Mathematics portfolios, NCTM goals, and students' perceptions: A complex analysis

The National Council of Teachers of Mathematics (NCTM) has recommended changes in mathematics curriculum, instruction, and assessment, with these three documents: Curriculum and Evaluation Standards for School Mathematics (1989), Professional Standards for Teaching Mathematics (1991), and Assessment Standards for School Mathematics (1995). Many mathematics educators advocate the use of portfolios as one possible assessment reform.;This study investigated mathematics portfolios from the perspective of high school students who created their own. In addition, the teacher's perspective was examined, as the teacher's role in the implementation of portfolios was significant to the final results. The research question was: What are high school mathematics students' perceptions about portfolios as a tool for assessment, that is, for demonstrating their progress in fulfilling mathematics goals? The goals are: (a) students learn to value mathematics, (b) students become confident in their mathematical ability, (c) students become mathematical problem solvers, (d) students learn to communicate mathematically, and (e) students learn to reason mathematically (NCTM, 1989).;The study was conducted during the first semester of the 1995-96 school year in a small, rural high school. The subjects were three twelfth grade students in a class using integrated, innovative mathematics curriculum featuring real-world applications and utilizing technology, group work, and investigation. Students were to select their own portfolio items specifically documenting their accomplishments relative to the five NCTM student goals. Qualitative methods of data collection and analysis were utilized. For data analysis, the researcher used the method of constant comparison.;Students' interpretations of some NCTM goals did not align with the intent of NCTM and also varied from student to student. As a result, grading the portfolios proved to be problematic for the teacher. However, the students reported thinking critically about the meanings of the goals. One semester may not have been an adequate time period for the students to completely develop their portfolios with respect to all five of the goals. More effective classroom communication may have helped the teacher in implementation of portfolios. However, the teacher employed varying strategies to facilitate portfolio implementation. It appeared that the real value of portfolios in this study was as an information source for the teacher and a learning tool for the students.