Making Sense

The key to effective math learning lies not in the regurgitation of isolated facts but in the ablility to reason with and use what is learned - in understanding the concepts. But what does it mean to design a classroom so that understanding is the primary objective? What would a system of instruction look like if we took seriously the goal of helping all students understand mathematics?

In this ground-breaking book, James Hiebert and his colleagues arm teachers with the best current research-based ideas for designing - and defending - classrooms that support students' mathematical understanding. It is based on the authors' work in four separate research programs, all of which investigated the effects of specific instructional approaches. Out of their ongoing discussions emerged a striking consensus about what features are essential and what features are optional, which they share in this book. They also provide glimpses into their individual projects and into the classrooms from which they have drawn many of their ideas.

By describing the essential features of classrooms that support students' mathematical understanding and by offering pictures of several classrooms that exhibit these features, Making Sense provides a valuable framework within which elementary teachers can reflect on their own practice and think again about what it means to teach for understanding.

This book presents several key principles for teaching mathematics for understanding that you can use to reflect on your own teaching, make more informed decisions, and develop more effective systems of instruction.

Thomas Carpenter is Professor of Curriculum and Instruction at the University of Wisconsin-Madison, where he has taught for twenty-five years. He is the former editor of the National Council of Teachers of Mathematics (NCTM) Journal for Research in Mathematics Education, and has received the NCTM Lifetime Achievement award for Distinguished Service to Mathematics Education among other awards.Elizabeth Fennema is Emerita Professor of Curriculum and Instruction and Senior Scientist at the Wisconsin Center for Education Research at the University of Wisconsin-Madison. She has studied the teaching and learning of mathematics throughout her professional career, and is well known for her work on gender and mathematics.Karen C. Fuson is a member of a working group of the National Center for Research in Mathematical Sciences Education at the University of Wisconsin-Madison. The purpose of the group is to consider the teaching and learning of whole-number arithmetic in elementary school.James Hiebert is a member of a working group of the National Center for Research in Mathematical Sciences Education at the University of Wisconsin-Madison. The purpose of the Group is to consider the teaching and learning of the whole-number arithmetic in elementary school.Hanlie Murray is a member of a working group of the National Center for Research in Mathematical Sciences Education at the University of Wisconsin-Madison. The purpose of the group is to consider the teaching and learning of whole-number arithmetic in elementary school.Diana Wearne is a member of a working group of the National Center for Research in Mathematical Sciences Education at the University of Wisconsin-Madison. The purpose of the group is to consider the teaching and learning of whole-number arithmetic in elementary school.

Introducing the Critical Features of Classrooms

The Nature of Classroom Tasks

The Role of the Teacher

The Social Culture of the Classroom

Mathematical Tools as Learning Supports

Equity and Accessibility

A Day in the Life of One Cognitively Guided Instruction Classroom

A Day in the Life of a Conceptually Based Instruction Classroom

Student Talk in a Problem-Centered Classroom

Snapshots Across Two Years in the Life of an Urban Latino Classroom

Revisiting the Critical Features of Classrooms