Developing Mathematical Reasoning

The Strategies, Models, and Lessons to Teach the Big Ideas in Grades 6-8

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 as they move through the content, but in reality students are not necessarily progressing in their ability to reason mathematically.

Using 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.

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 set rules for solving problems. This grades 6–8 companion volume equips you to confidently tackle traditionally difficult topics like integer operations, ratios, and proportional reasoning. Key features include:

• Reasoning-based strategies: Replace traditional algorithms with approaches that build multiplicative and proportional reasoning
• Problem Strings: Step-by-step guidance on using sequenced problems to spark insight and make thinking visible
• Visual models: Practical tools and graphics to make abstract mathematical concepts concrete

Learn how to teach undistorted math so every student can reclaim their confidence. By shifting from procedures to sense-making, you’ll help your middle schoolers build the flexible mathematical brains they need to thrive.