American students often leave high school with a fragmented and limited understanding of important mathematics (TIMSS, 1997). In response, educators have advocated dramatic changes in math teaching and learning over the past two decades (e.g. NCTM, 1989, 1995, 2000). Some strategies for reform have included: adoption of curricular materials that emphasize connections and meaning, teaching methods designed to foster sensemaking, increased emphasis on classroom activities which allow for direct student engagement with concepts and problems, and a broadening of classroom assessment tools to promote active learning.
The present study focuses on this last reform strategy, changes in classroom assessment to promote active learning on the part of students. Because of its direct relationship to the mathematical values of the larger reform effort, classroom assessment has been an important site for change (Clarke, 1995; NCTM, 1995; Resnick and Resnick, 1992). The idea is that change in teachers' classroom assessment practices will induce changes in teaching practices. This, in turn, will influence students' mathematical learning.
The current study investigates the latter part of this model of assessment reform - the assumption that changing assessment practices will, indeed, influence student learning in mathematics. It provides a close analysis of a high school classroom in the beginning stages of implementing a nontraditional assessment tool, mathematics portfolios. Mathematics portfolios are collections of student work accumulated over a period of time. Students select samples of their work and typically organize these into exhibitions. The exhibitions often require an explanation from the student, either in the form of written or oral reflections on the sample work. Portfolios customarily are evaluated using a criteria-based system, often in the form of a grading rubric, in which a teacher specifies her expectations for the students' work.
Portfolios are a departure from traditional norm-based assessments in several ways. In contrast to paper-and-pencil tests, students have some