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!
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.
Preface About this Book Acknowledgments Part 1: Setting the Stage Chapter 1: Mathematics for Teaching Part II: Developing Additive & Multiplicative Reasoning Chapter 2: Developing Additive Reasoning Chapter 3: Multiplicative Reasoning Part III: Developing Proportional Reasoning Chapter 4: Developing Proportional Reasoning Chapter 5: Proportional Reasoning Strategies Part IV: Putting It All Together Chapter 6: Tasks to Develop Mathematical Reasoning Chapter 7: Modeling and Models Chapter 8: Moving Forward References Index