Mathematics Classrooms That Promote Understanding

Mathematics Classrooms That Promote Understanding

Mathematics Classrooms That Promote Understanding

Mathematics Classrooms That Promote Understanding


Mathematics Classrooms That Promote Understanding synthesizes the implications of research done by the National Center for Research in Mathematical Sciences on integrating two somewhat diverse bodies of scholarly inquiry: the study of teaching and the study of learning mathematics.

This research was organized around content domains and/or continuing issues of education, such as equity and assessment of learning, and was guided by two common goals--defining the mathematics content of the K-12 curriculum in light of the changing mathematical needs of citizens for the 21st century, and identifying common components of classrooms that enable students to learn the redefined mathematics with understanding. To accomplish these goals, classrooms in which instruction facilitated the growth of understanding were established and/or studied. This volume reports and discusses the findings which grew out of this research, and subsequent papers and discussions among the scholars engaged in the endeavor.

Section I, "Setting the Stage," focuses on three major threads: What mathematics should be taught; how we should define and increase students' understanding of that mathematics; and how learning with understanding can be facilitated for all students. Section II, "Classrooms That Promote Understanding," includes vignettes from diverse classrooms that illustrate classroom discourse, student work, and student engagement in the mathematics described in Chapter 1 as well as the mental activities described in Chapter 2. These chapters also illustrate how teachers deal with the equity concerns described in Chapter 3. Section III addresses "Developing Classrooms That Promote Understanding."

The knowledge of the teaching/learning process gained from the research reported in this volume is a necessary prerequisite for implementing the revisions called for in the current reform movement. The classrooms described show that innovative reform in teaching and learning mathematics is possible. Unlike many volumes reporting research, this book is written at a level appropriate for master's degree students. Very few references are included in the chapters themselves; instead, each chapter includes a short annotated list of articles for expanded reading which provides the scholarly basis and research substantiation for this volume.


The concern with teaching for understanding is as old as the 20th century. the intuitive rightness of learning with understanding--as well as the work of mathematics educators such as Colburn, Brownell, and Van Engen, who wrote about it long before the current reform movement--has led to widespread acceptance of the importance of developing students' understanding of mathematics. These and other more contemporary scholars have studied and written about what understanding means as well as how the curriculum should be structured so that students' understanding could be developed. Most instruction in mathematics, however, has not considered this knowledge, and most students have not developed an understanding of mathematics. All this scholarly work from the past has had little impact on instruction.

Why, then, if the work from the past has had little impact, should we return once again to the subject of mathematical understanding? For two major reasons. First, among much of the public including parents, teachers, professional organizations, employers, and various state and federal governments, there is not only support but strong demand for changing schools and instruction to meet the needs of the 21st century. Second, there is an ever-growing body of knowledge about learning and teaching mathematics that we believe can give bold new direction to classroom instruction so that all students learn with understanding.

The research that led to the ideas in this book is based on the work of many scholars in diverse disciplines. Mathematicians and mathematics educators have provided new insight into the nature of mathematics and have worked to identify those processes, concepts, and ideas within the discipline that are critical to successful survival in the 21st century. Psychologists, sociologists, and educational scholars have provided insights into student learning and the process of educational change. Other researchers have demonstrated the merit of cooperating with practicing teachers to gain knowledge about classroom processes.

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