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
 |
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
 |
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
