An empirical four-dimensional model for the understanding of function
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Based on a synthesis of the relevant literature, this study explores students’ abilities in four aspects of the understanding of function: problem solving, concept definition, examples of function, recognizing functions in graphic form and transferring functions from one mode of representation to another. A main concern is to examine problem solving in relation to the other abilities. 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. Problem solving was found to have a predictive role in how students would apply the concept in various forms of representation, in giving a definition and examples of function.