### 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.

Original language | English (US) |
---|---|

Journal | Journal of Mathematical Behavior |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- Algebra and Algebraic thinking
- Computer algebra system (CAS)
- Learning
- Meaning
- Representational fluency
- Representations

### ASJC Scopus subject areas

- Education
- Applied Psychology
- Applied Mathematics

### Cite this

**Meaningfulness in representational fluency : An analytic lens for students’ creations, interpretations, and connections.** / Fonger, Nicole.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Meaningfulness in representational fluency

T2 - An analytic lens for students’ creations, interpretations, and connections

AU - Fonger, Nicole

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Algebra and Algebraic thinking

KW - Computer algebra system (CAS)

KW - Learning

KW - Meaning

KW - Representational fluency

KW - Representations

UR - http://www.scopus.com/inward/record.url?scp=85061722055&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061722055&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2018.10.003

DO - 10.1016/j.jmathb.2018.10.003

M3 - Article

AN - SCOPUS:85061722055

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

ER -