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

Math is not rote-memorizable. Math is not random-guessable. Math is figure-out-able._x000d_
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._x000d_
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. _x000d_
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._x000d_
Developing Mathematical Reasoning: 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.