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Instructional Supports for Representational Fluency in Solving Linear Equations with Computer Algebra Systems and Paper‐and‐Pencil
Author(s) -
Fonger Nicole L.,
Davis Jon D.,
Rohwer Mary Lou
Publication year - 2018
Publication title -
school science and mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.135
H-Index - 2
eISSN - 1949-8594
pISSN - 0036-6803
DOI - 10.1111/ssm.12256
Subject(s) - fluency , sophistication , pencil (optics) , symbolic computation , mathematics education , computer science , context (archaeology) , equivalence (formal languages) , algebra over a field , linear algebra , mathematics , pure mathematics , mathematical analysis , geometry , sociology , engineering , biology , mechanical engineering , social science , paleontology
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.