Middle school students' development of an understanding of the concept of function using an applet with no algebraic representations

Abstract

Abstract Middle school students ( n = 144) worked with an applet specially designed to introduce the concept of function without using algebraic representations. The purpose of the study was to examine whether the applet would help students understand function as a relationship between a set of inputs and a set of outputs and to begin to develop a definition of function based on that relationship. Results indicate that, by focusing on consistency of the outputs, the students, at a rate of approximately 80%, are able to distinguish functions from nonfunctions. Also, students showed some promise in recognizing constant functions as functions, a known area of common misconceptions. Students' main conceptual difficulty, likely caused by the context, was accepting nonintuitive outputs even if those outputs were consistent.