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What Does Effective Professional
Development Look Like?
Before analyzing in more depth how the
teacher learning needs identified in the previous chapter might
be addressed, we would like to provide some images of
professional development projects that have been successful in
supporting school mathematics reform.
It was difficult to select just a few out
of the many creative professional development programs of the
last two decades (as featured, for example, in Friel &
Bright, 1997; Fennema & Nelson, 1997; Loucks-Horsley,
Hewson, Love, & Stiles, 1998; Eisenhower National
Clearinghouse [ENC], 2000). We eventually chose the two
projects featured in this chapter because they differ
considerably in terms of scope, goals, complexity, audience,
context and grade levels. Therefore, we hope these examples
will begin to show how the teacher learning needs described in
Chapter 1 can be met in many diverse and viable ways.
In this chapter, we describe each project
in some detail to convey a sense of its vision and complexity.
Space constraints do not allow us for detailed descriptions of
specific professional development activities within each
project, although some of these will be described in more depth
in vignettes reported in later chapters.
An implementation of the Cognitive Guided
Instruction (CGI) program
We derived this first illustration from
one of the many implementations of the CGI program as reported
in Fennema, Carpenter, Franke, Levi, Jacobs and Empson (1996).
The same article also provides evidence of the effectiveness of
this specific professional development program in addressing
teachers’ beliefs, changing practices and increasing
student achievement.
In this four-year project, a group of
first-third grade teachers from four different schools
volunteered to participate for minimal compensation and the
option of receiving graduate credits for their work. The main
goal of this program was to “help teachers develop an
understanding of their own students’ mathematical
thinking and its development and how their students’
thinking could form the basis for the development of more
advanced mathematical ideas” (Fennema, Carpenter, Franke,
Levi, Jacobs, and Empson, 1996, p. 406), as a main vehicle to
improve mathematics instruction in their classes.
During the first two years, the teachers
attended a series of workshops: A 2 1/2-day workshop in late
spring of the first year, a 2-day workshop in the summer and 14
three-hour-long workshops during the following academic year.
The workshops introduced the teachers to a research-based model
of how young children understand basic number concepts and
operations (for empirical research on this issue, see
Carpenter, Fennema & Franke, 1994; Fuson, 1992; Greer,
1992). This approach is based on the assumption that increasing
teachers’ knowledge of students’ thinking helps
them design better instructional tasks, ask better questions
during mathematics lessons and support individual
students’ learning more effectively.
Although the teachers read articles
explaining the basis of the model in research, they primarily
focused on analyzing students’ mathematical thinking from
samples of written works or videotapes of problem-solving
sessions. Participants did not receive an explanation of each
child’s solution; rather, they examined the similarities
and differences among different children’s approaches and
generated hypotheses about the mathematical concepts underlying
them. Facilitators often asked participants to validate the
research model by observing students in their own classes and
discussing the results with the rest of the group.
The project purposefully made the
decision not to provide teachers with any instructional
materials or guidelines. Rather, they encouraged the teachers
to use their growing knowledge of students’ mathematical
thinking to inform their instructional decisions. However,
participants did receive support in translating their new
knowledge into instructional practice from a project staff
member and a mentor teacher assigned to each school. These
teacher educators attended all workshops, visited each
participant’s classroom about once a week and worked
individually with teachers to support their instruction.
In the following two years, teachers
continued to participate in some workshops during the school
year (four 2 1/2-hour workshops and a 2-day reflection workshop
in year three, and one 3-hour reflection workshop and two 2
1/2-hour review workshops in year four). These workshops,
however, did not introduce new information about the research
model. They focused instead on helping teachers observe the
mathematical thinking of their own students’ and make
instructional decisions based on what they had learned.
Participants continued to receive on-site support, but the
classroom visits were reduced gradually (once every two weeks
in year three and only occasionally in year four).
Making mathematics reform a reality in
middle schools
Making Mathematics Reform a Reality in
Middle School (MMRR) was one of the Local Systemic Change
projects that the National Science Foundation (NSF) funded to
promote school mathematics reform in whole schools or
districts. This three-year project was aimed at beginning the
process of systemic reform in four suburban middle schools that
had not adopted – nor yet decided to adopt – one of
the new NSF-funded curricula for middle school mathematics. As
such, the project involved all the teachers responsible for teaching
mathematics at these school sites, which included teachers
certified to teach secondary mathematics, special education
teachers and even a few elementary teachers. Professional
development, as the core of this project, consisted of several
initiatives designed for teachers at different stages of
development. In a recent national study (Killion, 1999), this
program was cited as one of only eight in the country that have
demonstrated a positive effect on students’ mathematical
learning in middle school.
Teachers joined the project by attending
a one-week introductory Summer Institute and participating in
related field experiences during the following year (as
described in Borasi, Fonzi, Smith & Rose, 1999, and in even
more detail in Borasi & Fonzi, in preparation). In the
Summer Institute, teachers learned about an inquiry approach to
teaching mathematics as a way to teach all students better.
In the spirit of the NCTM Standards, the Summer Institute and
its follow-up field experiences invited teachers to rethink
their mathematical and pedagogical beliefs from a
constructivist/inquiry perspective. It also enabled them to
experience the power of learning mathematics themselves through
inquiry activities and helped them actually begin the process
of instructional innovation in their classes. Finally, it
fostered a need to continue in the reform process.
Two illustrative inquiry units (i.e., the
unit on area formulas informing our classroom vignette in
Chapter 1 and another unit on tessellations) played a critical
role in this program. These units modeled how middle school
students could learn key ideas in geometry and measurement through
inquiry. A team of mathematics education researchers and teachers
had previously developed these units and successfully
field-tested them in a variety of middle school settings
(Borasi, Fonzi, Smith & Rose, 1999). They had also created
a set of materials to support teachers in implementing each of
these units (Borasi, 1994 a&b; Borasi & Smith, 1995;
Fonzi & Rose, 1995 a&b). To participate in the Summer
Institute, teachers had to commit to teaching one of the
inquiry units in the following school year.
During the Summer Institute, teachers
first participated, as learners, in two 5-hour mathematical
inquiries on tessellations and area similar to those in the
illustrative units. During these mathematical learning
experiences, the facilitators modeled several inquiry-based
teaching practices recommended by the NCTM Standards. These
“experiences as learners of mathematics” served as
the catalyst for teachers to reflect on the nature of
mathematics and on teaching and learning, as each inquiry was
followed by one or more sessions in which participants
discussed these experiences from different perspectives. These
inquiry-based experiences also introduced teachers to the unit
they had committed to teach as part of their follow-up field
experiences. The Summer Institute supported teachers in their
first experience of instructional innovation in other ways.
Teachers watched a video and read an accompanying narrative
that documented the implementation of these units with middle
school students. They were also introduced to the supporting
materials accompanying each unit, and they participated in an
initial planning session for their own unit.
As participants planned and implemented
their chosen unit, they were supported by a lead teacher or a
mathematics teacher educator assigned to be a facilitator in
their schools. They could also participate in a follow-up
meeting where other teachers who had implemented their first
inquiry unit shared and discussed these experiences. Then,
facilitators introduced teachers to some of the NSF-funded
exemplary mathematics curricula for middle school as resources
to support their planning of additional innovative
instructional experiences. Teachers were encouraged to try at
least a unit from one of these series in their classroom before
the end of the school year.
Teachers who participated in this
year-long component were then eligible to participate in a
second, 5-day Advanced Summer Institute and its related field
experiences. This second Summer Institute focused on the
teaching and learning of algebra in middle school and on
helping teachers become familiar with two of the NSF-funded
curricula for middle school: the Connected
Mathematics Project (CMP) and Mathematics in Context (MiC). As follow-up field experiences, teachers committed
to implement at least one algebra unit from one of these
curricula during the school year.
Continued
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CHAPTER 2