Our Publications

The power of a case lies not in the narrative but in the discussion that it generates. It is the role of the facilitator to maximize opportunities for discussion. This guide offers valuable help for anyone charged with that task, describing how to foster and enhance the professional development experience.

One of two papers in the Issues in Mathematics Education series, this paper explores issues related to both high-stakes and in-classroom assessments in mathematics. Intended for use by schools and teachers, possibly with parents, the paper clarifies common terminology and uses of test scores, and helps guide readers to think about ways of evaluating assessments.

Also check out Thinking (and Talking) About Technology in Math Classrooms

Beyond Classical Pedagogy: Teaching Elementary School Mathematics provides descriptions and analyses of the teaching that has evolved in mathematics classrooms of teachers who have been forerunners in the effort to implement the NCTM Standards in Elementary Mathematics. Research and insights from three disciplinary perspectives are presented: psychology, mathematics, and sociology

The mathematics education reform movement is built on very different ideas about the nature of learning, teaching, and, indeed, mathematics itself, than the views that have prevailed in American schooling for many years. This has implications for administrative practice, since an enterprise that exists to support rigorous thinking on the part of students requires different administrative supports than one that exists to transmit accepted knowledge from teacher or textbook to student. Understanding new ideas about mathematics, learning, and teaching, and exploring the implications of these ideas for administrative practice, requires conceptual change on the part of many administrators. This paper describes the pedagogical principles that underlie a program designed to provide opportunities for such conceptual change for administrators.

Each of the cases in this volume not only tells a story but also raises critical issues faced by teachers, administrators, and others striving to improve our schools. Together, the cases offer powerful opportunities for educators and others to analyze and reflect on the issues of school reform.

The current mathematics reform movement has recognized that new forms of mathematics teaching will be needed to support the proposed curricular changes. These new forms extend beyond the acquisition of new teaching techniques and strategies to the reconstitution of fundamental notions of teaching, learning, and the nature of mathematics as a discipline, and also to the creation of different classroom opportunities for learning. The means by which teachers effect this kind of transformation are, as yet, little understood. This paper describes a set of components of developmental models that can be used to guide efforts to build models of the process of teachers' development in mathematics practice. Drawing from theories of cognitive development, the paper focuses on three components of the change process: (1) qualitative reorganizations of understanding; (2) orderly progression of changes; and (3) the contexts and mechanisms by which transitions are effected; and suggests a fourth component-individual motivational and dispositional factors.

This guide describes a process for considering and reviewing standards-based mathematics programs and raises questions and issues for readers to consider in their own processes. The guide addresses curriculum selection and implementation and offers ideas to help districts work through both of these phases. Our focus for the selection phase is on assembling a selection committee, assessing resources and needs, and creating guidelines and criteria for evaluating different programs. The curriculum implementation section focuses on ways districts can work toward successful use of the materials they have purchased--planning a realistic and effective roll-out strategy, supporting teachers, and building community buy-in and assistance.

Connected Geometry, a geometry course developed with funding from the National Science Foundation, is a dynamic and engaging program rich in rigorous mathematics. Key features include: a focus on mathematical habits of mind, active student learning, a focus on proof, connections between geometry and other fields of study, and use of appropriate technology.

Connected Geometry has 6 components, all published by Everyday Learning Corporation:

* The Connected Geometry student text
* A Teacher's Guide
* A complete Solution and Problem Solving Resource
* Teaching Resources, including masters
* Assessment Resources, including tests and quizzes
* A CD-ROM with the Connected Geometry materials, including extensions and extra lessons, in modular format

This paper is available through Christine Atherton.

Compiles basic information about 12 standards-based, comprehensive mathematics curriculum programs, including a narrative description of each program and its fundamental philosophy and structure. Also includes descriptions of the programs components, as well as resources and contacts for more information about the program.
Published annually.

Developing Mathematical Ideas is a staff development/teacher education program designed to help educators think through the major ideas of K-6 mathematics and examine how children develop those ideas. The goal is to engage teachers in a process of inquiry--into mathematics; into learning mathematics; into students' mathematical thinking, in general, and the thinking of one's own students, in particular. In a DMI seminar, teachers discuss print and video cases, explore mathematical questions, investigate the mathematical thinking of their own students, analyze lessons from innovative curricula, and read and discuss essays about related research. DMI materials for two seminars have been completed: Buidling a System of Tens and Making Meaning for Operations. Currently under production are materials that will address geometry, measusrement, and data analysis.

Epistemological beliefs are about knowledge and learning. In a physics class, for example, some students might believe learning consists of memorizing facts and formulas provided by the teacher, whereas others might believe it entails applying and modifying their conceptualizations of phenomena. This paper explores, in the context of a debate about velocity from the author's high school physics class, how an epistemological perspective on students' knowledge and reasoning might influence a teacher's perceptions and intentions.

This book, a guide for the design of professional development with a focus on classroom assessment in mathematics, describes ideas developed in the Assessment Communities of Teachers project, in which EDC worked with middle-grades teacher leaders in Dayton, Memphis, Milwaukee, Pittsburgh, San Diego, and San Francisco.

New elementary curricula offer considerable promise in meeting new goals for student learning. These curricula represent a dramatic departure from more traditional textbooks. These new curricula, however, represent only one component of what is needed. New forms of instruction will become broadly available to students only if a substantial portion of the current teaching force transforms its current pedagogical practice. This transformation will require teacher professional development and support.

This book is written for teachers who want to reflect on, and perhaps redirect, their thinking about the learning and teaching of prealgebra and algebra, in light of the movement to base curriculum, instruction, and assessment on clearly defined standards. It is based on our work with teachers in grades 6 through 10, in several professional-development projects, especially the part of the work that has emphasized productive habits of algebraic thinking.

By emphasizing the ways of thinking that are essential in mathematics, one can design mathematics courses that simultaneously serve the needs of students who will go on to advanced mathematical study and students who will not. The authors address a series of mathematical "habits of mind," arguing that students should be pattern sniffers, experimenters, describers, tinkerers, inventors, visualizers, conjecturers, and guessers. Using mathematical examples, the authors discuss mathematical approaches to things, and how geometers and algebraists approach their world. Materials for teaching and learning school mathematics provide students with problems and activities that develop these habits of mind and put them into practice.

Each of the papers in this anthology has focused on a dimension of the process entailed for teachers as they embark on the project of moving their teaching toward that envisioned in the NCTM Standards-the impact of the nature of teachers' mathematical knowledge on their visions for teaching, the role of affect in the process of change; the essential characteristics of helpful materials, and the issues to be addressed in developing a teacher community that supports investigation into practice. The existence of the set of papers invites "conversation" about the relationships between these elements: What role does affect play in teachers' developing mathematical sophistication? How can materials help teachers become better mathematicians? Does the presence of a supportive culture enhance both the expression of affect and mathematical growth? and so on.

The first of two books published through MSEB’s Assessment in Practice initiative, this book discusses ways to assist teachers in learning about assessment and how student work can be a rich resource in professional development.

It is widely recognized that developing a successful teaching practice, one that is grounded in the principles that guide the current effort to reform mathematics education, requires a qualitatively different and significantly richer understanding of mathematics than most teachers in the 1990s possess. However, it is not as clear how teachers' mathematical understandings develop and how those understandings affect instruction. This paper explores two avenues for K--6 teachers' mathematical investigations--inquiry into mathematics itself, and inquiry into children's mathematical thinking--and illustrates how they arise in elementary teaching situations and how they can be explored in a professional development setting.

This course curriculum addresses a number of issues of importance to administrators in implementing new mathematics curricula. These include: What is the essence of the new curricula? What will reformed classrooms look like? What issues will teachers grapple with in learning to use these curricula? What are the criteria for student asessment? What about heterogeneous classrooms? How do we communicate with such stakeholders as parents and school boards?

If the intellectual norms and values embedded in the mathematics education reform movement are to move beyond individual classrooms and significantly influence entire schools and districts, school and district administrators will need to become centrally, rather than peripherally, involved. This paper discusses the way that administrators' ideas about the nature of mathematics, learning, teaching, and school culture affect their interpretations of the nature and intent of the mathematics reform movement and their thoughts about how they might support it. In particular, administrators' views of parents' concerns, professional development for teachers, and how new ideas move around in a school are discussed. I suggest that administrators have well-formed ideas about mathematics, learning, and teaching, and that these ideas influence their views of reform and how to provide support. These ideas need to be taken into account if administrators are to be central actors in reform.

Lenses on Learning is a seminar for school and district administrators on the ideas that underlie contemporary instruction in elementary mathematics and the implications for their own administrative practice. Three modules are published: Module 1, Instructional Leadership in Mathematics; Module 2, Teacher Learning for Mathematics Instruction, and Module 3, Observing Today's Mathematics Classroom. Facilitators package includes facilitator book, participant book of readings, and a videocassette. Students will need to purchase the book of readings.

The notion that students come to science courses with misconceptions has become quite widely accepted by those who follow or participate in education research. DiSessa and his colleagues (diSessa, 1988, 1993; Smith, diSessa, & Roschelle, 1993) have challenged the theoretical and empirical validity of the misconceptions perspective and offered an alternative account of cognitive structure in "phenomenological primitives," or "p-prims." The purpose of this article is to further clarify and contrast the two accounts, in particular to consider their utility and generativity as conceptual tools for teachers; in other words, how might each perspective influence instructional perceptions and intentions? The article recounts a discussion about forces and motion from a high school physics class; analyzes how a teacher might perceive students' participation in that discussion from either perspective; and considers what, based on those perceptions, the teacher might see as tasks for instruction.

Features edited interviews with teachers and administrators who have implemented Standards-based, mathematics programs in their schools, as well as interviews with the developers of each program. Interviewees talk about their experiences using the programs and explain the selection and implementation strategies used in their settings. This series includes three books, covering the elementary, middle, and high school grades.

This article addresses how administrators can better support standards-based instruction by shifting their approaches to supervision to attend to the intersection of process and content. The article reports on a study that looked at what administrators thought significant when viewing the same videotape of a fifth grade mathematics lesson at the beginning and end of a professional development seminar on supervision.

This booklet presents a professional development process for teachers to do mathematics investigation together and analyze student work from the same investigations. The goal is to deepen teachers' understanding of mathematics concepts and increase their capacity to focus on student thinking. The text outlines steps in the process, focusing on three elements: use of inquiry, cross-grade groups, and open-ended investigations.

Committed to improving instructional programs, more and more teachers are playing an active role in mathematics and science reform. Teacher Leadership in Mathematics and Science was written to assist these efforts. This unique book will both help current teacher leaders be more effective in this role and support the development of aspiring teacher leaders.

This is a book about the journeys of elementary school teachers across one year's time, as they participated in a teacher development seminar focused on mathematics, and changed their beliefs, their knowledge, and their practices. The book grows from the project When the Learners' Thinking Takes Center Stage -- an investigation of teacher learning in the Developing Mathematical Ideas Seminar

This is a book about the journeys of elementary school teachers across one year's time, as they participated in a teacher development seminar focused on mathematics, and changed their beliefs, their knowledge, and their practices. The book grows from the project When the Learners' Thinking Takes Center Stage -- an investigation of teacher learning in the Developing Mathematical Ideas Seminar

This annotated bibliography of articles related to Standards-based mathematics curriculum reform is intended for educators and communities considering the selection and implementation of Standards-based curriculum materials. The articles fall under four large categories: what makes Standards-based mathematics curricula different from traditional programs, impact studies about the use of these programs, professional development and teacher support, and challenges in implementing these curricula.

The Fostering Algebraic Thinking Toolkit is a set of professional development materials whose goal is to help mathematics teachers in grades 6-10 learn to identify, describe, and foster algebraic thinking in their students. Underlying the Toolkit is a core belief that good mathematics teaching begins with understanding how mathematics is learned.

The Roles of Representation in School Mathematics focuses on how students learn mathematics--in particular, how they learn to form abstractions and build mathematical representations of phenomena. It is an excellent resource for teachers who want to make smart decisions about content and pedagogy.

This book explains how students learn mathematics, how they come to develop mathematical habits of mind, and even how they develop misunderstandings about mathematics. It discusses the nature and roles of representation, the use of representation tools for gaining insights, various symbol systems used in mathematics, and the role of context in the interplay between modeling and representation. Hardback

One of two papers in the Issues in Mathematics Education series, this paper explores the impact of new technologies on the teaching and learning of mathematics. It advocates the use of good judgment in choosing educationally appropriate technology for the classroom--and in designing the use of that technology as a tool in the learning of mathematics.

Also check out Assessing Students' Mathematics Learning

Detailed descriptions of classroom process are needed in order to ground discussion of the principles animating the mathematics education reform movement. In response to this need, teachers who were already engaged in transforming their mathematics instruction were invited to write reflective narratives about their evolving instructional practice. This paper describes the structure of that project and presents excerpts from some representative narratives. It also considers how writing these narratives contributed to the continuing development of their authors and discusses how reading them affected students in teacher education courses. Finally, it urges that such narratives be seen as a medium through which teachers can become centrally involved in the national conversation about mathematics education reform.

National, state, and local curriculum requirements and recommendations increasingly emphasize active student involvement in exploratory investigations. Teachers now face new demands when they field unexpected student discoveries, determine when some open-ended activity has played out its usefulness or is just on the verge of paying off in a major way, and judge which student-initiated directions are likely to lead to development of important mathematical ideas and which are dead ends. These pedagogical judgments depend heavily on deep mathematical knowledge.

Ways to Think About Mathematics uses immersion experiences in algebra, geometry, and statistics to help mathematics teachers improve their knowledge and understanding of mathematical concepts. By experiencing open-ended problems, making and checking conjectures, and evaluating problem solving strategies, every math teacher can become better prepared to deal with day-to-day classroom decisions.

Also available: Facilitator's Guide with "Extras" CD. For more information, visit http://www2.edc.org/wttam.

Researchers agree that achieving the fundamental changes called for by current reforms in mathematics education requires new learning on the part of teachers. To meet this challenge, a tremendous variety of teacher-enhancement projects, representing a range of perspectives and approaches to supporting teachers? learning, currently exists across the country. This paper presents a comparative analysis of three teacher educators using a curriculum, Developing Mathematical Ideas (DMI), designed to serve elementary teachers in an inquiry-group setting. The aim of the study was to examine the process and demands of supporting teachers? learning and their efforts to reform their practices. Analyses revealed that the central demand of supporting teachers? learning through inquiry involved navigating through what we have called openings in the curriculum. These openings took the form of unanticipated questions, challenges, observations, or actions by participating teachers and required facilitators to make on-the-spot judgments about how to guide the discourse. Examinations of the teacher educators? processes for navigating these openings revealed that they used a set of three activities in determining how to respond. Analysis of facilitators? activities further illuminates the work involved in supporting teachers? learning and offers implications for the type of support needed by teacher educators engaged in this work.

This volume presents 13 remarkable essays written by teachers working with constructivist methods and principles to transform their own mathematics instruction, largely along the lines of the Standards of the National Council of Teachers of Mathematics.

Nine teachers describe their struggle to understand constructivist mathematics and to transform their practice. As these teacher-authors invite us into their classrooms and tell us about their experiences, their stories become narratives of changing professional identities.

Drawing from her extensive experience of using cases in teacher education and in-service courses, Windos on Teaching Math offers this practical, hands-on guide to improving the teaching of mathematics. This book, the first to focus on the secondary school classroom (grades 7–12), provides a collection of cases that blend important mathematics content with the real complexities of school and classroom life.