Exploring secondary students' conceptualization of functions in three curriculum contexts

An important goal in school mathematics is for students to develop a comprehensive and multifaceted conceptualization of function. Yet studies have found that undergraduate students often hold limited concept images for function. This study investigated 240 middle and upper secondary (15- to 18-year-old) students' conceptualizations of function at different year levels (Years 9 to 12) to consider their conceptualizations relative to certain prior learning, as theorized by an epistemological model for concept development in mathematics. In this article we draw on data from students and their teachers in three Western national curriculum contexts (Israeli, English, and Australian) to explore possible relationships among students' exposure to the word `function', familiarity with different examples of functions, and their conceptualizations of function. Eighty high-achieving students from each context, 20 per year level, were prompted to respond to several fictitious students' views on what a function is, and then to provide their own definition. The students' responses were analyzed for evidence of a dominant meaning and any contributing ideas, as well as the use of any specific examples or non-examples of function to illustrate or clarify their views. Twenty teachers also participated in the study. Analysis of curriculum content and the teachers' perspectives on their students led to our search for possible reasons for similarities and differences found among the responses.