Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in Grades 3-5

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 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 im