Advanced Mathematical Thinking Vol.2-23 AN ANALYSIS OF STUDENTS ’ IDEAS ABOUT TRANSFORMATIONS OF FUNCTIONS

This study intends to contribute to better understand students ’ difficulties with transformations of functions. Students were interviewed while solving problems involving transformations of functions. Results were analyzed using APOS theory (Asiala, et al., 1996). They show that few students can work confidently with these problems because they do not seem to have interiorized the processes involved in transformations, or encapsulated those processes into objects. The study of families of functions and transformations on them (such as translations, reflections and stretches) has become important in pre-calculus courses at universities. Transformations give students new opportunities to use and reflect on the concept of function, and they can become a useful tool in more advanced topics of mathematics. Research on students ’ understanding of transformations of functions is important not only because it is a topic in many pre-calculus courses, but also because it provides an opportunity to analyze students ’ ideas on functions and variables. It also permits to study students ’ flexibility with the use of different representations of function. All this information can be used as a guide in the design of teaching materials and class strategies with the purpose of trying to foster students ’ understanding of both functions and transformations of functions. Antecedents Some researchers have worked on the concept of transformations of functions (Baker, et al.