The effectiveness of portfolios in assessing students' connections between mathematical symbols and mathematical concepts

Abstract

The purpose of this study was to assess the effectiveness of mathematics portfolios in determining the type of connections students were making between mathematical concepts and mathematical symbols. A mathematics portfolio is a purposeful collection of student work where a variety of assignments, projects, reports, and writings are collected that exhibit the students' efforts, progress, and achievements in one or more areas of mathematics. This study evaluated portfolios collected from 5th grade mathematics classes taught by the researcher. The regular class consisted of twenty students while the advanced class consisted of twenty-five students. This study compared responses to a ten-item student survey given at the beginning and the end of the school year. Student responses were evaluated according to the degree of change between their beginning response and their ending response and the results were compared between the classes. The study looked for evidence of connections in student writings by evaluating common components of student work found in the portfolios. Ten student portfolios were randomly selected from the total pool of portfolios. Each portfolio selected was evaluated using the "Student Writing Scale" instrument. The study compared student portfolios to determine if the use of symbols in student writing was evidence that students were making mathematical connections. Portfolios rated as having "high-levels" of connections were compared with those rated as having "low-levels" of connections. The findings on the student survey showed a significant difference in the amount of change from the beginning to the end of the year between the regular class and the advanced class on 2 of the 10 questions. Seven of the 10 portfolios were rated as "developing", 2 portfolios were rated as "understanding and applying", and I portfolio was rated "not understanding." The study also revealed three components of student writing which illustrated that mathematical connections were being made. The study also showed a connection between the use of symbols in student writing and an understanding of those symbols. Findings of this study suggest that portfolios offer valuable insight into the learners head enabling the instructor to determine if connections are being made between symbols and concepts.