Elementary and Middle School Mathematics

This handy reference is particularly useful for elementary teachers who are changing grade levels and special education teachers who teach multiple grades and multiple ability levels.

Guide teachers to help all PreK-8 learners make sense of mathematics
Elementary and Middle School Mathematics: Teaching Developmentally illustrates how children learn mathematics, and then shows pre-service teachers the most effective methods of teaching PreK-8 math through hands-on, problem-based activities.

As you engage with the activities, you'll boost your own knowledge of the math and learn concrete, developmentally appropriate ways to incorporate problem-based tasks in your classroom. Examples of real student work and new common challenges and misconception tables help you visualize good mathematics instruction and assessment that supports and challenges all learners. An important reference to consult throughout your teaching career, this book reflects the Common Core State Standards and NCTM’s Principles to Actions, as well as current research and coverage of the latest teaching technology.

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The late John A. Van de Walle was a professor emeritus at Virginia Commonwealth University. He was a leader in mathematics education who regularly gave professional development workshops for K—8 teachers in the United States and Canada focused on mathematics instruction that engaged students in mathematical reasoning and problem solving. He visited and taught in many classrooms and worked with teachers to implement student-centered mathematics lessons. He co-authored the Scott Foresman-Addison Wesley Mathematics K—6 series and contributed to the original Pearson School mathematics program enVisionMATH. Additionally, John was very active in the National Council of Teachers of Mathematics (NCTM), writing book chapters and journal articles, serving on the board of directors, chairing the educational materials committee, and speaking at national and regional meetings.
Karen S. Karp is a professor at Johns Hopkins University (Maryland). Previously, she was a professor of mathematics education at the University of Louisville for more than twenty years. Prior to entering the field of teacher education she was an elementary school teacher in New York. Karen is the volume editor of Annual Perspectives in Mathematics Education: Using Research to Improve Instruction and is the co-author of Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in PreK—Grade 2, Discovering Lessons for the Common Core State Standards in Grades K—5, and Putting Essential Understanding of Addition and Subtraction into Practice PreK—Grade 2. She is a former member of the board of directors for the National Council of Teachers of Mathematics (NCTM) and a former president of the Association of Mathematics Teacher Educators. She continues to work in classrooms to support teachers in ways to instruct students with disabilities.
Dr. Jennifer Bay-Williams is a mathematics teacher educator, author, and life-long learner with a passion for making mathematics meaningful for all students. She has written many articles and books around K-12 mathematics education, including the three book series related to this book, Teaching Student Centered Mathematics (with John Van de Walle, LouAnn Lovin, and Karen Karp), and various other books including Mathematics Coaching: Resources and Tools for Coaches and Other Leaders, Developing Essential Understanding of Addition and Subtraction in Prekindergarten—Grade 2, On the Money (financial literacy book series), Math and Literature: Grades 6—8, and Math and Nonfiction: Grades 6—8. Jennifer is a professor at the University of Louisville (Kentucky) and previously taught elementary, middle, and high school in Missouri and in Peru. She continues to learn and work in K-8 classrooms in rural and urban settings. Jennifer is very active in national mathematics organizations, having served is on the NCTM board of directors, AMTE secretary, president, and lead writer for Standards for the Preparation of Teachers of Mathematics (AMTE, 2017), and currently serving on the TODOS: Mathematics for All Board of Directors as Chair of the Advocacy Committee.

Brief Contents Section I: Teaching Mathematics: Foundations and Perspectives 1. Teaching Mathematics in the 21st Century 2. Exploring What It Means to Know and Do Mathematics 3. Teaching through Problem Solving 4. Planning in the Problem-Based Classroom 5. Creating Assessments for Learning 6. Teaching Mathematics Equitably to All Students
Section II: Development of Mathematical Concepts and Procedures 7. Developing Early Number Concepts and Number Sense 8. Developing Meanings for the Operations 9. Developing Basic Fact Fluency 10. Developing Whole-Number Place-Value Concepts 11. Developing Strategies for Addition and Subtraction Computation 12. Developing Strategies for Multiplication and Division Computation 13. Algebraic Thinking, Equations, and Functions 14. Developing Fraction Concepts 15. Developing Fraction Operations 16. Developing Decimal and Percent Concepts and Decimal Computation 17. Ratios, Proportions, and Proportional Reasoning 18. Developing Measurement Concepts 19. Geometric Thinking and Geometric Concepts 20. Developing Concepts of Data Analysis 21. Exploring Concepts of Probability 22. Developing Concepts of Exponents, Integers, and Real Numbers

Appendix A. Standards for Mathematical Practice A-1 Appendix B. NCTM Mathematics Teaching Practices: from Principles to Actions A-5 Appendix C. Guide to Blackline Masters A-7 Appendix D. Activities at a Glance A-13

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Elementary and Middle School Mathematics Teaching Developmentally

Summary

Author Biography

Table of Contents

Supplemental Materials