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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 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
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 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 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
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.
296 pages, Kindle Edition
Published February 18, 2025
21 people are currently reading
34 people want to read
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Displaying 1 - 3 of 3 reviews
June 19, 2025
I listen to Pam Harris Podcast called “Math is Figure Out Able”. I’ve always been curious about how she looks at math and how she perceives math traps for students. When I was given the opportunity to join a book club with her book, I jumped on it.
We had some great discussions about the ideas she points out and the ways we can build mathematical reasoning.
I do t totally agree with everything she says but it has open my mind to adjust the way we teach mathematics.
We had some great discussions about the ideas she points out and the ways we can build mathematical reasoning.
I do t totally agree with everything she says but it has open my mind to adjust the way we teach mathematics.
August 27, 2025
I've been listening to Pam's podcast so most of this was a repeat, but it's great content, worth the time.
July 14, 2025
Pam Harris puts voice to what I have been wanting for my students since around 2006. Math classroom should be about reasoning and developing reasoning skills instead of just memorizing steps. Truly understanding and then explaining thinking can help so many people.
Displaying 1 - 3 of 3 reviews