Nicole L. Fonger

Doctoral Dissertation Announcement

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Candidate: Nicole L. Fonger

Degree of: Doctor of Philosophy

Department: Mathematics

Title: Characterizing and Supporting Change in Algebra Students’ Representational Fluency in a CAS/Paper-and-Pencil Environment

Committee:
Dr. Jon D. Davis, Chair
Dr. Steven W. Ziebarth
Dr. Rose Mary Zbiek
Dr. Christine A. Browning

Date: Friday, June 29, 2012 10:00 a.m. to Noon
6625 Everett Tower

Abstract:
Representational fluency includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students’ representational fluency in learning environments that utilize both computer algebra systems (CAS) and paper-and-pencil. The purpose of this research is to: (a) characterize change in ninth-grade algebra students’ representational fluency in solving problems involving linear equations, and (b) determine conditions of a CAS and paper-and-pencil learning environment in which those students change their representational fluency.

Change in representational fluency is measured by comparing results from initial to final semi-structured task-based interviews using a specifically designed framework. Conditions of the learning environment are conjectured prior to the study, tested during a five-week collaborative teaching experiment, and revised during ongoing and retrospective analyses.

Results from case studies of three select students, and several components of an empirically-based instructional theory will be presented including: an activity structure, a learning progression, and classroom expectations. A revised activity sequence will also be suggested. Improving one’s representational fluency may be connected to affect and disposition toward mathematics. Implications for instructional design including the coordinated use of CAS and paper-and-pencil will be discussed.