Examination of the Concept Images of Pre-service Teachers for Single-Variable and Multi-Variable

Abstract

This study aims to examine the concept images of pre-service mathematics teachers for the concepts of single-variable and multivariable functions. In the present research, which was conducted with the case study method, a test consisting of three open-ended questions was used to obtain data about the definition of the concept of function and the concept images of the single and multivariate functions of the pre-service teachers. The data obtained were coded with the descriptive analysis method and analyzed qualitatively. Each coding was given as a theme with frequency and percentage values and the answers given by the pre-service teachers were presented as examples. The findings obtained in this study showed that the pre-service teachers' concept images about function consisted of different representations of the concept of a function and concept images were generally classified as matching, transformation and equation. The pre-service teachers' concept images of the concept of function also had incomplete learning and misconceptions. That definition and value sets, which are important components of the concept of function, were not included in the answers. The pre-service teachers defined the functions as f(x) in multivariate function examples, and they ignored that x represents the only variable in the function. In addition, pre-service teachers who had misconceptions in single-variable function examples (equation and algebraic expression) made the same mistake in multivariable functions and could not make a correct representation although they used two variables in their expressions. It was determined that misinformation and misconceptions in concept images for multivariable functions were caused by incomplete information and mislearning in the function definition and single-variable function examples. The findings suggest that supporting the course designs on single and multivariable functions with examples and concept knowledge would be beneficial for an effective learning process.