 6.28, and a light bulb goes off. The six that they counted with their pipe cleaners and the “little bit” extra is 0.28! From this breakthrough, defining a radian becomes effortless. I ask them to define what they just did. They didn’t just measure a curve; they used the radius as a unit of measurement along the arc of the circle. I tell them, “You just invented the radian.” This helps them visually grasp why

Myka.collett@francistuttle.edu, Francis Tuttle Technology Center, Danforth Campus, Edmond, OK

a full circle is 2𝜋. By anchoring the unit in this physical phenomenon, radians stop being an abstract concept and instead become a tangible, logical reality that students discovered themselves.

The Oklahoma State STEM Teacher (2026) 1: pp. 46-48

A Phenomenon for Productive Struggle – Physical Science Staci Thomas1 Energy Choices This phenomenon centers on the pie chart below, which displays Oklahoma’s energy sources (data adapted from the U.S Energy Information Administration [EIA], 2025). Throughout the unit, students will use this phenomenon to anchor their learning about energy conservation and transfers as they investigate the driving question: How is energy in Oklahoma conserved and transferred? Figure 1 Sources of Oklahoma Utility-scale Electricity Generation

This phenomenon is designed to serve as the anchoring phenomenon for a Physical Science unit addressing Oklahoma Academic Standards for Science performance expectations PS.PS3.1– PS.PS3.4 (Oklahoma State Department of Education, 2026). Begin by removing the labels from the pie chart and asking students to predict which energy source corresponds to each percentage.

Staci.thomas@okstate.edu, Oklahoma State University, School of Teaching, Learning and Educational Sciences, Stillwater, OK

Introduce the discussion by asking, "How have you used energy today?" Encourage students to consider examples such as heating breakfast, charging a mobile device, or turning on lights. Then explain: "This pie chart represents the primary sources of energy used in Oklahoma. Can you predict which section of the chart represents each energy source?" After students have discussed their ideas and shared their predictions, reveal the correct labels. Continue the discussion by asking: “Have you ever thought about how energy moves from its original source to the forms of energy you use every day?” or “Do you have a preferred energy source? Why?” Next, assign (or allow students to choose) an energy source to investigate. Explain that, at the end of the unit, the class will host an Energy Forum. Each energy-source team will create a poster illustrating how energy is transferred and conserved from its original source to its everyday uses. As students investigate their assigned energy source throughout the unit, they will gather evidence to answer the driving question: How is energy in Oklahoma conserved and transferred?

References Oklahoma State Department of Education. (2026). Oklahoma academic standards for science. U.S. Energy Information Administration. (2025). Electric power annual 2024. U.S. Department of Energy. www.eia.gov