Student Understanding of the Cartesian Connection: An Exploratory Study

The topic of multiple representations of functions is important in secondary school mathematics curricula, yet many students leave high school lacking an understanding of the connections among these representations. Research results are presented from a study in which students' understandings of the connections between algebraic and graphical representations of functions were examined. Responses from 178 students, enrolled in 1st-year algebra through calculus, revealed an overwhelming reliance on algebraic representations, even on tasks for which a graphical representation seemed more appropriate. The findings indicate that for familiar routine problems many students have mastered the connections between the algebraic and graphical representations; however, such mastery appeared to be superficial at best.