The Effects of Multi-Representational Methods on Students' Knowledge of Function Concepts in Developmental College Mathematics

Abstract

The purpose of this study was to investigate the potential benefits of a multi-representational curriculum on students' understanding of and connections among graphical, tabular, and symbolic representations of algebraic concepts.

The participants of the study were 313 college students enrolled in developmental college algebra at two southern universities. This study utilized a quasi-experimental design in which instructors at one university (control) taught the course from a traditional algebraic perspective while instructors at the other university (treatment) taught the course from a functional approach simultaneously introducing multiple representations.

The effect of a multi-representational curriculum on student success and representational preference was assessed with a pretests and posttests of five problems, each with three representations; graphic, tabular, and symbolic. The problems were chosen because of their prevalence in most developmental college algebra curricula. Although both curricula were successful in increasing student achievement, students from the multi-representational curriculum scored significantly higher and were significantly more adept in using representational methods other than algebraic to solve the problems.

Qualitative interviews were also conducted with eight participants from each school to examine the connections that students were making and their ability to move flexibly among the graphical, tabular, and algebraic representations. The interviews were analyzed using Biggs and Collis's SOLO Taxonomy. This research showed that a multi-representational curriculum could be effective in expanding students' web of connected knowledge of algebraic and functional concepts. The SOLO Taxonomy and rubric defined in this research gives teachers an effective way of measuring student learning.