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

School Science and Mathematics, Dec 2004 by Hartmann, Christopher

Based upon the evidence from Margaret's portfolio, this prompt resonated with her beliefs about the importance of structuring student activity in her classroom. In response she investigated the hypothesis that unsuccessful students failed to take full advantage of all of the ways she structured their activity. Margaret planned a study to explore whether or not her students take notes when homework is reviewed in class. One day in class she distributed marking pens to all of her students prior to reviewing homework so that she could distinguish between their original work on the assignment and the notations made during the review. After the review she collected the students' work and sorted the papers into five groups by the students' current performance (A, B, C, D, U). Then, she compared the quality and quantity of the corrections that were made by the students in each group. The work of one successful student (Grade=A) and one unsuccessful student (Grade = U) are illustrated in Figures 1 and 2, respectively.

As Margaret presented the evidence from her investigation in her teaching portfolio, the successful students in her class made the most detailed corrections to their home work. For example, consider the students' annotations to Problem 2 in Figure 1 and Figure 2. In Figure 1 the successful student originally found that 2/9 2/6 = 4/15. During the review the student rewrote the sum in terms of a common denominator and made explicit note of the fact that the denominator "stays same." In Figure 2 the student simply recorded the correct the answer. Although both students originally answered the problem incorrectly, the student in Figure 1 made corrections that identified her mistake and labeled it in reference to the rules for adding fractions that were taught in the class.

Margaret's commentary below the images in Figures 1 and 2 presents her interpretation of the differences between these two students' work during the review session. Margaret used this evidence to infer that taking detailed notes during homework review time led to differences in student achievement in her class. The inference she made from this evidence was consistent with her belief that the teacher must play a strong role in structuring students' mathematical activity. When I interviewed her at the end of the semester, Margaret described how this investigation influenced her learning as a prospective mathematics teacher:

Instructor: What does that tell you about the students, then, and what you might do as a teacher?

Margaret: I guess if you started at the beginning of the year emphasizing that they need to show their work and maybe just stressing more that they need to take notes if they didn't understand something and let them know that that's a part of their grade that might help. (Portfolio Interview 1)

Because Margaret identified the importance of active participation in the review of homework, her study appeared to be a success. Most good teachers promote classroom norms such as active participation in the review of homework. In this case the evidence in her portfolio supported her identification of this goal.