AN ANALYSIS OF PROFESSIONAL DEVELOPMENT

UTILIZING REFORM CURRICULA

M. Lynn Breyfogle	Kate Kline	Laura R. Van Zoest
Western Michigan University	Western Michigan University	Western Michigan University
mary.breyfogle@wmich.edu	kate.kline@wmich.edu	laura.vanzoest@wmich.edu

Abstract: The goal of this study was to analyze the planning and implementation of a workshop that was part of a larger, long-term professional development project for middle and high school mathematics teachers using reform curricula. This workshop focused on developing teachers’ understanding of the reform curricula’s approach to the teaching of algebra. Teachers worked on problems from the curricula and reflected on the algebraic ideas developed from these problems. Transcripts of planning/debriefing meetings before, during and after the workshop, and pre- and post-workshop interviews with the facilitator and participants were analyzed. Tensions were revealed particularly around goals and content, shedding light on the issues that must be addressed when planning and implementing professional development.

Objectives or Purpose of Study

This study analyzed the planning and implementation of a two-day workshop for middle and high school teachers on the development of algebraic concepts. The workshop was set in the context of a larger National Science Foundation Local Systemic Change (LSC) professional development project for secondary school mathematics teachers implementing the Connected Mathematics Project (CMP) and the Core-Plus Mathematics Project (CPMP) curricula. The goal of the four-year project is to support teachers as they learn about the content and pedagogical approach of these reform curricula through professional development utilizing CMP and CPMP and through the creation of a collaborative community of learners. We chose to focus on the two-day algebra workshop because we felt it was representative of the professional development offerings in the larger project and the smaller scale allowed us to analyze the situation in greater depth. Specifically, we focused on the tensions that arose during the planning and implementation of this workshop and their resolutions.

Perspective or Theoretical Framework

Regarding the structure of professional development, researchers have found that modeling best teaching practice has a greater impact on the participants than just sharing information (Cobb, Wood, & Yackel, 1990). Best teaching practice in this context refers to that which is aligned with the recommendations of the National Council of Teachers of Mathematics (1991, 1998). This includes providing tasks that require participants to investigate and discuss results and allowing for multiple approaches and a variety of representations. Furthermore, programs that allowed participants to investigate and construct their own learning were more successful (i.e. improved students’ achievement in mathematics) than those programs that simply talked about the content (Kennedy, 1999). The algebra workshop, along with professional development opportunities throughout the larger project, was based on these premises.

Successful professional development is clearly dependent upon effective planning. Our planning of the two-day workshop was guided by the Professional Development Design Process for Mathematics and Science Education Reform (Loucks-Horsley, Hewson, Love, & Stiles, 1998, p. 17). This process entails setting goals, planning the implementation, implementing the plan and reflecting. Professional developers are advised to reflect on the following as they are setting goals and planning: knowledge and beliefs about learning, strategies for best meeting objectives, context and background of participants, and critical issues that may jeopardize the success of a program. Finally, the authors explain that it is inevitable in the process of negotiating all of these factors that tensions will arise and compromises must be made. This study looks in detail at the tensions that arose in one professional development setting and the subsequent resolutions.

Methodology

Data Collection

There are two groups involved in the research of this professional development experience: four mathematics educators (including the researchers and the workshop facilitator) who developed the workshop and 18 middle and high school teacher participants. Three planning meetings of the development team over the three months prior to the workshop and five debriefing sessions at half-day intervals during the workshop were audio-taped, transcribed and coded. Additional pre- and post- interviews were completed with the workshop facilitator to determine how she had implemented the ideas generated in the development team planning meetings. Questions asked of the workshop facilitator focused on the rationale for including particular activities, the thinking process that took place during individual planning, and adjustments she made.

A pre- and post-workshop phone interview with each participant included questions that attended to both the participants' beliefs and mathematical knowledge. All interviews were audio-taped, transcribed, and analyzed. A follow-up mailed survey was sent to each of the participants to spark further reflection on the algebraic content of the workshop. An end-of-workshop evaluation was completed by each participant prior to leaving the workshop and an outside evaluator submitted an evaluation of the professional development as well.

Analysis

We began our analysis by using preliminary categorizations based on our initial research questions. These categorizations were: mathematical ideas; adjustments made during the workshop; pedagogical tools--related to decisions made about how to help teachers understand the content and what artifacts to share with the teachers; and effectiveness--used for both evidence of teacher growth and the developers’, participants’, and outside observers’ perceptions of growth. The transcripts were coded individually by the research team members who then met to identify themes across the different types of transcripts and to refine categories. A finer categorization crossing all initial categories emerged around predominant tensions that arose as developers planned and implemented the workshop.

Results and Evidence

As in all instances of professional development, time was a tension. We discuss this briefly, and then focus our attention on the more substantial tensions of the goals and content of the workshop. Although we address goals and content separately for ease of discussion, there is overlap and interaction between the two. We conclude this section with a discussion of the effectiveness of our responses to these tensions.

Time Tension

The first time tension involved planning for the workshop. Given the number of people involved in planning and their involvement in several projects, the end result was three collaborative planning meetings during a three-month period with individual planning in between. Another time tension involved balancing the amount of time needed to do justice to the topics with the amount of time the teachers were willing to give out of their busy schedules. In particular, we wanted to reach teachers who had not been willing to participate in week-long workshops in the past. Two was arrived at as the optimal number of days to do minimal justice to the content and encourage maximum participation. Once the length of the workshop was determined, the tension of how to best use that time emerged. Our response to this tension is discussed in both of the following sections.

Goal Tension

Much of the development team’s discussion, especially during and after the workshop, focused on the tension between what we wanted the teachers to learn and what seemed realistic for them to learn in two days. In this context, we had difficulty deciding which goals were most important. When asked in the pre-workshop interview what she hoped participants would take away from the workshop, the facilitator responded with a litany of goals. When asked what she would be satisfied with them attaining, she replied, "All of the above. Nothing less. … All of those are really important and I think that the materials are so rich that if those things weren’t realized, I’d feel like I hadn’t done a very good job." In the end, the development team agreed that the main goal of the workshop was for the teachers to come away with an understanding and appreciation of the approach to the development of algebra taken by the CMP and CPMP curricula.

In addition, the interviews with the participants prior to the workshop identified discrepancies between their goals and those of the workshop developers. For example, many of the teachers were looking for ideas for hands-on activities and opportunities to share ideas with other teachers. One resolution of this tension was to have teachers who had taught the unit under discussion share their experiences. As the facilitator explained in the post-workshop interview, “I think that one of the things that I get out of workshops is that people like to listen to other people. They want to hear experienced teachers share their own experiences. And so [having them share experiences] gets to that desire.”

Content Tension

In the process of considering which algebraic concepts to include in the workshop, the development team came to the conclusion that the content had to be narrowed to one key concept. After much deliberation, we chose “rate of change” because it is a fundamental concept of both CMP and CPMP, and arguably of algebra in general. Once this was agreed upon, making decisions about what problems to look at and which activities to engage the participants in raised additional issues.

The first was choosing between problems rich with opportunities for mathematical learning versus problems that were narrower in their scope and therefore predictable. For example, one unit was left out because it may have detracted from the mathematical focus of the workshop. As the facilitator said in her post-interview: “That particular unit, one of the difficulties with it is that they have some really wonderful experiments that would be engaging, but the trouble is, because they’re experiments, the data doesn’t come out nice. And so what’s supposed to be a linear model turns out very often not to be. So you’re getting to some important ideas, but you’re not getting to this rate of change idea.”

The second issue dealt with balancing coverage of content with time for reflection. Since it was difficult for us to predict how well the reflection segments of the workshop would turn out, the facilitator made allowances for variances in the agenda. In the pre-workshop interview she reported that “I’ve tried to build in some flexibility. Some places where I can remove things if we get into conversations that seem so valuable that I don’t want to cut them off.”

Discussion/Conclusion

In many ways, the workshop would be considered a success. The most significant change was in the teachers’ conceptions of algebra. The language they used for describing algebra during the workshop changed from “equations, variables, rules for manipulating variables and solving for a variable” to “identifying a pattern and coming up with a representation of that pattern, predicting change, and understanding that there are multiple representations for situations and thinking about how these representations are related.” The comments on the post- interview corroborated this shift away from symbol manipulation to a broader perspective of algebraic reasoning. Our conscious decision to spend time addressing teachers’ conceptions of algebra was worthwhile in this sense.

An area in which the workshop was less successful was in the teachers’ mastery of content knowledge. For example, in the post-workshop interviews, although the teachers had a strong understanding of linear relationships, less than half of the participants correctly identified a quadratic relationship. During the workshop, little time was spent on attaching labels to particular relationships and investigating the differences between the rate of change in quadratics versus exponential relationships. Although the teachers had learned much over the two days, their understanding was still far from ideal. Perhaps the facilitator stated it best in the post-workshop interview when she said, “I felt like they had come a long way, but they weren’t quite where, at the point I would have liked them to be.”

Researchers have discussed the inevitability of tensions that occur during the planning and implementation of professional development (Loucks-Horsley et al., 1998). Our study identified some critical components of the goal and content tensions and the effects of possible resolutions. Teasing out what helps make professional development effective is complicated at best. If professional development providers are conscious of the aspects of the goal and content tensions in advance, both the planning and implementation of professional development sessions will be more efficient, and perhaps more effective.

References

Cobb, P., Wood, T., & Yackel, E. (1990). Classrooms as learning environments for teachers and researchers. In R. B. Davis, C. A. Maher & N. Noddings. (Eds.), Constructivist views of mathematics(125-146). Reston, VA: National Council of Teachers of Mathematics.

Kennedy, M. M. (1999). Form and substance in mathematics and science professional development. NISE Brief: Reporting on issues and research in science, mathematics, engineering, and technology education, 3 (2), 1-7.

Loucks-Horsley, S., Hewson, P. W., Love, N., & Stiles, K. (1998). Designing professional development for teachers of science and mathematics. Thousand Oaks, CA: The National Institute for Science Education.

National Council of Teachers of Mathematics (1998). Principles and standards for school mathematics (Draft). Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics (1991). Professional standards for teaching school mathematics. Reston, VA: National Council of Teachers of Mathematics.