Compose Yourself: It's Just a Function!

Abstract

This research examines students’ understanding and ability to work with composition functions in different representations. Its underlying purpose is to analyze students’ level of procedural knowledge and conceptual understanding of composite functions and to identify common errors and misconceptions associated with these functions. It was hypothesized that college students would incorrectly substitute one function into another when evaluating at a variable. Furthermore, it was hypothesized that evaluating a function value at a constant would produce better results as well as working with visual representations, such as tables and graphs. The results of this study indicate that non-mathematics major college students have neither strong conceptual understanding nor adequate procedural fluency in terms of composition functions. However, there was no significant difference between evaluating constants versus variables in the functions. Additional results revealed that while visual and algebraic representations produced no significant differences in their means (p-value = 0.545), algebraic notation negatively influenced students’ solving capabilities (p-value = 0.000).