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!
Who better than Pam Harris to help you introduce K–2 students to mathematical reasoning—the language, the music, and the poetry of
mathematics. A must-read book filled with teaching strategies and creative ideas.
The abilities to count and to add are foundational to mathematics. All that follows is built upon these cornerstones. Get it right and math becomes
‘figure-out-able.’ In this book, Harris gives us the tools to get it right. Through real classroom examples, Harris takes us through strategies that
are easy to adopt and effective in getting and keeping students engaged in the work of understanding mathematics.
It is with great enthusiasm that I endorse this transformative book. At the heart of this work is a compelling discussion of reasoning. Through
rich narratives and classroom vignettes, we see that math fact fluency is not only figure-out-able but enjoyable—sparking curiosity and confidence
in every student. In short, this book is a masterclass in making math fact fluency meaningful and accessible for all.
This book is a gift to primary teachers. It offers clear ideas we can use right away to help students build real understanding and develop as
mathematical thinkers. From counting to additive reasoning, and through the power of models and Problem Strings, this book supports teachers in
making instruction more purposeful and responsive.
Finally, the book that K–2 educators have been waiting for is here! Harris wrote a book that explores the complexity of foundational numeracy skills and shares research-based approaches to develop mathematical reasoning with our youngest learners. This book will not only help
teachers cultivate curiosity and confidence and build a community of mathers, but it will also help teachers become the mathers they were
always meant to be.
This book empowers K–2 teachers to deeply explore and understand the mathematics of the early grades, equipping them to foster
students’ mathematical reasoning and conceptual understanding. Grounded in research and filled with practical classroom examples,
it offers valuable guidance for transforming early elementary math instruction.
What a powerful resource for equipping mathematics educators with the knowledge and skills necessary to develop their students’ mathematical
reasoning and promote their confidence as mathematicians!
If you’ve ever heard Pam Harris talk about the Levels of Sophistication in Mathematical Reasoning and thought, ‘I get it but what does that look like with MY students??’ This book delivers! It reveals how young children develop counting skills and thinking strategies for mathematical operations.
You’ll gain insights into student development, practical tasks to showcase their thinking, and modeling techniques that benefit every child in your classroom.
Pam Harris offers teachers another invaluable resource for transitioning from repetitive procedural instruction to helping students develop deeper,
more conceptual understanding of mathematics. Through numerous examples of student thinking about mathematical concepts in the
K–2 classroom, she provides extensive treatment of the ways children approach problem solving. This comprehensive approach will certainly
prove helpful for teachers who are developing their understanding of how students learn to make sense of mathematics independently.
This is a must-read for all K–2 teachers. Harris helps teachers understand how they can set their young learners up for long-term success in the math
classroom. This book provides teachers with a resource that combines content knowledge, high quality instructional practices and ready-made
instructional materials all in one! Upper elementary, middle school and even high school math teachers would all benefit from reading this book
and better understanding the development of mathematical reasoning, too.