Framework for Evaluating Written Explanations of Numerical Reasoning

Abstract

Reasoning in mathematics requires communication as often measured through 1:1 think-alouds. Reasoning can also be measured via disciplinary writing in mathematics, which uses a variety of representations to convey meaning, including mathematical words, abstract symbols, and visuals. This study measured numerical reasoning as conveyed via the written explanations of 417 fourth-grade students. Whole group administration procedures were followed to collect data on reasoning about fraction magnitude. Explanations were scored using a validated framework for evaluating numerical reasoning. Results include descriptive statistics and qualitative analyses of examples across the framework's five categories. Written explanations coded as “conceptual” reflected the richest examples of disciplinary writing in mathematics. Conclusions include the usability of this framework to adequately measure numerical reasoning at the elementary level. Implications include the importance of using formative assessment tools in the classroom.