Developing Mathematical Reasoning
The Strategies, Models, and Lessons to Teach the Big Ideas in Grades K-2
Corwin Mathematics Series
Math is not rote-memorizable. Math is not random-guessable. Math is figure-out-able.
Author Pamela Weber Harris argues that teaching real math—math that is free of distortions—will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do.
Memorization tricks and algorithms meant to make math “easier” are full of traps that sacrifice long-term student growth for short-lived gains. Students and teachers alike have been led to believe that they’ve learned more and more math, but in reality their brains never get any stronger. Using these tricks may make facts easier to memorize in isolation, but that very disconnect distorts the reality of math.
In her landmark book Developing Mathematical Reasoning: Avoiding the Trap of Algorithms, Pam emphasized the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. Now, in this first companion volume, Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in Grades K-2, she demonstrates how counting and additive strategies serve as the foundation for creating efficient, accurate, and flexible thinkers.
Everyone is capable of understanding and doing real math. This book:
- Gives step-by-step guidance on how to teach the strategies, models, and big ideas that foster confidence and long-term success, preparing students for increasingly complex mathematical challenges
- Offers the “what to do” to teach counting, addition, and subtraction in ways that promote reasoning over rote memorization
- Provides practical tools such as problem strings, models, classroom routines, and discussion questions designed to implement reasoning-based practices
- Includes supporting resources for creating a classroom culture where students see math as figure-out-able and gain confidence as mathematical thinkers
By addressing common misconceptions about math and providing practical strategies for teaching real math, this book shows that everyone can use the mathematical relationships they already know to reason about new relationships. In other words, everyone can math—even the very youngest students!
This book is a game-changer for educators. With clear examples and practical strategies, it empowers teachers to transform their instructional
practices. Packed with ‘aha’ moments and insights into the teaching and learning of mathematics, it inspires confidence in all of us. This is a must-read for anyone looking to make math instruction more meaningful for students while supporting the teacher with the ‘why’ behind it all.
Math reasoning kicks algorithms to the curb when students engage their brains (not just their pencils) to solve problem strings using a variety
of strategies. Harris takes the guess work out of teaching computation strategies intentionally by providing problem strings, teaching tips, and
sentence frames for beginning and experienced teachers.
This latest book from Pam Harris takes research related to the major milestones of mathematical development in the primary grades and
transforms it into a language that is easy to understand. Using carefully chosen examples, real world experiences, and student voices, Harris
has written a book that is illuminating and practical. Primary educators, whether new to the profession or seasoned experts, will find ideas here
that resonate and challenge them to listen closely in order to further thinking.