Exploring different aspects of the understanding of function: Toward a four-facet model

Abstract

Based on a synthesis of the relevant literature, this study explored students’ display of behavior in four aspects of the understanding of function: effectiveness in solving a word problem, concept definition, examples of function, recognizing functions in graphic form, and transferring function from one mode of representation to another. A main concern was to examine problem-solving in relation to the other types of displayed behavior. Data were obtained from students in grades 11 and 12. Findings indicated that students were more capable in giving examples of function rather than providing an appropriate definition of the concept. The lowest level of success was observed in problem-solving on functions. Students’ problem-solving effectiveness was found to have a predictive role in whether they would successfully employ the concept in various forms of representation, in giving a definition and examples of function.