Using Teacher Portfolios to Enrich the Methods Course Experiences of Prospective Mathematics Teachers

In this paper two ways that my reading of Margaret's teaching portfolio positively impacted my instruction during the methods course are described. First, her teachingportfolio helped me identify how the prospective teachers in my course were reflecting on their beliefs about teaching mathematics. Second, Margaret's portfolio enabled me to respond to her needs as an individual teacher in ways that resulted in a richer dialogue about the teaching of mathematics within the methods course as a whole. In this way, the process of mentoring prospective teachers in the methods course became more dialectic. Although I had similar engagements with Margaret's peers through reflection on and conversation about their teaching portfolios, Margaret's case is discussed in this paper because the data best illustrate the ways the use of the portfolio influenced my practice.

Discussions of Sases of Student Thinking

During meetings of the methods class the prospective teachers regularly engaged in small group discussions of examples of their students' work on mathematical tasks. This activity structure generated most of the examples presented in the case study, so it will be described in detail. At the beginning of the semester I divided the class into groups of four teachers per group. Student teachers were required to collect artifacts of student work from their field experience classroom to present to the group during a 30-minute discussion held every other week. During these discussions teachers briefly described ways that the student work in the artifacts influenced their thinking as mathematics teachers. Afterward, the group reacted to the artifacts. As the semester proceeded I began to offer prompts to better focus the student teachers' selection of student work samples. The decision to provide these prompts was motivated by two observations: (a) Some individuals had difficulty identifying examples of student work that would interest other teachers, and (b) often the diversity of the examples of student work within a group did not lend itself to a general conversation at the conclusion of the presentations. After making these two observations I used specific artifacts from the prospective teachers'portfolios to identify prompts to focus the collection of student work. For instance, my interpretation of one of the artifacts in Margaret's portfolio led me to offer the following prompt: What distinguishes a successful student of mathematics from a struggling student in your classroom? The case study described in this article follows the development of this intervention across the semester.

Case Study: Margaret Explores Her Teaching

Margaret completed her student teaching in a middle school. During this experience she taught several units from the Connected Mathematics Program (CMP) curriculum (Lappan, Fey, Fitzgerald, Friel, & Phillips, 1998). Margaret described the curriculum materials as "poorly designed" based on her perceptions of her students' needs as learners of mathematics (Portfolio Interview 1). In response, Margaret frequently revised worksheets from the curriculum before using them with her students. Within her teaching portfolio these revisions were collected in a separate, optional section entitled, "Things I Modified." In describing one of the artifacts from this section Margaret argued that worksheets should include tables designed to help students collect and organize data, because some students are not capable of organizing their own mathematical investigations: