Developing Mathematical Reasoning: Avoiding the Trap of Algorithms (Corwin Mathematics Series)

Review

Are you teaching operations, fractions or functions? If so, Harris has some gorgeous ideas for you―showing us the ways they are all ‘figure-out-able’ with mathematical reasoning. -- Jo Boaler ― Stanford, CADeveloping Mathematical Reasoning is every teacher’s guide to breaking away from algorithmic-centered teaching. From the three distortions of mathematics to the hierarchies of mathematical reasoning, Harris helps us understand how math and math teaching have become entangled in a tension between algorithms and reasoning, and then shows us how to untangle this tension through a series of real classroom examples. In so doing, Harris shows us that math is, actually, ‘figure-out-able.’ -- Peter Liljedahl ― Vancouver, CanadaHarris explores the limitations of an algorithm-centered classroom and emphasizes the need for true mathematical reasoning. By presenting a hierarchy of reasoning domains and advocating for a strategy-centered approach, this book equips educators with vital tools to empower students and deepen their understanding of mathematics. -- Graham Fletcher ― Atlanta, GAChock full of real stories about real people engaging with real math, Developing Mathematical Reasoning lives up to its title. Harris beautifully empowers educators with practical insights and steps to help students become true mathematical thinkers, not just mimickers―essential for a world that needs confident reasoners. -- James Tanton ― Paradise Valley, AZThis book is a gem that should be read by every teacher of mathematics. Harris offers a K–12 continuum of narratives from classrooms and builds a strong argument for why algorithms should not be the focus of instruction if we truly want to produce numerate, mathematically empowered thinkers. -- Catherine Fosnot ― Vero Beach, FLThis book is a gift for all teachers, especially those of us raised in the era of algorithms and rote memorization. Harris walks you through how to help students reason their way to understand math conceptually. With each step in the progression, you learn how to help students graduate to more sophisticated ways of thinking and math-ing. -- Liesl McConchie ― San Diego, CAFrom the very first page, this book grabbed me and refused to let go. Harris’s insights into the challenges of learning mathematics, as well as her joyful explanations of what can be possible when we have the right attitude and mindset, are essential for today’s educators to absorb and integrate into their classrooms. -- Eddie Woo ― Sydney, New South Wales, AustraliaHarris critiques traditional math instruction by highlighting three key distortions about what math truly is. She encourages educators to move beyond algorithm repetition and instead promote real mathematical reasoning and problem solving, raising expectations and fostering deeper understanding for all students. A transformative read for anyone looking to elevate math instruction. -- Pamela Seda ― Atlanta, GAHarris takes you on an adventure that fast-tracks you along her journey of discovering how students learn best. A must-read for anyone wanting to open students’ horizons and get them to use what they already know to tackle new problems. -- Christopher Hogbin ― Canberra, ACT, AustraliaThis is a timely and, ultimately, brave book about mathematics. Harris shines a light on ineffective practices and reminds us that math is so much more than memorized procedures. Her insights may ruffle some feathers about long held beliefs on math instruction. But the invitation to reach more deeply into real mathematics will open many eyes. -- John R. Tapper ― Burlington, VTThis book is a must-have! I grew up in the trap of the algorithm. I made it through school with good math grades because I was a good rule follower. It wasn’t until I was getting my master’s degree that I learned I didn’t know mathematics, I was just good at arithmetic. -- Christina Tondevold ― Orofino, IDHarris is not only a dear friend but also an incredible advocate for teaching math in a way that truly empowers students. In this book, she beautifully abstracts the essence of math, guiding teachers on how to help students deeply understand concepts rather than just memorize procedures. Harris has always been a brilliant resource for educators, helping them uncover the ‘why’ behind the math, and this book is a testament to her passion and expertise. -- India White ― Brooksville, FLDeveloping Mathematical Reasoning makes the bold assertion that math instruction should teach students to think mathematically. In this day and age when quick answers are coming quicker than ever, Pamela Weber Harris encourages us to slow down. Using concrete examples and vignettes, Harris demonstrates how traditional teaching methods tend to short-change development by pushing procedural thinking. This book teaches how to navigate around those traps and build classrooms rich with reasoning. -- David Woodward ― Boulder, CO

About the Author

Pamela Weber Harris is changing the way we view and teach mathematics. Pam is the author of several books, including the Numeracy Problems Strings K-5 series, Building Powerful Numeracy, and the series Foundations for Strategies. As a mom, a former high school math teacher, a university lecturer, and an author, she believes everyone can do more math when it is based in reasoning rather than rote-memorizing or mimicking. Pam has created online Building Powerful Mathematics workshops and presents frequently at national and international conferences.  Her particular interests include teaching real math, building powerful numeracy, sequencing rich tasks to construct mathematics, using technology appropriately, and facilitating smart assessment and vertical connectivity in curricula in schools PK-12. Pam helps leaders and teachers to make the shift that supports students to learn real math because math is figureoutable!