Developing Mathematical Reasoning: Avoiding the Trap of Algorithms

Math is not rote-memorizable. Math is not random-guessable. Math is figure-out-able.

Author Pam 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. The mountain of trivia piles up until students hit a breaking point. Humanity′s most powerful system of understanding, organizing, and making an impact on the world becomes a soul-draining exercise in confusion, chaos, and lost opportunities.

Developing Mathematical Reasoning: Avoiding the Trap of Algorithms emphasizes the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. This book illuminates a hierarchy of mathematical reasoning to help teachers guide students through various domains of math development, from basic counting and adding to more complex proportional and functional reasoning.

Everyone is capable of understanding and doing real math. This book:

• Highlights the important mathematical relationships, strategies, and models for students to develop
• Offers personal stories, reflection sections, and extensive practical exercises for easy implementation
• Includes real math--a lot of it--to provide teachers with examples they can put to use in their classrooms immediately

This book is a valuable resource for educators looking to reach more students by building a strong foundation of mathematical thinking in their students. 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.

Author: Pamela Weber Harris
Publisher: Corwin Publishers
Published: 03/18/2025
Pages: 296
Binding Type: Paperback
ISBN: 9781071948262

About the Author
Pamela Weber Harris is the author of Building Powerful Numeracy (Heinemann), Lessons & Activities for Building Powerful Numeracy (Heinemann), Building Powerful Numeracy: A Facilitator′s Guide (self-published); Algebra Problem Strings (Kendall Hunt); Advanced Algebra Problem Strings (Kendall Hunt); and Discovering Advanced Algebra (Kendall Hunt). She was a main writer for Bridges in Mathematics, a K-5 textbook series by the Math Learning Center. A former secondary mathematics teacher, Pam currently teaches at Texas State University, is a K-12 mathematics education consultant, a T3 (Teachers Teaching with Technology) Instructor, and an author and coauthor of several professional development workshops. She also cohosts a regular (and popular) podcast. Pam presents frequently at international and national conferences. Her particular interests include teaching real math-ing, building powerful numeracy, sequencing rich tasks to construct mathematics, using technology appropriately, smart assessment, and vertical connectivity in curricula in schools PK-12.