A phenomenographic research of the opinions of pre-service teachers about the concept of function

ABSTRACT The aim of this study was to investigate pre-service teachers? opinions about questions on the concept of function which is one of the most important subjects of mathematics education. So, pre-service teachers? difficulties and priorities about concept of function are investigated. The problems about the concept of function were selected from an educational web portal named ?Ask Dr. Math? after expert?s view. For this purpose, 236 questions about concept of function were reviwed and then 22 of them were selected to represent fundamental principles of functions. The selected questions were interviewed by 7 pre-service teachers from the Department of Secondary Science and Mathematics Education of a university in Ankara by employing the phenomenographical research method. Interview records analyzed and their responses coded and categorized for each question. Number of categories were minimized according to reflecting pre-service teachers? responses. According to analysis of data, pre-service teachers have difficulties about - Interrelating the concept of function, the graphics of a function, linear functions and inverse functions with real-life - Graphical drawing, effecting usage of graphics and transforming algebraic representation to graphical representation or vice versa - Determining the domain set of a function and domain set of a composite function - Determining differences and relations between concepts of function, equality and mathematical expressions. - Determining irrational power of a positive irrational number In addition to these results, it was seen that pre-service teachers gave importance to necessities for defining a function and expressed exact rules for defining functions.