chap_bar.gif
Summary

What have we learned about professional development that works?

The many illustrations from actual professional development that we included in this monograph are an indication of the large number of successful professional development initiatives currently supporting school mathematics reform. The literature on mathematics teacher education reports positive outcomes for these initiatives, showing that high quality professional development can make a difference in the future of mathematics instruction. Yet, it is more difficult to pinpoint the role that specific professional development activities play in the effectiveness of different programs.

No single model of professional development emerges from the many successful examples reported in the literature on mathematics teacher education. Instead, we find many examples of worthwhile experiences that address the multiple needs of teachers engaged in school mathematics reform. In Chapter 1, we identified and discussed these needs, categorizing them as follows:

 Developing a vision and commitment to school mathematics reform.
 Strengthening one’s knowledge of mathematics.
 Understanding pedagogical theories that underlie school mathematics reform.
 Understanding students’ mathematical thinking.
 Learning to use effective teaching and assessment strategies.
 Becoming familiar with exemplary instructional materials and resources.
 Understanding equity issues and their classroom implications.
 Coping with the emotional aspects of engaging in reform.
 Developing an attitude of inquiry toward one’s practice.

In Chapter 3, we argued that in order to address these teachers’ learning needs effectively, professional development programs need to have the following characteristics:

 Be sustained and intensive.
 Be informed by what we know about how people learn best.
 Center around the critical activities of teaching and learning rather than focus primarily on abstractions and generalities.
 Foster collaboration.
 Offer a rich set of diverse experiences.

These characteristics can be embodied in a number of different types of professional development experiences. We found it convenient for our analysis to categorize the many forms of professional development activities suggested in the literature into five main categories:

 Engaging teachers in mathematical experiences-as-learners.
 Having teachers analyze in-depth exemplars of student work and thinking.
 Using “cases” as the catalyst for reflections and discussions on important issues related to school mathematics reform.
 Supporting teachers as they engage in structured and scaffolded attempts at instructional innovation.
 Empowering teachers to gather and make sense of information.

Our explanation and discussion of each type of professional development experiences in Chapters 4 through 8 make clear that these categories are not mutually exclusive. Rather, these five types sometimes overlap. For example, certain experiences-as-learners may provide a scaffold for instructional innovation, and many “cases” may involve the analysis of student thinking among other things. However, distinguishing these five major types of professional development experiences allowed us to study each in depth. Thus, we have been able to identify the characteristic elements of each type, consider the theoretical and empirical support for it and discuss the variations and conditions that may maximize its effectiveness. In our analysis, we also show how each type of professional development experiences may be used to address several of the teacher learning needs we identified in Chapter 1. We summarize the results of this analysis in Figure 11.

Figure 11
Teacher learning needs addressed by each type
of professional development experience


matrix showing 9 different teacher learning needs

 


NOTE: In this chart, a large dot indicates that the teacher learning need can be effectively addressed by at least some variations of the corresponding type of professional development experience. A small dot indicates that the teacher learning need can be met somewhat, but it is not a primary goal of that type of professional development experience.

This analysis suggests that certain types of professional development experiences are more appropriate than others to further specific goals. It also shows that whether a type of professional development experience addresses any specific goal effectively depends to a great extent on the choices providers make in its implementation.

The analysis in this monograph supports the principle that professional development programs should include a variety of experiences. Furthermore, it suggests that programs should be comprised of a combination of the types of professional development experiences we have described, carefully selected to meet specified teacher learning needs.

While there are significant differences in the preparation, mathematical background, teaching experience and attitude of elementary and secondary mathematics teachers, we found nothing to suggest that any type of professional development experience is more or less appropriate for one or the other group of teachers. Indeed, illustrations showed successful implementation of a strategy with both levels of teachers. Working with elementary or secondary teachers, however, may affect some important choices within each implementation; for example, the mathematical content of experiences-as-learners or cases, or the exemplary instructional materials used in scaffolded field experiences. Despite these differences it is both possible and valuable to provide opportunities – at least occasionally – for elementary and secondary mathematics teachers to participate together in professional development experiences (as shown by the teachers’ inquiry on area reported in Illustration 1, and the case discussion on rational numbers reported in Illustration 5).

Effective professional development may take a variety of formats, including intensive Summer Institutes, a series of workshops held during the school day or after school, study groups of teachers who meet on a regular basis, one-on-one interactions between a teacher and a teacher educator, and independent work done by the teacher. Most successful programs combine different formats to respond to the needs and constraints of their audience. They must also make sure that the chosen formats are appropriate for the type of professional development experiences planned. Figure 12 summarizes the relationship between the format and the type of professional development activity that providers might consider in designing a program:

Figure 12
Acceptable formats for each type of
professional development experience


matrix showing 5 types of professional development experiences

 


Our analysis in Chapters 4 through 8 also confirms that different types of professional development experiences call for somewhat different sets of skills and expertise in the facilitator. Interestingly, in each case we described, the provider could be a mathematics educator, a mathematician, an experienced teacher or a staff development administrator. What really matters is whether the provider has expertise in the discipline of mathematics, pedagogy, and/or mentoring, as required by the specific activity s/he is expected to facilitate.

However, with a few exceptions (e.g., sessions on developing leadership skills), some expertise in mathematics emerges as an important prerequisite for facilitating successful professional development on the teaching and learning of mathematics. At the same time, knowledge of mathematics alone is not sufficient to ensure a facilitator’s success. While mathematicians with an interest in K-12 education are a powerful resource, they too need to become familiar with what helps or hinders adult learning and school reform in order to be effective professional development providers of specific professional development experiences.

Finally, our analysis also identified a number of exemplary materials for mathematics teacher educators. Each of these materials has been developed to support teacher educators in adapting and implementing a specific professional development program with documented effectiveness in supporting school mathematics reform. Just as we encourage mathematics teachers to take advantage of exemplary instructional materials, we also urge teacher educators to take advantage of these resources to strengthen the quality of the programs they offer.

We have provided some information about these materials at the end of Chapters 4 though 8. A more extensive list of worthwhile materials that can support mathematics teacher educators, along with in-depth reviews, can be found in the database for mathematics and science teacher educators (TE-MAT) recently developed by Horizon Research with the support of the National Science Foundation. This database is available on the World Wide Web (address: www.te-mat.org).

Continued
previous page
TOC.jpg
next_page.jpg
CHAPTER 9