A Cluster Analysis of Precalculus Student Performance on Function Translation Fluency Test Items

Abstract

To determine the existence of individual and group differences in 199 precalculus students' abilities to interpret graphs of mathematical functions and relationships between graphical and algebraic function representations, two parallel cluster analyses were performed on the results of a ten item dichotomous test of mathematical function literacy and translation fluency. Cluster means from two hierarchical methods, Ward's (N =199) and average linkage (N =187), were used as seed values for two separate nonhierarchical k-means cluster analyses. Four clusters emerged from the Ward's based nonhierarchical solution and three clusters emerged from the average linkage based nonhierarchical solution. Both nonhierarchical solutions were externally validated using Likert-type scale items measuring mathematics anxiety, attitudes toward the precalculus teacher, visualization skills, and gender. Gender was associated with cluster membership for both nonhierarchical solutions. Student perception that the precalculus teacher skipped steps in demonstrating problems in lecture predicted cluster membership for both nonhierarchical solutions.