The Effect of Concept Mapping on Community College Precalculus Students' Conceptual Understanding of Inverse Functions

Abstract

The purpose of this study was to investigate the efficacy of concept mapping on community college precalculus students' conceptual understanding of inverse functions. This study employed a quasi-experimental nonequivalent control group design in which a single instructor taught one experimental precalculus algebra class and one control precalculus algebra class. Students in the experimental group (n = 15) participated in one collaborative 'System of Equations' concept mapping exercise. These students also individually constructed maps given the seed concepts 'Inverse' and 'Functional Inverse.' Other than the concept mapping treatment, all assignments, assessments and instruction were equivalent for the experimental and control groups (n = 21). The duration of the experiment was about 12 weeks.

Three veteran mathematics community college instructors and two professors of mathematics education from a local university collaborated to create criterion maps for this study. The Markham, Mintzes and Jones' rubric for scoring science-oriented concept maps and these criterion maps were used to quantify students' individual maps. Quantification of the maps relied on seven components: concept, link, hierarchy, initial branching, successive branching, crosslink, and example. Other data collected for analysis in this experiment includes pretest diagnostic scores, unit test scores and selected subscores, a routine writing assignment score, final examination subscore, and a variety of demographic data. ANOVA and a Backward Elimination model (alpha = .05) revealed that the inverse function map score is significant and contributes to significant variation in the final course grade. However, distribution-free and independent non-equivalent t-tests disclose very few significant differences between the two groups for the duration of the course. Qualitative analyses of the (1) mathematics instructors and professors surveys on concept mapping usefulness, (2) system of equations and inverse function maps, and (3) the follow-up survey provided further evidence that concept mapping supports the NCTM and AMATYC Standards.