Preface

Purpose of This Monograph

We live in a time of great change in mathematics education. The National Council of Teachers of Mathematics (NCTM) Standards and other influential reports have called for radical reform in U.S. school mathematics in order to prepare all students to meet the mathematical demands of today’s society (NCTM, 1989, 1991, 1995, 2000; National Research Council [NRC], 1989; U.S. Department of Education, 1996). These reports challenge the content and pedagogy of current mathematics instruction. Most importantly, they highlight the need for more student-centered and constructivist-based instruction so that problem-solving, meaning-making and conceptual understanding are emphasized, not rote memorization of facts and procedures.

This new focus departs radically from the way mathematics has traditionally been taught. Putting the reports’ recommendations into practice will require teachers to rethink not only their teaching practices but also the very goals of teaching mathematics. Schools and districts will also have to revise their mathematics curricula and assessments and work together to redefine expectations for students’ learning and teaching practices. These changes are not easy to accomplish; they demand not only supportive school structures but also high quality professional development programs to guide and support teachers’ individual and collaborative efforts.

Such professional development programs present a new challenge for providers and consumers. As principal investigators of a few NSF-funded professional development projects in mathematics, we have learned that neither typical university courses nor traditional in-service workshops go far enough. Different kinds of experiences are needed if we wish to promote radically different beliefs and practices and create learning communities engaged in reform.

Fortunately, several examples of successful professional development initiatives that support school mathematics reform have emerged in the last twenty years (as reported, for example, in Friel & Bright [1997] and Eisenhower National Clearinghouse for Mathematics and Science Education [ENC] [2000]). These initiatives include not only a new set of goals and principles but also new kinds of professional development activities, such as innovative mathematical learning experiences for teachers, in-depth examinations of students’ mathematical work, “case discussions” and various kinds of supported field experiences.

The main purpose of this monograph is to identify and critically examine these promising professional development practices, with the goal of enabling professional development providers and users to better evaluate how each can best be used to support school mathematics reform.

Because systematic research studies on effective mathematics teacher education are still limited, many questions about teacher change, school reform, and the effects of specific professional development strategies remain unanswered. At the same time, some theories and empirical data are emerging that may help providers and users evaluate the potential contributions of alternative professional development initiatives. In this monograph, we will synthesize and critique these theoretical and empirical contributions by looking at both the published literature and the “informal knowledge” shared among successful practitioners. As a main source for the latter, we draw primarily upon the results reported by the many Teacher Enhancement and Local Systemic Change projects funded by the National Science Foundation during the last twenty years.

We hope that the monograph will be useful for those who design and facilitate professional development for mathematics teachers of all grade levels. Even more importantly, however, our goal is to support informed decisions on the part of a wide range of education professionals who are consumers of professional development. Consumers include school administrators who make decisions about the kind of professional development that should take place in their district, teachers who must choose professional development initiatives to participate in, and officials at government agencies and private foundations who fund teacher enhancement projects.

Assumptions informing this monograph

Before embarking on an in-depth analysis of specific professional development practices, we want to clarify some assumptions that inform our perspective.

Along with Susan Loucks-Horsley and her colleagues (1998), we believe that good professional development programs result from knowing the unique goals, needs and constraints of each audience:

Professional development, like teaching, is about decision making – designing optimal opportunities tailored to the unique situation.

(Loucks-Horsley, Hewson, Love & Stiles, 1998, p. xiii)

Thus, if professional development is audience-based, no single model of professional development will work for all. Rather, content, format and activities should be considered in light of each situation to determine which would be most appropriate and effective, and in which combination and sequence. At the same time, knowing about a variety of practices and their potential contributions to achieving specific goals will be critical to making informed decisions.

To accomplish this end, we suggest that professional development providers and consumers should know about, and take into consideration, the following elements:

• The needs of teachers engaging in school mathematics reform and how these needs may be effectively addressed,

• The principles informing the most successful professional development initiatives and the theoretical and empirical basis of those principles, and

• The strengths and limitations of different types of professional development activities that have been successfully developed and field-tested by the mathematics teacher education community.

We have created this monograph to help readers gain this knowledge base.

We are aware that there are other key logistical issues that professional development providers need to address, such as scheduling initiatives, organizing the space for them, grouping participants, and offering compensation or other incentives for participants, just to name a few. While we recognize that these issues are critical to the success of any professional development initiative, they are beyond the scope of this monograph.

How the monograph is organized

The next three chapters of the monograph are devoted to developing a framework to evaluate specific professional development initiatives and practices.

To this end, in Chapter 1 we examine what teachers may need in order to successfully engage in school mathematics reform. Based on what we have learned about teacher development and reform from research and exemplary practice, we identify and discuss nine categories of “teacher learning needs” that should be addressed by professional development that aims at supporting instructional innovation in mathematics.

Chapter 2 provides some images of effective professional development. Here we portray two of the several professional development programs in the literature that have documented success in supporting school mathematics reform. We selected these examples to illustrate significantly different approaches that can be used to address the teacher learning needs identified in Chapter 1 at different grade levels. We hope these descriptions will reveal the complexity of good professional development programs and show the many alternatives available.

In Chapter 3, we compare the programs described in Chapter 2 to identify both elements that are shared by most effective professional development programs and some options consumers and providers can choose from. Among these options, we identify the various formats that professional development can take on, the possible areas of expertise for professional development providers and, most importantly, a few categories of professional development experiences that represent quite different yet complementary approaches to address the needs of mathematics teachers engaging in reform.

In Chapters 4 to 8 we then examine in depth each of these types of professional development experiences, which we have characterized as engaging teachers in:

• Experiences-as-learners where they experience first-hand some innovative ways to learn and teach mathematics (Chapter 4).

• In-depth analysis of students’ mathematical work (Chapter 5).

• “Case discussions” where a selected example of practice serves as the catalyst for reflecting on and discussing important issues related to school mathematics reform (Chapter 6).

• Structured and scaffolded attempts at instructional innovation (Chapter 7).

• Gathering and making sense of relevant information about various aspects of school mathematics reform, using a variety of tools (Chapter 8).

In each of these chapters, we use the framework developed in the first part of the monograph to examine what characterizes professional development activities within that given category, and how and why these activities can contribute to support teachers engaged in school mathematics reform. More specifically, we begin by discussing the theoretical rationale and empirical evidence that support the featured type of professional development experience. Next, we provide two illustrations to give a rich image of this type of experience in action, while also showing the many differences that could occur in its implementation. Referring to these examples, we then articulate the characteristic elements of this type of professional development experience and discuss some of its main variations. We follow this with an analysis of how each of the teacher learning needs identified in Chapter 1 can be addressed by variations within this kind of professional development experience (further summarized in Figure 11 in our concluding chapter). Each chapter concludes with suggestions for follow-up readings.

The monograph closes with a summary chapter in which we briefly review our major findings about what kinds of professional development can best support school mathematics reform. We also provide some suggestions about how providers and consumers can ensure that mathematics teachers are offered the high quality professional development they need to significantly improve mathematics instruction.


	Preface Purpose of This Monograph We live in a time of great change in mathematics education. The National Council of Teachers of Mathematics (NCTM) Standards and other influential reports have called for radical reform in U.S. school mathematics in order to prepare all students to meet the mathematical demands of today’s society (NCTM, 1989, 1991, 1995, 2000; National Research Council [NRC], 1989; U.S. Department of Education, 1996). These reports challenge the content and pedagogy of current mathematics instruction. Most importantly, they highlight the need for more student-centered and constructivist-based instruction so that problem-solving, meaning-making and conceptual understanding are emphasized, not rote memorization of facts and procedures. This new focus departs radically from the way mathematics has traditionally been taught. Putting the reports’ recommendations into practice will require teachers to rethink not only their teaching practices but also the very goals of teaching mathematics. Schools and districts will also have to revise their mathematics curricula and assessments and work together to redefine expectations for students’ learning and teaching practices. These changes are not easy to accomplish; they demand not only supportive school structures but also high quality professional development programs to guide and support teachers’ individual and collaborative efforts. Such professional development programs present a new challenge for providers and consumers. As principal investigators of a few NSF-funded professional development projects in mathematics, we have learned that neither typical university courses nor traditional in-service workshops go far enough. Different kinds of experiences are needed if we wish to promote radically different beliefs and practices and create learning communities engaged in reform. Fortunately, several examples of successful professional development initiatives that support school mathematics reform have emerged in the last twenty years (as reported, for example, in Friel & Bright [1997] and Eisenhower National Clearinghouse for Mathematics and Science Education [ENC] [2000]). These initiatives include not only a new set of goals and principles but also new kinds of professional development activities, such as innovative mathematical learning experiences for teachers, in-depth examinations of students’ mathematical work, “case discussions” and various kinds of supported field experiences. The main purpose of this monograph is to identify and critically examine these promising professional development practices, with the goal of enabling professional development providers and users to better evaluate how each can best be used to support school mathematics reform. Because systematic research studies on effective mathematics teacher education are still limited, many questions about teacher change, school reform, and the effects of specific professional development strategies remain unanswered. At the same time, some theories and empirical data are emerging that may help providers and users evaluate the potential contributions of alternative professional development initiatives. In this monograph, we will synthesize and critique these theoretical and empirical contributions by looking at both the published literature and the “informal knowledge” shared among successful practitioners. As a main source for the latter, we draw primarily upon the results reported by the many Teacher Enhancement and Local Systemic Change projects funded by the National Science Foundation during the last twenty years. We hope that the monograph will be useful for those who design and facilitate professional development for mathematics teachers of all grade levels. Even more importantly, however, our goal is to support informed decisions on the part of a wide range of education professionals who are consumers of professional development. Consumers include school administrators who make decisions about the kind of professional development that should take place in their district, teachers who must choose professional development initiatives to participate in, and officials at government agencies and private foundations who fund teacher enhancement projects. Assumptions informing this monograph Before embarking on an in-depth analysis of specific professional development practices, we want to clarify some assumptions that inform our perspective. Along with Susan Loucks-Horsley and her colleagues (1998), we believe that good professional development programs result from knowing the unique goals, needs and constraints of each audience: Professional development, like teaching, is about decision making – designing optimal opportunities tailored to the unique situation. (Loucks-Horsley, Hewson, Love & Stiles, 1998, p. xiii) Thus, if professional development is audience-based, no single model of professional development will work for all. Rather, content, format and activities should be considered in light of each situation to determine which would be most appropriate and effective, and in which combination and sequence. At the same time, knowing about a variety of practices and their potential contributions to achieving specific goals will be critical to making informed decisions. To accomplish this end, we suggest that professional development providers and consumers should know about, and take into consideration, the following elements: • The needs of teachers engaging in school mathematics reform and how these needs may be effectively addressed, • The principles informing the most successful professional development initiatives and the theoretical and empirical basis of those principles, and • The strengths and limitations of different types of professional development activities that have been successfully developed and field-tested by the mathematics teacher education community. We have created this monograph to help readers gain this knowledge base. We are aware that there are other key logistical issues that professional development providers need to address, such as scheduling initiatives, organizing the space for them, grouping participants, and offering compensation or other incentives for participants, just to name a few. While we recognize that these issues are critical to the success of any professional development initiative, they are beyond the scope of this monograph. How the monograph is organized The next three chapters of the monograph are devoted to developing a framework to evaluate specific professional development initiatives and practices. To this end, in Chapter 1 we examine what teachers may need in order to successfully engage in school mathematics reform. Based on what we have learned about teacher development and reform from research and exemplary practice, we identify and discuss nine categories of “teacher learning needs” that should be addressed by professional development that aims at supporting instructional innovation in mathematics. Chapter 2 provides some images of effective professional development. Here we portray two of the several professional development programs in the literature that have documented success in supporting school mathematics reform. We selected these examples to illustrate significantly different approaches that can be used to address the teacher learning needs identified in Chapter 1 at different grade levels. We hope these descriptions will reveal the complexity of good professional development programs and show the many alternatives available. In Chapter 3, we compare the programs described in Chapter 2 to identify both elements that are shared by most effective professional development programs and some options consumers and providers can choose from. Among these options, we identify the various formats that professional development can take on, the possible areas of expertise for professional development providers and, most importantly, a few categories of professional development experiences that represent quite different yet complementary approaches to address the needs of mathematics teachers engaging in reform. In Chapters 4 to 8 we then examine in depth each of these types of professional development experiences, which we have characterized as engaging teachers in: • Experiences-as-learners where they experience first-hand some innovative ways to learn and teach mathematics (Chapter 4). • In-depth analysis of students’ mathematical work (Chapter 5). • “Case discussions” where a selected example of practice serves as the catalyst for reflecting on and discussing important issues related to school mathematics reform (Chapter 6). • Structured and scaffolded attempts at instructional innovation (Chapter 7). • Gathering and making sense of relevant information about various aspects of school mathematics reform, using a variety of tools (Chapter 8). In each of these chapters, we use the framework developed in the first part of the monograph to examine what characterizes professional development activities within that given category, and how and why these activities can contribute to support teachers engaged in school mathematics reform. More specifically, we begin by discussing the theoretical rationale and empirical evidence that support the featured type of professional development experience. Next, we provide two illustrations to give a rich image of this type of experience in action, while also showing the many differences that could occur in its implementation. Referring to these examples, we then articulate the characteristic elements of this type of professional development experience and discuss some of its main variations. We follow this with an analysis of how each of the teacher learning needs identified in Chapter 1 can be addressed by variations within this kind of professional development experience (further summarized in Figure 11 in our concluding chapter). Each chapter concludes with suggestions for follow-up readings. The monograph closes with a summary chapter in which we briefly review our major findings about what kinds of professional development can best support school mathematics reform. We also provide some suggestions about how providers and consumers can ensure that mathematics teachers are offered the high quality professional development they need to significantly improve mathematics instruction.