The use of computer algebra systems in a procedural algebra course to facilitate a framework for procedural understanding

Abstract

This dissertation study evaluated the implementation and effectiveness of an introductory algebra curriculum designed around a Framework for Procedural Understanding. A Computer Algebra System (CAS) was used as a tool to focus lessons on the Framework and help students gain a deeper, well-connected understanding of algebraic procedures. This research was conducted in response to the prevalence of remedial mathematics and addresses the need for students in remedial mathematics to have a successful learning experience. The curriculum was implemented in the Spring 2007 semester at a western land-grant university. In this quasi-experimental study, one section of introductory algebra was taught using the CAS/Framework curriculum. This treatment section was determined based on a pretest used to judge equivalency of groups. Data sources included procedural understanding assessments with follow-up student interviews, procedural skill exams, classroom observations, and a debriefing interview with the treatment instructor. Qualitative analysis of student and instructor interview transcripts was done to supplement independent observation reports to evaluate the implementation of the curriculum.

Analyses of covariance and independent samples t-tests were used to compare treatment and control groups based on the quantitative measures. The treatment instructor and students were able to integrate CAS technology into the classroom without difficulty. The instructor implemented the curriculum with fidelity but the discourse in the classroom did not reach the desired level. No significant difference was found between treatment and control students on the skills-based final exam, indicating that the introduction of CAS did not diminish procedural skill levels. No difference in procedural understanding based on the Framework was observed. The data indicated that the students viewed mathematics as learning how to do procedures. This philosophy of mathematics and the limited classroom discourse impeded progress towards learning other aspects of the Framework. Recommendations include changing classroom norms to foster more discussion and placing more emphasis on Framework-based understanding in the assessment structure and course grade.