https://ebookmass.com/product/original-pdf-making-mathmeaningful-3rd-edition/
Instant digital products (PDF, ePub, MOBI) ready for you
Download now and discover formats that fit your needs...
Top 50 ACT Math Skills, 3rd Edition Brian Leaf
https://ebookmass.com/product/top-50-act-math-skills-3rd-editionbrian-leaf/
ebookmass.com
Digital SAT Math Prep For Dummies 3rd Edition Mark Zegarelli
https://ebookmass.com/product/digital-sat-math-prep-for-dummies-3rdedition-mark-zegarelli/
ebookmass.com
College Algebra (Collegiate Math) 2nd Edition, (Ebook PDF)
https://ebookmass.com/product/college-algebra-collegiate-math-2ndedition-ebook-pdf/
ebookmass.com
Andrew Marvell Matthew C. Augustine
https://ebookmass.com/product/andrew-marvell-matthew-c-augustine/
ebookmass.com
Lookingbill and Marks’ Principles of Dermatology E Book 6th Edition, (Ebook PDF)
https://ebookmass.com/product/lookingbill-and-marks-principles-ofdermatology-e-book-6th-edition-ebook-pdf/
ebookmass.com
Enthralled to the Alien: An Alien Sci-Fi Romance (Fated Mates of Enchor's Heart Book 4) Tammy Walsh
https://ebookmass.com/product/enthralled-to-the-alien-an-alien-sci-firomance-fated-mates-of-enchors-heart-book-4-tammy-walsh/
ebookmass.com
CURRENT Diagnosis & Treatment Pediatrics, 25E 25th Edition
William W. Hay
https://ebookmass.com/product/current-diagnosis-treatmentpediatrics-25e-25th-edition-william-w-hay/
ebookmass.com
The Forgotten Giant of Bletchley Park: Brigadier John Tiltman Harold Liberty
https://ebookmass.com/product/the-forgotten-giant-of-bletchley-parkbrigadier-john-tiltman-harold-liberty/
ebookmass.com
The Ambivalent State: Police-Criminal Collusion At The Urban Margins Javier Auyero
https://ebookmass.com/product/the-ambivalent-state-police-criminalcollusion-at-the-urban-margins-javier-auyero/
ebookmass.com
Design, Build, and Customize Your Own Drones: Design, Build, and Customize Your Own Drones Ian Cinnamon
https://ebookmass.com/product/diy-drones-for-the-evil-genius-designbuild-and-customize-your-own-drones-design-build-and-customize-yourown-drones-ian-cinnamon/
ebookmass.com
Assessing
Applying What You’ve Learned
Selected
In
Appropriate Manipulatives
Appropriate Children’s Books
Appropriate Digital Resources
Assessing Student Understanding
Applying What You’ve Learned
Selected References
Chapter 9: Developing Fact Fluency
Chapter
In a Nutshell
What
Learning
Larger Numbers in the Student’s World
Common Errors and Misconceptions
Appropriate Manipulatives
Appropriate Children’s Books
Appropriate Digital Resources
Assessing Student Understanding
Applying What You’ve Learned
Selected References
Chapter 11: Estimation and Calculation
Strategies with Larger Whole Numbers
Chapter Problem
In a Nutshell
Addition and Subtraction
Estimating Sums and Differences
Communicating about Adding and Subtracting
Common Errors and Misconceptions
Appropriate Manipulatives
Multiplication and Division
and Dividing Using Powers of 10
Communicating about Multiplying and Dividing
Common Errors and Misconceptions
Appropriate Manipulatives
Appropriate Children’s Books
Appropriate Digital Resources
Assessing Student Understanding
Applying What You’ve Learned
Selected References
Chapter 12: Fractions
Chapter Problem
In a Nutshell
Representing
219
13: Decimals
Percent
Principles for Percent
Common Errors and Misconceptions
Appropriate Manipulatives
Appropriate Children’s Books
Appropriate Digital Resources
Assessing Student Understanding
Applying What You’ve Learned
Selected References
Chapter 15: Extending the Number System to Negative and Irrational Numbers
Chapter Problem
In a Nutshell
Introducing Integers
Integer Contexts
Reading and Writing Integers
Comparing Integers
The Zero Property
Adding Integers
Subtracting Integers
Multiplying Integers
Dividing Integers
Exponents
Using Powers
Appropriate Manipulatives
Appropriate Children’s Books
Appropriate Digital Resources
Assessing Student Understanding
Applying What You’ve Learned
Selected References
Chapter 16: Patterns and Algebra
In
Dissecting and Combining Shapes
Combining Shapes
Dissecting Shapes
Congruence and Similarity
Congruence of 2-D Shapes
Congruence of 3-D Shapes
Similarity of 2-D Shapes
Determining Similarity of 2-D Shapes
Constructing Similar 2-D Shapes
Common Errors and Misconceptions
Appropriate Manipulatives
Appropriate Children’s Books
Appropriate Digital Resources
Assessing Student Understanding
Applying What You’ve Learned
Selected References
Chapter 18: Location and Movement
Chapter Problem
In a Nutshell
Location and
Volume: The Nonstandard Unit Stage 523
Volume: The Standard Unit Stage
Introducing Mass Concepts 530
Mass: The Definition/Comparison Stage
Mass: The Nonstandard Unit Stage 532
Mass: The Standard Unit Stage 534
Common Errors and Misconceptions
Appropriate Manipulatives
Measuring Time and Temperature
Introducing Time Concepts
Time: The Definition/Comparison Stage ����������������������������������
Time: The Nonstandard Unit Stage 543
Time: The Standard Unit Stage 544
Measuring and Calculating Elapsed Time
Introducing Temperature Concepts
Interpreting Negative Temperatures
Estimating Temperatures
Measuring and Calculating Temperature Change
Common Errors and Misconceptions
Appropriate Manipulatives
Measuring Angles
Introducing Angle Concepts
Angles: The Definition/Comparison Stage
Angles: The Nonstandard Unit Stage 558
Angles: The Standard Unit Stage 560
Common Errors and Misconceptions 563
Appropriate Manipulatives
Appropriate Children’s Books
Appropriate Digital Resources
Assessing Student Understanding
Applying What You’ve Learned
Selected References
Chapter 21: Data
Chapter Problem
In a Nutshell
Data Organization
567
Appropriate
Appropriate
Common Errors and Misconceptions
Appropriate Manipulatives
Appropriate Children’s Books
Appropriate Digital Resources
Assessing Student Understanding
Applying What You’ve Learned
Selected References
Index
Credits
This text is designed to provide you with insight into how to make mathematics make sense to students and capture their interest.
Preface
To the prospective or practising K–8 teacher using this book: Many teachers who teach at the K–8 level have not had the luxury of specialist training in mathematics, yet they are expected to teach an increasingly sophisticated curriculum to an increasingly diverse student population in a climate where there are heightened public expectations. They deserve help.
This text is designed to support you in teaching mathematics by providing you with insight into how to make mathematics make sense to students and how to capture their interest. Many practising teachers have told me that there were so many ideas in math that they never understood; they just did what they were told. This text provides you with those missing explanations. As a result, you are more likely to gain the confidence to teach mathematics with a student-centred, problem-solving approach. You will be better able to let students explore because you will have a deeper understanding of the mathematics, which will make it easier for you to deal with students’ varied ideas.
You will be better able to focus discussion in your classroom because you will be more aware of possible misconceptions and of what aspects of the mathematics are worthy of development. You will also be better able to critically evaluate other people’s ideas about how to approach mathematics instruction because you will be starting with a well-founded base of knowledge.
More than that, this text can serve as a resource to which you will return again and again when you are ready to focus on particular content or particular strategies.
Some of the features you will notice include
• chapters dealing with many different aspects of mathematics instruction
– background chapters dealing with the fundamentals of the kind of mathematics students should and can learn, how to focus instruction on the big ideas and the mathematical processes that span grade levels, assessment and evaluation, and planning instruction
– chapters dealing with the mathematical processes of problem solving and communication
– chapters that will make the content clearer and more meaningful to you
• chapter problems to engage you mathematically and that you can later use with students
• the “In a Nutshell” feature to help you focus on the main ideas of each chapter
• highlighted sections that clearly articulate the main principles associated with the content of many chapters
• activities—some of which are open tasks (identified by a blue activity box with an open “top”), and all of which build number sense, algebraic thinking, proportional reasoning, spatial reasoning, critical thinking, or creative thinking—that you can use with students
• teaching tips that reflect the kind of advice an experienced teacher would offer
• student sample responses to show you how students typically respond to certain mathematical tasks
• a focus on Canadian curricula and Canadian approaches to math instruction
• an indication of valuable manipulatives for each content area, with descriptions of how to use them
• charts with common errors and misconceptions described, and strategies to deal with them for each content topic
• some important assessment considerations for each content topic, to supplement the chapter that is dedicated to assessment
• children’s literature suggestions to support the various content topics
• suggestions for appropriate digital resources (an online component)
• opportunities to apply what you have learned in the chapter through self-reflection, talking with your classmates, and interacting with students and teachers in schools
• references to allow you to delve more deeply into topics of interest
To the instructor or facilitator:
There are many texts already available for courses for teacher education in mathematics, so what makes this one different?
I think you will find that this text is particularly accessible while also being thorough. Many prospective and practising teachers who have used the text have commented on how readable it is, with many ideas presented visually as well as with words.
I think you will appreciate the Canadian focus. It was written by a Canadian for a Canadian audience. Decisions made about what curriculum should be addressed are based on the various regional curricula in Canada.
I also think you will appreciate the recognition that most of our teacher education programs in Canada do not allow us the instructional hours to introduce our students to as much as we would like. This resource, along with an instructor’s manual available on the instructor’s website, provides a way to supplement the instruction you offer with the material you would like your students to encounter but do not have time to introduce during class hours. A book study guide is also available on the instructor’s website and is designed to help facilitate professional learning activities for practising teachers. The website has other useful resources such as blackline masters, web links, and a glossary. Go to www.nelson.com/instructor.
What Is New in This Third Edition?
In this third edition, you will find
• increased attention to the issue of mindset
• an enhanced chapter, Chapter 2, on what big ideas in math are and how to teach toward them, including discussion of proportional reasoning, algebraic reasoning, and spatial reasoning, which are spelled out in more detail throughout the resource
• a separate chapter on the acquisition of number facts
• expanded attention to solving proportions, including visual models
• an expanded chapter on integers to encompass order of operations, exponents, and irrational numbers as well
• significant changes in the fraction chapter related to new perspectives on fraction instruction
• very significant changes in the patterns and algebra chapter, with more attention to the link between patterns and algebra and more material on algebra
• streamlining of data chapters
• updates to the reference lists
This resource provides a way to supplement the instruction you offer with the material you would like students to encounter.
Acknowledgments
It has been a privilege to be able to take my many years of working in and thinking about mathematics education and translate it into this text. So many people have played a part—my wonderful university colleagues; the thousands of university students with whom I have worked over the years; the many teachers in whose classrooms I have been invited to work; and my many other professional colleagues across the country and internationally, in school board offices, ministries of education, and other universities.
I have certainly appreciated the many positive comments I have received personally on the usefulness of this text to practising teachers, and I have also appreciated the number of faculty members and school district personnel who have chosen this text as a resource for their students and teachers.
I wish to acknowledge the work of the many editors who have shaped my thoughts into text and graphics that make those ideas so much easier to access. Although many editors have contributed, I must single out the enormous contribution of Jackie Williams, an editor who, over the 25 years we have worked together, constantly challenges and impresses me.
For this third edition, I received excellent advice from
• Ralph Connelly, Brock University
• Limin Jao, University of Toronto
• Laura Jones, York University
• Ann Kajander, Lakehead University
• Tim Pelton, University of Victoria
• David Watson, Western University
I must also thank Nelson Education Ltd., both the Higher Education Division and the School Division, for their faith in me and for their support.
Last, but certainly not least, I would like to thank my friends and family, who always support me.
About the Author
Marian Small is the former Dean of Education at the University of New Brunswick. She has been a professor of mathematics education and worked in the field for close to 40 years. Dr. Small is a regular speaker on K–12 mathematics throughout Canada and around the world.
The focus of Dr. Small’s professional work has been the development of curriculum and text materials for students of mathematics. She has been an author on eight text series at both elementary and secondary levels in Canada, the United States, Australia, and Bhutan, and a senior author on six of those series. She has produced materials for and been distributed by several ministries of education across the country. She has served on the author team for the National Council of Teachers of Mathematics Navigation series, Pre-K–2; for four years as the NCTM representative on the Mathcounts question writing committee; and on the editorial panel of the 2011 yearbook on motivation and disposition.
Dr. Small has led the research resulting in the creation of maps describing student mathematical development in each of the five mathematical strands for the K–8 level, and has created the associated professional development
program, PRIME. She has also written many professional books focusing on differentiated instruction, big ideas in math, and teacher questioning: Big Ideas from Dr. Small, K–3; Big Ideas from Dr. Small, 4–8; and Big Ideas from Dr. Small, 9–12, published by Nelson Education; Good Questions: Great Ways to Differentiate Instruction; More Good Questions: Great Ways to Differentiate Instruction; Uncomplicating Fractions to Meet Common Core Standards in Math, K–7; and Building Proportional Reasoning Across Grades and Math Strands, K–8, co-published by Teachers College Press, the National Council of Teachers of Mathematics, and Nelson Education; Uncomplicating Algebra to Meet Common Core Standards in Math, K–8, co-published by Teachers College Press and Nelson Education; and Open Questions for the Three-Part Lesson, K–3 and 4–8, published by Rubicon Publishing. Recently she has also produced intervention materials for Grade 3–8 students, Leaps and Bounds toward Math Understanding, also published by Nelson Education.
Instructor Resources
The Nelson Education Teaching Advantage (NETA) program delivers research-based instructor resources that promote student engagement and higher-order thinking to enable the success of Canadian students and educators. Visit Nelson Education’s Inspired Instruction website at http:// www.nelson.com/inspired/ to find out more about NETA.
The following instructor resources have been created for Making Math Meaningful to Canadian Students. Access these ultimate tools for customizing lectures and presentations at www.nelson.com/instructor.
Image Library
This resource consists of digital copies of figures and art, charts, and student work used in the book. Instructors may use these jpegs to create their own PowerPoint presentations.
Instructor Guide
This resource was written by Marian Small. It is organized according to the textbook chapters and addresses key educational concerns, such as typical stumbling blocks students face and how to address them. Other features include teaching suggestions, assessment tools, and possible projects or demonstrations.
Book Study Guide for Professional Learning
In a number of school districts, this text is purchased for teacher reference. The Book Study Guide has been written by Marian Small to be used as a resource for teaching professionals who are taking part in a “book study” of Making Math Meaningful, usually set up informally by several teachers within a school, or school-wide, or teachers within a family of schools, or board-wide on a voluntary basis.
Blackline Masters
Blackline masters have been created by Marian Small. The author has provided a set of 35 generic reproducible blackline masters including 10-frames, 100-charts, place value charts, clock faces, tangrams, and many others.
MindTap
Offering personalized paths of dynamic assignments and applications, MindTap is a digital learning solution that turns cookie-cutter into cutting-edge, apathy into engagement, and memorizers into higher-level thinkers. MindTap enables students to analyze and apply chapter concepts within relevant assignments, and allows instructors to measure skills and promote better outcomes with ease. A fully online learning solution, MindTap combines all student learning tools—readings, multimedia, activities, and assessments—into a single Learning Path that guides the student through the curriculum. Instructors personalize the experience by customizing the presentation of these learning tools to their students, even seamlessly introducing their own content into the Learning Path.
Student Ancillaries
MindTap
Stay organized and efficient with MindTap—a single destination with all the course material and study aids you need to succeed. Built-in apps leverage social media and the latest learning technology. For example,
• ReadSpeaker will read the text to you.
• Flashcards are pre-populated to provide you with a jump start for review—or you can create your own.
• You can highlight text and make notes in your MindTap Reader. Your notes will flow into Evernote, the electronic notebook app that you can access anywhere when it’s time to study for the exam.
• Self-quizzing allows you to assess your understanding.
Visit http://www.nelson.com/student to start using MindTap. Enter the Online Access Code from the card included with your text. If a code card is not provided, you can purchase instant access at NELSONbrain.com.
