Meaningfulness in representational fluency: An analytic lens for students’ creations, interpretations, and connections

Abstract

Representational fluency—the ability to create, interpret, translate between, and connect multiple representations—is key to meaningful understanding of mathematics. This research develops an analytic framework for meaningfulness in representational fluency in linear equation solving tasks. The analytic lens was developed by adapting a structure of observed learning outcome (SOLO) taxonomy. The framework advances a continuum of perspectives including disfluencies and fluencies both within and across representation types. Data from interviews with ninth-grade algebra students solving linear equations with computer algebra systems exemplify the fine-grained analyses of problem solving made possible with this lens. Findings also reveal how lesser meaningfulness in representational fluency may be a productive starting point for more sophisticated reasoning. Implications for research and practice on the interplay between students’ representing and understanding of mathematical ideas are discussed.