Instructional Supports for Representational Fluency in Solving Linear Equations with Computer Algebra Systems and Paper‐and‐Pencil

Abstract

This research addresses the issue of how to support students' representational fluency-the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is targeted as a rich and pressing context to study this issue. We report results of a collaborative teaching experiment in which we designed for and tested a functions approach to solving equations with ninth-grade algebra students, and link to results of semi-structured interviews with students before and after the experiment. Results of analyzing the five-week experiment include instructional supports for students' representational fluency in solving linear equations: (a) sequencing the use of graphs, tables, and CAS feedback prior to formal symbolic transpositions, (b) connecting solutions to equations across representations, and (c) encouraging understanding of equations as equivalence relations that are sometimes, always, or never true. While some students' change in sophistication of representational fluency helps substantiate the productive nature of these supports, other students' persistent struggles raise questions of how to address the diverse needs of learners in complex learning environments involving multiple tool-based representations.

Research on curriculum resources in mathematics education: a survey of the field

“…Altogether 11 studies (3.5%) belong to the category "technology". These studies either use technology that comprises sequenced OTL and thus match the definition of CRs used in this paper, or they investigate issues related to the integration of technology into a curriculum or matters of coordination of different resources including technology and CRs (e.g., Clark-Wilson & Hoyles, 2019;Fonger, 2018). In the latter case, the technology itself is not a CR but an amendment to CRs.…”

GeoGebra Assisted Multiple Representations for Enhancing Students’ Representation Translation Abilities in Calculus

“…Students also lack to relate and translate the representation with the underline mathematical concept (Samsuddin & Retnawati, 2018). Fonger, Davis, and Rohwer (2018) in turn, reported that instructional support enabled student to enhance RF. Students have a huge gap in flexible implementation of MRs during problem solving and bridging them through translation .…”