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

Discussion on the Case

In developing her portfolio Margaret collected evidence from multiple investigations that related to a common theme: the importance of structuring activity in the classroom. Although Margaret, herself, did not use her portfolio to reflect on the issue of structure in her classroom, she developed the "Things I Modified" section, and the evidence was there for me to interpret and act upon during the semester. Margaret's teaching portfolio helped me as her instructor discern a pattern in her beliefs about teaching mathematics and to use it to reflect on her growth as a teacher. In doing so, her portfolio enabled me to make connections between Margaret's beliefs and practices and my goals for the methods course. Since the "Things !Modified" section was created by Margaret and not required for her portfolio, Margaret created the space where this engagement occurred. By portraying this aspect of her teaching in her teaching portfolio, she enabled me to better assess and assist in her growth.

Margaret's investigations are noteworthy because of the different ways her beliefs about structure manifested themselves in her instructional practices. In the case study Margaret's beliefs about structure were apparent in two ways in her portfolio: (a) structuring activity time and (b) structuring mathematical tasks. The first, a positive manifestation of her beliefs, helped her identify an instructional goal that may lead to improved student achievement. The second instance, however, might illustrate a way that Margaret's beliefs were denying some of her students an opportunity to develop skills necessary to be successful in the mathematics classroom.

Although both of these interpretations are somewhat speculative, the collection of investigations of student work in Margaret's portfolio is an observable fact. This fact identifies a benefit from the use of the portfolio in the methods course: It helps prospective teachers acquire methods to document their teaching and describe it in a medium designed to support reflection on multiple performances. Although in this case the comparative analysis was conducted by Margaret's instructor, the substance of the analysis resulted from her own inquiries. As aresult, Margaret' s portfolio held the potential for her to undertake similar comparative analysis, as well as further investigation.

In planning for teaching the methods course in future semesters, I used the evidence from Margaret's portfolio to generate several conjectures about her learning and that of other prospective mathematics teachers. As discussed previously, my recognition of Margaret' s belief that students succeed in mathematics when teachers structure their opportunities for learning led me to offer a prompt for further investigation (i.e., "What distinguishes a successful student of mathematics from a struggling student in your classroom?"). In following up on Margaret's initial exploration, I might have asked the student teachers to collect evidence showing that the assessment practices they used to measure success were aligned with the learning opportunities they afforded their students. Such a formative assessment would create the opportunity for the student teachers to delve deeper into the relationship between their own beliefs about practice and their students' learning. By identifying such openings in the methods course curriculum, Margaret's portfolio supported my own pedagogical inquiries at two levels : (a) What are the beliefs that currently orient the student teachers' instructional practices? and (b) In what ways can the methods class influence those beliefs and the practices that result from their enactment?