Understanding the Math We Teach and How to Teach It

Marian Small has written the kind of book teachers will keep on their closest shelf as they explore and return to the big ideas of mathematics. In her new resource, Understanding the Math We Teach and How to Teach It, Marian brings the support and insight teachers need to teach math with clarity and confidence.

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Marian Small has written a landmark book for a wide range of educational settings and audiences, from pre-service math methods courses to ongoing professional learning for experienced teachers to a just-in-time resource that is always within reach. Understanding the Math We Teach and How to Teach It, K-8 focuses on the big mathematical ideas in elementary and middle school grade levels and shows how to teach those concepts using a student-centered, problem-solving approach.


  • BOTH COMPREHENSIVE AND READABLE: Dr. Small helps all teachers deepen their content knowledge by illustrating core mathematical themes with sample problems, clear visuals, and plain language.
  • FOCUS ON STUDENT THINKING: The book’s tools, models, and discussion questions are designed to understand student thinking and nudge it forward. Particularly popular features include charts listing common student misconceptions and ways to address them, a table of suggested manipulatives for each topic, and a list of related children’s books.
  • IMPLEMENTING STANDARDS IN WAYS THAT MAKE SENSE: By focusing on key mathematics principles, Understanding the Math We Teach and How to Teach It, K-8  helps to explain the “whys” of state standards and provides teachers with a deeper understanding of number sense, operations, algebraic thinking, geometry, and other critical topics.

Dr. Small, a former dean with more than 40 years in the field, conceived of the book as an essential guide for teachers throughout their career: “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.”


About the Author(s)

Marian Small is the former Dean of Education at the University of New Brunswick in Canada. 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. Her focus is on teacher questioning to get at the important math, to include and extend all students by appropriately differentiating instruction, and to focus on critical thinking and creativity. 


Table of Contents

Chapter 1: How Students Learn Math and What Math We Want Them to Learn
Chapter 2: Focusing Instruction on Big Ideas and Mathematical Processes
Chapter 3: Assessment and Evaluation
Chapter 4: Planning Instruction
Chapter 5: Early Number
Chapter 6: Early Operations
Chapter 7: Developing Fact Fluency
Chapter 8: Representing Larger Whole Numbers
Chapter 9: Estimation and Calculation Strategies with Larger Whole Numbers
Chapter 10: Fractions
Chapter 11: Decimals
Chapter 12: Ratio and Proportion
Chapter 13: Extending the Number System to Negative and Irrational Numbers
Chapter 14: Patterns and Algebra
Chapter 15: 3-D and 2-D Shapes
Chapter 16: Location and Movement
Chapter 17: The Nature of Measurement, with a Focus on Length and Area5
Chapter 18: Volume, Mass, Time, and Angles
Chapter 19: Data
Chapter 20: Probability


Product Details

Grades: K, 1, 2, 3, 4, 5, 6, 7, 8
Media: 648 pp/pages
Year: 2019
Item No: 1335
ISBN: 978-1-62531-335-5
Publisher: Stenhouse Publishers
Hashtag: #TheMathWeTeach