James Tanton - Böcker

What mathematics truly matters for student success in middle and high school? Can we really declutter the content while accomplishing more?Too often, secondary mathematics instruction is cluttered with disconnected procedures, jargon, and "drill-and-kill" computational practice. This approach hands students a huge pile of tiny puzzle pieces where students never build or even see the picture of the puzzle on the box, leading to confusion and fragile thinking that unravels the moment a memorized formula is forgotten. This book, co-published with the National Council of Teachers of Mathematics, draws upon mathematics education research and offers an alternative that prioritizes fundamental understandings.Drawing on over a century of combined experiences, including an NSF-funded project involving over 300 educators, this book identifies five fundamental understandings that serve as a bedrock for student thinking in grades 6–12. By centering on these core ideas, teachers can reduce clutter in both content and student thinking by elevating sense-making and meaning. The authors provide practical examples and show how unleashing student thinking pays off in amazing ways.This book guides teachers and instructional coaches to reimagine the mathematics they teach and to bring it to life in the classroom. The five fundamental understandings act as big puzzle pieces that support students to accomplish bigger things with mathematics. Whether you are a veteran educator or a preservice teacher, this book helps create a robust, mathematical environment in which every student can experience the joy of true sense-making.Book Features:Five Fundamental Understandings: Identifies essential mathematical ideas—including measurement, comparisons, proportional relationships, equivalence, and graphical representations—to help teachers prioritize what matters most for student success.What Really Matters: Describes how the fundamental understandings unleash student thinking.The Math Attic: Recommends the mathematical clutter that can (and should) be de-prioritized in light of the five understandings.High-Profile Expertise: Authored by a team of experts and award-winning educators.

What mathematics truly matters for student success in middle and high school? Can we really declutter the content while accomplishing more?Too often, secondary mathematics instruction is cluttered with disconnected procedures, jargon, and "drill-and-kill" computational practice. This approach hands students a huge pile of tiny puzzle pieces where students never build or even see the picture of the puzzle on the box, leading to confusion and fragile thinking that unravels the moment a memorized formula is forgotten. This book, co-published with the National Council of Teachers of Mathematics, draws upon mathematics education research and offers an alternative that prioritizes fundamental understandings.Drawing on over a century of combined experiences, including an NSF-funded project involving over 300 educators, this book identifies five fundamental understandings that serve as a bedrock for student thinking in grades 6–12. By centering on these core ideas, teachers can reduce clutter in both content and student thinking by elevating sense-making and meaning. The authors provide practical examples and show how unleashing student thinking pays off in amazing ways.This book guides teachers and instructional coaches to reimagine the mathematics they teach and to bring it to life in the classroom. The five fundamental understandings act as big puzzle pieces that support students to accomplish bigger things with mathematics. Whether you are a veteran educator or a preservice teacher, this book helps create a robust, mathematical environment in which every student can experience the joy of true sense-making.Book Features:Five Fundamental Understandings: Identifies essential mathematical ideas—including measurement, comparisons, proportional relationships, equivalence, and graphical representations—to help teachers prioritize what matters most for student success.What Really Matters: Describes how the fundamental understandings unleash student thinking.The Math Attic: Recommends the mathematical clutter that can (and should) be de-prioritized in light of the five understandings.High-Profile Expertise: Authored by a team of experts and award-winning educators.

This book is a collection of 34 curiosities, each a quirky and delightful gem of mathematics and each a shining example of the joy and surprise that mathematics can bring. Intended for the general math enthusiast, each essay begins with an intriguing puzzle, which either springboards into or unravels to become a wondrous piece of thinking. The essays are self-contained and rely only on tools from high-school mathematics (with only a few pieces that ever-so-briefly brush up against high-school calculus).The gist of each essay is easy to pick up with a cursory glance--the reader should feel free to simply skim through some essays and dive deep into others. This book is an invitation to play with mathematics and to explore its wonders. Much joy awaits!In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.