Making Sense: Teaching and Learning Mathematics with Understanding

The air is full of ideas on how to teach maths better. But many of these ideas are single features, such as "use manipulatives" or "ask high-level questions". Other are based solely on intuitions or anecdotal evidence. "Making Sense" attempts to break new ground by describing a system of instruction that fits together the individual pieces and provides the theoretical arguments and empirical evidence to support the system. It presents several key principles for teaching mathematics for understanding that teachers can use to reflect on their own teaching, make more informed decisions, and develop more effective systems of instruction. "Making Sense" reflects current research-based ideas on how to design classrooms that help students learn mathematics with understanding. It is based on the author's work in four different research programmes, all of which investigated the effects of specific instructional approaches. Out of their ongoing discussions emerged a 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 in 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.

Thomas Carpenter was Professor Emeritus of Curriculum and Instruction at the University of Wisconsin-Madison, where he 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 (2004) among other awards. Tom passed away in August 2018, leaving behind a vast legacy to mathematics education thanks to his research into Cognitively Guided Instruction (CGI). That work, created by him and his team of researchers and authors, is available to all teachers in his influential and popular books Children's Mathematics, Thinking Mathematically, and Young Children's Mathematics. In addition, members of Tom's team have already begun the process of extending out from his work in CGI with Extending Children's Mathematics. ?Read more about Tom and his legacy, including warm remembrances from other influential members of the field of mathematics education.

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.

Thomas Carpenter was Professor Emeritus of Curriculum and Instruction at the University of Wisconsin-Madison, where he 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 (2004) among other awards. Tom passed away in August 2018, leaving behind a vast legacy to mathematics education thanks to his research into Cognitively Guided Instruction (CGI). That work, created by him and his team of researchers and authors, is available to all teachers in his influential and popular books Children's Mathematics, Thinking Mathematically, and Young Children's Mathematics. In addition, members of Tom's team have already begun the process of extending out from his work in CGI with Extending Children's Mathematics. ?Read more about Tom and his legacy, including warm remembrances from other influential members of the field of mathematics education.

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.

Math Expressions author, Dr. Karen Fuson, is Professor Emerita of Learning Sciences in the School of Education and Social Policy and the Department of Psychology at Northwestern University. She was a member of the National Research Council's Committees that wrote Adding It Up, Mathematics Learning in Early Childhood, and How Students Learn. Professor Fuson worked on the Common Core State Standards-Math and on the learning progressions for these standards and has advised PARCC and Smarter Balance on their math test design and items. She has published over eighty research articles on mathematics teaching and learning. She directed the Children's Math Worlds (CMW) Research Project-a 10-year study of how to effectively teach students math from an early age. The CMW Research Project examined how teachers can build conceptual supports, including meaningful language, drawings, manipulatives, accessible written methods, and classroom communication methods, to facilitate mathematical competence. The results from this research are a major source of the approaches in Math Expressions, her PK through Grade 6 math program. This program is also based on the research in the NRC reports, on aspects of international math programs, and on her research from around the world. Please see her website karenfusonmath.com for 23 hours of Teaching Progressions explaining the Common Core math domains, videos of classrooms, publications, and resources for remote learning.

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.