Generalizing Single Variable Functions to Two-variable Functions, Function Machine and APOS

Abstract

The focus of this study in which the theoretical framework of APOS was used is students' generalizing function notion from single variable to two-variable function concepts in Analysis II course in the elementary mathematics education program. In the teaching process, teaching activities that support generalizing the function notion with multiple representations and relations between them and the function machine were used. For data collection, two tests on each of single and two-variable function concepts and interviews with six students were used. It was concluded that the students' understanding level of function concept and students' schema of three-dimensional space is fundamental for their construction of two-variable function. Moreover, significant results that can support prospective studies for students' conceptual levels of two-variable functions were obtained.