Planning and Implementing Professional Development for Systemic Reform: What We've Learned About the Process

Judith Fonzi
University of Rochester

Project Overview
Having recently completed our three-year, NSF-funded Local Systemic Change Project (hereafter, LSC) for middle school mathematics my colleague, Raffaella Borasi, and I have been engaging in some in-depth reflection focusing on what we've learned about planning and implementing professional development for systemic reform. In the spirit of collaborating with colleagues in the larger community, I would like to share some of the things we have come to know. I'll do so first by providing an overview of the project context, then briefly engage in a "walk down memory lane" where I'll share with you what we actually did and why, and finally I'll provide a synthesized list of what we consider our most important lessons learned.

Our project included four small suburban school districts; each district had only one middle school. Each of our four key staff members, all mathematics teacher educators at local universities, was assigned to one of the schools as the "school facilitator" to support the school's efforts towards reform. As a project, our task was to bring about significant reform in the entire mathematics program and provide 130 hours of professional development for every math teacher in each of the middle schools.

We began the project with an outline of the major professional development initiatives we expected to implement, but we found ourselves making changes almost immediately. As the project proceeded and we learned more about where the teachers were in their thinking about mathematics, teaching and learning, and their abilities to put new ideas into practice, we found ourselves re-inventing our professional development program to better meet their needs. In addition, our program was modified in response to the steady stream of new resources that were becoming available for use in both classrooms and professional development.

In retrospect, the most important lessons we learned about planning and designing professional development that is meant to bring about systemic reform were:

• Listen carefully to what your evidence tells you about what teachers and schools need;
• Look for ways to design professional development initiatives so that they can address more than one goal at a time; and
• Engage in regular conversations with other professional development providers who are doing similar work.

Our Goals, Audience, and Initial Hurdles and How We Thought about Them
Our primary goal was to reform the entire middle school mathematics program in light of the NCTM Standards and the newly developed state standards, in each of our four participating districts. Exactly what that meant we didn't really know. We did know that:

• The current programs were designed in the 80s (or maybe it was the 50s!) where students were typically passive receivers of mathematical information, and learning was evaluated according to how much they could tell back on an exam. And, it was clear that most teachers, administrators, parents, and even students thought this was precisely as it should be!
• We needed to change attitudes about what mathematics is and what it means to learn mathematics.
• We needed to change instructional and assessment practices if we were to have any effect on the implemented mathematics program.

In our previous work, we had considerable success fostering and supporting the development of an inquiry approach to teaching and learning mathematics in a few teachers from each of the participant schools. These teachers had been quite pleased with both the new role students were taking in this learner-centered environment and with the level of understanding students demonstrated as they engaged in complex mathematical tasks and articulated their thinking. We therefore decided to capitalize on the fact that there were a few "role models/converts/believers" in each school and promote "teaching through inquiry" as a vehicle for reforming both instructional and assessment practices. We soon learned that it would take a whole lot more than that!

Our audience did indeed include a few "old friends," teachers who had volunteered to work with us in previous NSF teacher enhancement projects, but it also included many new folks. A condition of LSC projects is that all math teachers in a school must participate in 130 hours of professional development over the life of the project. We felt strongly that reforming the mathematics program meant the entire mathematics program, so we included both regular education and special education teachers. Our schools included sixth grade, so we also had several elementary certified teachers among our participants. The diversity among our districts and our teacher participants presented some interesting opportunities as well as some serious challenges.

We had several other hurdles, or downright obstacles, we knew about from the very beginning-we discovered others as we proceeded. We knew, for example, that:

• None of the districts had a mathematics coordinator, thus no one was responsible for developing a common vision for the district's mathematics program nor for charting a course for continuous improvement.
• Collaborative planning was not part of the culture of any of these schools, and most of the teacher teams that had developed during our previous work had been disbanded because of grade level changes.
• There was a revised state level assessment system being phased in amid a great deal of misinformation and misunderstanding which, of course, was made worse because of the lack of leadership and collegiality at the district level. Fortunately, none of our schools had serious "test score" problems coming into this project, but they were nevertheless all anticipating the pressure of the "new" tests.

Our Original Professional Development Plan
We knew from the very beginning that we needed to develop some leadership and collegiality, and we used the development of our project proposal to immediately begin modeling such behavior. We included teachers and administrators in our planning meetings, and, as a group, we discussed what we felt were crucial components to successfully fostering and supporting reform. Through this process, we made commitments to each other, and we developed a "big picture" of a professional development program.

We planned several complementary initiatives, each with a distinct purpose:

• One-week Introductory Summer Institute with follow-up field experiences (developed in our previous project) to introduce all new participants to an inquiry approach to teaching mathematics, to develop a shared vision of what a reformed math classroom could look like, and to provide some support materials for teachers to plan and implement innovative units in their own classroom. Participants would commit a priori to develop and implement at least two innovative units based on what they had learned. Lead teachers would support the field experiences. (This initiative would be implemented in Years One and Two.)
• One-week Advanced Summer Institute with follow-up field experiences focused on rethinking what algebra is, and how it should be taught in middle school. Participants would commit a priori to develop and implement an innovative unit, and lead teachers and the university faculty serving as school facilitators would support the field experiences. (To be implemented in Years Two and Three.)
• Monthly Leadership Seminar for two teachers from each school (hereafter, lead teachers) and school facilitators to develop leadership capacities, enhance current knowledge of math, teaching, learning, and systemic reform and to provide a forum for sharing experiences and learning from each other. (To be implemented during the school year for all three years.)
• "Ad-hoc" professional development provided by the school facilitators to respond to specific needs at the individual schools. (Equivalent to about one-half day per month.)

What Really Took Place the First Year and Why

Introductory Institute
We implemented our Introductory Summer Institute essentially as it was originally conceived. The Summer Institute and facilitator's support materials (Introducing Math Teachers to Inquiry: Framework and Supporting Materials to Design Professional Development, Borasi and Fonzi, (under review) we developed in our previous project had proven to be very successful at beginning to challenge teachers' views of mathematics, teaching and learning, and in supporting them to implement innovative units in their classrooms. Therefore only minor revisions were needed to address the LSC requirement that teachers become familiar with the exemplary curricula and consider them for adoption. We decided to introduce these curricula in this Institute so that teachers would consider them as possible resources for their second innovative unit.

Leadership Seminar: Summer Institute
In contrast, our Leadership Seminar was dramatically reconceived. Because of the timing of our funding, our Leadership Seminar would begin the September after our first Summer Institutes. We knew this would not work. "Lead teacher" was a brand new idea in this region, so the teachers filling these positions would need some time and support to think about what "lead teacher" could mean and to develop at least a preliminary plan for enacting this new role. They were also going to need some experience with the new curricula if they were going to be able to support their colleagues' use of these materials. Meeting these needs would take considerable time. Teachers would need time to brainstorm, to read, to think, to explore, and to share.

To address this issue, we decided to add a two-part "kick-off" Summer Institute for lead teachers, including three days at the beginning of the summer and two at the end. We designed the first segment to act as a catalyst and to develop a framework for work that the lead teachers would do throughout the summer. During this time we raised issues about teacher change and systemic reform and the lead teachers' role in these processes. Lead teachers later followed up on these issues by reflecting on their own journeys and writing autobiographies of the experiences that most influenced their growth and by reading and reflecting on some relevant articles ("Rethinking Restructuring: Building Habits of Effective Inquiry," Szabo, 1996; "Assisting Teachers and Students to Reform the Mathematics Classroom," Brown et al., 1996.

We also used this Institute to continue to develop our shared vision of an inquiry pedagogy, using some examples from practice to provoke thinking, (Borasi, 1996). We also introduced the lead teachers to some of the new curricula by using them to challenge lead teachers' beliefs about probability. We engaged them as learners in several probability experiences from Seeing and Thinking Mathematically (STM Project, 1998), Connected Mathematics (Lappan, 1998), and Mathematics in Context (NCRMSE and Freudenthal Institute, 1997) and asked them to read and reflect on the entire probability units in each curriculum project.

At the same time participants were also reading and discussing articles which identified important probability concepts ("Uncertainty," Moore, 1990); "Probability and Coincidence," Paulos, 1988, the current research on teaching and learning probability ("Research in Probability and Statistics: Reflections and Directions," Shaughnessy, 1992), and the NCTM and state standard on probability. Lead teachers became intrigued with how the new curricula put current research into practice, and agreed to examine a few units during the summer.

During the two days at the end of the summer, lead teachers shared their thoughts about when and how to use the new curriculum materials, and we discovered that they had all decided to develop new units, taking inspiration and some activities from these materials. While we would later come to realize the limitations inherent in teacher-developed materials, we were surprised and delighted with the commitment underlying their decisions. We spent the majority of the end-of-the-summer meetings discussing lead teacher roles and developing a preliminary year-long plan for implementing their roles in their schools. It was clear to all of us that this "kick-off" Summer Institute for lead teachers was the critical element that made start-up so smooth.

Leadership Seminar: School Year Activities
Our half-day, monthly Leadership Seminar "officially" began in September of our first year and continued for the next three years. During the first year, the sessions were divided such that one-third of the time was for sharing and two-thirds of the time was devoted to a more focused learning experience.

As the first year of work with lead teachers unfolded, a number of issues surfaced that significantly affected what and how we planned our professional development program.

We realized from our summer work explicating the groups' conceptions of an inquiry pedagogy that we needed to continue to work in this area. Lead teachers needed to develop a language for talking about practice so that they could better communicate and support others. So, during Leadership Seminar we periodically examined examples from practice, sometimes published examples (Lampert et al., 1998), and sometimes examples from teachers' own work, to identify evidence of an inquiry pedagogy.

Despite the fact that our Introductory Summer Institute highlighted some very different geometry and measurement content, and lead teachers used our support materials to develop similar experiences for their own students, they tended to change their pedagogy but maintain their content. Since it seemed to be more difficult for teachers to challenge or change content than pedagogy, we began to think about how to help them develop images and knowledge about new mathematical content.

The probability experiences we developed in the "kick-off" Summer Institute, though primarily designed to introduce the new curricula, had also introduced lead teachers to new probability concepts for middle school. So, we decided to use the same types of materials orchestrated differently, to introduce lead teachers to new ideas in geometry.

• First, to help lead teachers become aware of the geometric concepts that are critical for applying geometric knowledge in today's world, we asked them to read some current research ("Shape," Senechal, 1990) and the section regarding geometry from some NSF-funded curricula (Connected Mathematics and Mathematics in Context).
• We then asked them to read some current research in the teaching and learning of geometry ("Geometry: Research and Classroom Activities," Geddes and Fortunato, 1993) and the section about the approach to teaching and learning geometry from the curriculum.
• Finally, to help lead teachers develop images of what this could look like in practice, we asked them to carefully examine some units from the curricula and note the content choices made by the authors.
• After developing the authors' list of "big ideas" in geometry, we invited a local university mathematics professor to comment on the list from his perspective of what's important for students to learn.

At the same time that we were focusing on geometry in Leadership Seminar, we redesigned one of our graduate courses to challenge students' conceptions of important mathematical content for middle schools. We divided the course into a collection of "mini-series" designed to accomplish goals similar to those of the geometry experience in Leadership Seminar but for much smaller mathematical ideas, and we invited the lead teachers to participate in as many mini-series as they wished.

School-Based Professional Development
We also learned early in the first year, when we discovered that the lead teachers were not yet comfortable with the idea of mentoring their colleagues, that our plans for school facilitators would need to change dramatically. So, university mathematics educators serving as school facilitators took on most of the responsibility for supporting the new participating teachers as they planned and implemented their first innovative units (Borasi and Fonzi, under review). They also participated in the school's Math Department meetings and had lengthy discussions and strategy meetings with the lead teachers.

A few months later, the lead teachers expressed a common need to continue to work on their own practice and a common desire to have the support of the school facilitator as well. Funding for school facilitators covered only about one day per week, and we were all already putting in several additional days per week on a volunteer basis. It was clear we needed to find more efficient ways to meet everyone's needs rather than working with each teacher individually.

We began to think about the lead teachers' classes as professional development sites. Other participants were invited to observe the lead teachers' classes and debrief with the lead teacher and school facilitator. Same-grade colleagues were invited to participate in the planning meetings between the lead teacher and school facilitator.

We also held a one-day project-wide session devoted to planning. We explicitly shared the unit planning process that had emerged from our previous work (Borasi and Fonzi, under review), and then we worked intensively with small groups as they worked through the stages of the process to develop a thematic unit on the Olympics. These "new" practices proved to be more efficient, and at the same time good ways to begin building collaborative communities within each of the schools.

Project-Wide Professional Development
Additional concerns surfaced as we continued to work with participating teachers as they planned and implemented innovative experiences. Though we initially were comfortable with teachers "picking and choosing" activities from various units of the NSF-funded curricula, we began to reconsider. Teachers' decisions about what content to cover, what to focus on, what pieces of the unit to use or cut were often troubling to us. They were making some headway with the general pedagogy but very little with content. They were beginning to hear students' voices, appreciate that they could engage in mathematical thinking, and include them in more roles, but most teachers had not yet recognized how limited their view of important mathematical content was. Those that did recognize it maintained that they were not free to change the content, just the approach. We suspected that these beliefs were grounded more in lack of understanding of what the mathematics could be, than in the realities of the system. At the same time that this was happening, the project staff was becoming more familiar with the NSF-funded curricula and were beginning to recognize that the curricula had the potential to help teachers develop images of new or deeper content and to support them to teach that content--if the units were read and implemented in their entirety.

Recognizing the need for teachers to have experiences identifying and teaching "new" content, we decided to address the content problems from several angles. In the Leadership Seminar we analyzed a sample of the new state assessments and determined that the amount of content that was actually required on the exam was minimal and surely didn't represent an entire middle school program, thus providing "room" to add some additional content. Then, with the goals of introducing teachers to some new content that was already carefully developed for classroom implementation and to begin a practice of collaborative planning, school facilitators volunteered to facilitate school-based "planning groups" around individual units in the NSF-funded curricula.

We invited all of the teachers at a grade level across the four schools to participate in the planning groups, specifically designing the experience to engage teachers as learners in the mathematics of the unit and then to invite them to reflect on the significance of each activity in developing the mathematical concept. The group examined the entire unit before they began to plan their own implementation. This practice proved to be quite effective, as teachers came to value the authors' careful sequencing of activities and thus made only minor cuts when they implemented the unit in their classes. In addition, teachers were beginning to see the value of shared experiences and one school's faculty even decided to attend the Advanced Summer Institute as a team. This unanticipated set of professional development experiences was the precursor to "study groups," a component of our Year Two professional development program that proved to be a critical element in advancing systemic reform.

Taking Stock: Year One
At the end of the first year, we reflected on what we had learned to inform our planning of the next year of professional development.

Participation
At the end of the first year we took stock of who was participating in what types of professional development and noticed that special education teachers were not participating at the same rates as the regular education teachers. When we pursued this, they told us that math was only one of several subjects they must support so they didn't feel they could give it all of their professional development time. Several regular education teachers were also finding it difficult to devote the amount of time necessary to learn all these new things and still keep up with their day-to-day responsibilities.

We also discovered that there were many "cultural" and policy barriers that were influencing attendance at professional development initiatives. For example, teachers were free to use whatever instructional materials they wanted and teachers were expected to attend department meetings, but no one followed up if they did not. Similarly, decisions could be made at department meetings but there were no vehicles to enforce them or consequences for not following through. Teachers were not required to participate in professional development outside of the school day and principals were not requiring them to participate during the school day either.

Classroom Practices
We also took stock of what we, the professional development providers, were learning about classroom practices:

• We were developing a genuine appreciation for the quality of the NSF-funded curricula.
• We had learned that, despite the fact that all of our schools had written grade-level curriculum documents, the teachers' implemented curricula were always very different from each other. While this made trying out NSF curricula units possible, it also allowed for not trying them out if a teacher didn't want to.
• We realized that, like the lead teachers, most participating teachers were generally making progress towards pedagogical reform but were not making much progress in content reform.

The two sets of information, who was participating in what, and what we were learning about classroom practices, had a significant influence on the design of our second year program.

What Year Two Looked Like and Why
In light of all that we had learned, we felt that in order to reform the entire school program we had to first develop a need for a comprehensive and coherent program. We made developing collaborative communities our primary goal and decided to concentrate most of our energies on school-based initiatives. Fortunately, lead teachers were now willing to take on more roles with their colleagues, including promoting peer collaboration and even taking the lead in some initiatives.

Introductory Summer Institute
Year Two began with the Introductory Summer Institute with only minor revisions, as it was continuing to serve us well. But this time, in order to provide supported experiences in implementing professional development initiatives, lead teachers co-facilitated the experience with project staff.

Advanced Summer Institute
Our planning for the Advanced Summer Institute was influenced significantly by what we were learning about teachers' reluctance to modify the content of their curriculum and the wide variations within their actual implemented curriculums. We designed our Advanced Summer Institute, which was to focus on rethinking algebra, to take full advantage of the NSF-funded curricula. Once again we divided a week-long institute into two parts, four days in the beginning of the summer and one day at the end. In an effort to challenge participants' views of "what counts as algebra" we asked them to read Jim Fey's "Quantity" paper (1990) prior to coming to the institute. We followed up on this reading with a discussion of the ideas in the paper and additional readings that explicated the algebra philosophies of the Connected Mathematics and Mathematics in Context curricula. We then engaged the participants as learners in some algebra activities that put these new ideas into practice. Many of these activities were taken from the NSF-funded curricula. Then, during the remainder of the summer, each participant read one of the algebra units from either Mathematics in Context or Connected Mathematics and prepared a presentation to highlight the big ideas in the unit and how they are developed. At the end of the summer the units were presented in the order in which they would be taught so that we could develop an image and appreciation of the entire algebra strand. This experience prompted the participants to suggest that they all try teaching a unit and share the results. School facilitators once again offered to facilitate "planning groups" (now called "study groups") for each of the units chosen for implementation.

Algebra Study Groups
The algebra study groups served as the catalyst for several additional study groups as teachers found these experiences to be both valuable and time efficient; they were engaging in the same mathematical experiences they would be planning for their classes, and the units proved to be powerful and exciting. In several of the schools, teachers continued to plan together and ultimately implemented several additional common units. School facilitators were purposefully explicit about how they were planning and facilitating the first few study groups so that lead teachers could eventually take over the responsibility, which several did by the end of the year.

We complemented the unit study groups with a repeat of the first year's mini-series which focused on rethinking specific mathematical topics. In addition to addressing teacher content needs, we saw the mini-series as a way to continue to promote school-based collaboration while at the same time promoting cross-site collaboration. This time participation was open to all teachers. We encouraged them to come as grade level teams and to use this experience as a springboard for identifying and implementing an innovative unit on the topic.

Leadership Seminar
The Leadership Seminar for Year Two was essentially the same as Year One, except for the "sharing sessions." Lead teachers were no longer interested in sharing the details of what was happening in their sites because the schools had moved towards systemic reform in different ways and therefore had mostly individualized needs at this point. Thus, sharing sessions shifted from spontaneous discussions to pre-planned sessions focused on a particular topic. For example, one of the lead teachers, who was the regional liaison to the state for the new assessment program, shared what she would be doing in the assessment training session with area teachers. On another occasion lead teachers shared their experiences with alternative scheduling as each school continued to struggle with finding the ideal schedule.

The Final Phase of Professional Development: The Transition Year
In general, we were pleased with how our professional development program progressed. By the beginning of the third year, we recognized that:

• We were well on our way to establishing collaborative cultures in 3 of our 4 schools;
• Considerable changes were taking place in both pedagogy and content as a result of implementing some of the NSF-funded curricula units; and
• Some teachers were beginning to see the advantages of a comprehensive and well-articulated curriculum.

Advanced Summer Institute
We also repeated our Advanced Summer Institute. In order to capitalize on the implementation experiences of the previous year's teachers, promote collaboration, and provide opportunities for additional teachers to take on leadership roles, we invited a few teachers to spend a day sharing their experiences with implementing one of the NSF-funded algebra units. We encouraged them to talk about the level of mathematics students were engaged in, the role it played in students' understanding of algebraic concepts, and the benefits of planning the unit in collaboration with their colleagues. As we had hoped, the participants decided to implement some of the units and formed study groups to do the planning. All of these study groups were school-based and were facilitated by lead teachers or other experienced teachers in the school.

Leadership Seminar
During this final year, our Leadership Seminar was devoted to helping lead teachers and schools become independent. We concentrated our attention in three areas. We helped lead teachers begin to develop leadership capacities in colleagues by urging them to identify some of their colleagues who had particular skills that could be of benefit to others, such as knowledge and experience using graphing calculators. We then worked with the teachers who had special talents to plan and implement small-scale professional development experiences for others. We helped school communities learn to identify professional development that would promote their reform agenda. To do so, we offered mini-grants to support initiatives that would help faculties gain skills to continue their own reform agendas. Faculties had to reflect on their experiences, identify initiatives that would move them further along, and then submit a proposal for funding the initiative. And finally, we wanted to help lead teachers learn how to navigate local and regional systems to identify and secure resources. Accordingly, we invited district and regional administrators to our Leadership Seminar to share detailed information about the types of funding that are available, when and how to go about securing funds, and more general advice about how to navigate these systems. This experience provided lead teachers with the background information necessary to tap into the resources of the system in appropriate and timely ways.

Some Key Lessons Learned about Planning Professional Development Experiences

As we began preparing for a new project (a five-year K-12 project to develop the foundations for systemic reform), we realized that we had learned some very important lessons about planning for professional development experiences. Among the most important are:

• Begin with a basic plan based on what you think your learners will need.
• Be open enough to hear your learners' needs, to uncover and understand their cultures, and be flexible enough to respond to them.
• Find ways to make professional development immediately useful without succumbing to "make it and take it."
• Take a flexible stance toward resources; imagine how they can be used in new ways to accomplish different purposes.
• Plan professional development experiences that are meaningful and rich; they can, and probably should, address multiple goals at one time but caution should be exercised so as not to lose the primary focus.
• Teachers should be the primary decision-makers in selecting a new curriculum but only after they have spent considerable time reading and discussing recent research in mathematics, teaching, and learning, and have had supported experiences trying out units from several of the new curricula.
• Teachers must receive substantial and on-going support to implement the NSF-funded curricula successfully. They need to engage in the units as learners, develop an understanding of the mathematical content and the pedagogical practices, and they need to reflect on their implementation in light of their goals.
• Quite possibly the most important lesson we learned for our own professional growth is to collaborate with other professional development providers.

For the most part, we have learned these lessons the hard way, through our own trial and error. We came to appreciate the importance of collaborating with other professional development providers through our experiences at our annual principal investigator meetings. We discovered that many other people were indeed engaged in the same work and experiencing many of the same needs. We began to identify other professional development providers whose ideas we felt comfortable with and whose work we admired and initiated on-going relationships. As a result, we have been able to enrich some of our practices and miss some of the potholes in the road by learning from other's experiences. We also found that discussing our own work with others helped us to reflect more deeply and develop a language for our practice.

Recently some materials have been published that identify some of the same issues we identified and support professional development providers through the planning process. See for example:

• Designing Professional Development for Teachers of Science and Mathematics (Loucks-Horsley et al., 1998) for ideas about the planning process, the overall design of professional development, and a description of several formats for professional development.
• Guide to Facilitating Cases in Education (Miller and Kantrov, 1998) for a very detailed description of the key issues and practices to be considered when implementing and facilitating cases as a method of professional development.
• Introducing Math Teachers to Inquiry: Framework and Supporting Materials to Design Professional Development (Borasi and Fonzi, available from the authors) for a detailed framework and supporting materials for designing a one-year professional development program to introduce teachers to teaching mathematics through inquiry and systemic reform.

References

Borasi, R. (1996). Reconceiving Mathematics Instruction: A Focus on Errors. Norwood, NJ: Ablex.

Borasi, R. and Fonzi, J. (under review). Introducing Math Teachers to Inquiry: Framework and Supporting Materials to Design Professional Development.

Brown, C.A., Stein, M.K., and Forman, E.A. (1996). Assisting teachers and students to reform the mathematics classroom. Educational Studies in Mathematics, 31 (1-2).

Fey, J. T. (1990). Quantity. In L. A. Steen (Ed.), On the Shoulders of Giants. Washington, DC: National Research Council.

Geddes, D. and Fortunato, I. (1993). Geometry: Research and classroom activities. In D. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics. NY: MacMillan.

Lampert, M. and Ball, D.L. (1998). Teaching, Multimedia, and Mathematics: Investigations of Real Practice. NY: Teachers College Press.

Lappan, G., Fey, J., Fitzgerald, W., Friel, S., and Phillips, E. (1998). Connected Mathematics. Menlo Park, CA: Dale Seymour.

Loucks-Horsley, S., Hewson, P.W., Love, N. and Stiles, K. E. (1998). Designing Professional Development for Teachers of Science and Mathematics. Thousand Oaks, CA: Corwin Press.

Miller, B. and Kantrov, I. (1998). Guide to Facilitating Cases. Portsmouth, NH: Heinemann.

National Center for Research in mathematical Sciences Education (NCRMSE) and the Freudenthal Institute (1997). Mathematics in Context. Chicago, IL: Encyclopedia Britannica Educational Corporation.

National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM.

Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the Shoulders of Giants. Washington, DC: National Research Council.

Paulos, J. A. (1989). Probability and Coincidence. In Innumeracy: Mathematical Illiteracy and its Consequences. New York, NY: Hill and Wang.

STM Project (1998). Seeing and Thinking Mathematically. Chicago, IL: Creative Publications, Inc.

Senechal, M. (1990). "Shape." In L. A. Steen (Ed.), On the Shoulders of Giants. Washington, DC: National Research Council.

Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning. Reston, Virginia: National Council of Teachers of Mathematics.

Szabo, M. (1996). Rethinking restructuring: Building habits of effective inquiry. In M.W. McLaughlin and I. Oberman (Eds.), Teacher Learning: New Policies, New Practices. NY: Teachers College Press.

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TE-MAT
Teacher Education Materials Project
A Database for K-12 Mathematics and Science Professional Development Providers