We both were present as participant-observers at each of several class sessions for each
teacher, while she implemented three selected activities developed in the summer workshop. We
took extensive field notes, structured as chronological records of all class activities during each
observation session. After each observation, we reviewed and revised our notes, adding
parenthetical remarks noting our impressions and questions to ask each teacher during post-
activity reflective interviews.
Interview Protocols
Interviews were conducted with each teacher after each classroom observation to reflect on
how well the activity went. In addition, joint interviews with both teachers were conducted after
we had observed the same activity in both teachers’ classes, to discuss common problems,
activity revisions, and extensions. Interviews were loosely structured to allow free-ranging
exploration of issues related to their practices, including mathematical content knowledge and
pedagogical perspectives. We audio-taped each interview and took notes as well. Interview
tapes were then transcribed.
Data Analysis
Two data matrices were designed to help organize the data, one for each teacher. These
matrices focused on (1) mathematical knowledge and abilities, (2) perspectives, and (3) teaching
practices at each of six different points during the professional development project: (a) pre-
workshop, (b) post-workshop, (c-e) each of three activity observations, and (f) project
conclusion. Each cell of each data matrix contained relevant evidence drawn from written
responses to journal prompts, comments during interviews, and practices exhibited during
classroom observation. These data matrices were analyzed for changes in each teacher’s
knowledge, perspectives, and practices over the course of the project.
Discussion
Over the year-long course of our professional development activities, these teachers
exhibited significant changes in their knowledge, perspectives, and practices. Moreover, these
three aspects of teaching seem to be interconnected in a fairly complicated way.
Knowledge
Pre-Workshop Knowledge
Over the course of getting to know Celia, she revealed some insecurity about her knowledge
of mathematics. In an early journal entry, she commented, “In high school, I was a failure in
math because I knew basic math well, but I could not comprehend the abstract in algebra
.
”
Celia’s completion of a 40-hour professional development institute in fall 2002 and a special
three-unit university course for in-service mathematics teachers in spring 2003 contributed to a
significant broadening of her mathematical knowledge and abilities. In a later interview, she
mentioned that these experiences resulted in greater confidence in her abilities.
Dee began her college career majoring in math. She took four quarters of calculus as well as
abstract algebra and symbolic logic before switching to another major. Dee completed the same
institute and university course as Celia during the 2002-2003 academic year, but in Dee’s case,
these experiences deepened and strengthened her mathematical knowledge and abilities. She
commented in an early journal entry, “I was far better prepared to teach probability, ratio and
proportion, and percent than before.” In both her written and oral work, she appears to have a
greater understanding of mathematics than the average middle school mathematics teacher.
Changes in Knowledge
Changes in their knowledge and abilities occurred during the professional development
sessions and throughout the following school year. Their knowledge of mathematics broadened
Convention