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Journal of Undergraduate Research

Keywords

open-response task, fifth-grade students, fractions

College

Physical and Mathematical Sciences

Department

Mathematics

Abstract

Inferring student understanding is at the heart of improvement in mathematics learning and teaching. Assessment provides valuable information which can be used to “promote growth, modify programs, recognize student accomplishments, and improve instruction” (NCTM, 1995, p.27). It is imperative that the methods for assessing student understanding be constantly explored and evaluated. Ou decision to research the open-response task as an assessment tool results from our perspective that students make sense of mathematics by exercising personal agency. Personal agency is the freedom and responsibility to choose to act (Walter & Gerson, 2006). Open-response tasks allow students to exercise personal agency, hence eliciting not only what students know, but also how students explore concepts. Open-response tasks require “students to explain their thinking and thus allow teachers to gain insights into…the ‘holes’ in their understanding” (MOON &Schulman, 1995, p.30). How can “holes” in student understanding be inferred from analyses of student strategies in solving open-response tasks? Does a student’s strategy choice indicate a lack of proficiency or conceptual understanding that may be evidenced in alternative strategies?

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