(Page 3 of 7) - Sixth Grade Mathematics Teachers in Transition: A Case Study authored by Bergthold, Trisha. and Roddick, Cheryl.

(2001), the primary data consist of teachers’ written responses to structured journal prompts,
written learning activities and teacher notes, oral comments made during interviews, and actions
exhibited during classroom observations. These data were analyzed to identify turning points in
these teachers’ knowledge, perspectives, and practices.

Participants

The two sixth-grade mathematics teachers in this case study, Celia and Dee, were

purposefully selected. Both researchers had worked with these teachers during a year of content-
based professional development institutes. Over this period, both of these teachers demonstrated
initiative to improve their teaching, a desire to learn new mathematical and pedagogical content,
a willingness to try new teaching practices, and engagement in ongoing reflections on
mathematics and the teaching of mathematics. On the other hand, Celia and Dee varied
significantly in their mathematical knowledge and teaching experience. Dee, with over 30 years
of teaching experience, had taken calculus in college, whereas Celia, with 7 years of teaching
experience, had taken the required 6 hours of mathematics coursework for future elementary
school teachers while in college. The researchers felt that this combination of qualities would
provide sufficient variability in knowledge and teaching experience to elicit rich comparative
data while minimizing the need to account for motivation.

Selected Learning Activities

Three of the learning activities developed during the summer workshop were selected for

intensive study and follow-up support. It was agreed that these three activities were well-
developed and well-spaced throughout the curriculum. The first two activities involve a birthday
party business, called Perfect Party Place, which provides and sets up card tables for birthday
parties. Each table is square and seats one child on each side. These square tables are arranged
into a single rectangle at each party. Depending on the location, the tables must be set up
differently each time. The first activity involves exploring the possible rectangular table
arrangements for a party with 18 children and identifying patterns in table arrangements,
dimensions, and areas. This scenario stipulates a fixed perimeter and requires an investigation of
different areas that correspond to the perimeter of 18. The second activity involves exploring
possible table arrangements for a party that can accommodate 24 tables and identifying patterns
in table arrangements, dimensions, and perimeters. A connection can be made between the
dimensions of the different tables and the factors of 24. The third activity, Rectangle Ratios,
involves the exploration of similar rectangles. Students are given a collection of 14 rectangles
and asked to sort them into “families”. This is followed by exploration of ratios of length to
width and how this relates to the idea of similarity of rectangles. In the results, we refer to the
first and third activities.

Data Collection and Preparation

Journal Prompts

We asked each teacher to respond in writing to journal prompts at three points in time during

the project: before the summer workshop, after the summer workshop, and at the conclusion of
the project. In the first set of journal prompts, we asked Celia and Dee to write a math
autobiography and describe some of their current teaching practices. In the second set of journal
prompts, we asked Celia and Dee to comment on the effectiveness of the workshop activities.
The final set of journal prompts asked for their reflections on the overall project as well as their
impressions of how and why their knowledge, perspectives, and teaching practices had changed
over the course of the project.
Classroom Observation Protocols