Modelling of Student Teachers’ Mathematical Conceptions According to Ck¢ Theory: The "Knowledge Transfer" Conception

Abstract

This study aims to examine the basic mathematical knowledge of primary education student teachers according to the Ck¢ theory. The data of this qualitative study is collected through exams applied and clinical interviews undertaken with student teachers. To determine mathematical conceptions of student teachers, examinations on the subjects of Sets, Equations, Functions, and Numbers were applied to 61 classroom teachers , and then 26 of them were interviewed. A detailed analysis of the exam questions was undertaken and all types of knowledge that student teachers used whilst solving these problems were identified. Student teachers’ general mathematical conceptions were revealed through the classification of the related parts of such knowledge that were expressed as “operator” in the conception phase of Ck¢ theory. In this study, the conception of knowledge transfer is presented as one of the determined conceptions. It has been identified that student teachers use the knowledge they have previously experienced as effective in problems, whilst they solve problems, and that they thus think that they will be effective in future problems as well. Operators involving such knowledge underpin the ‘knowledge transfer’ conception. Yet, it has also been found that this knowledge transfer leads students to make mistakes as they usually rely on the idea that a rule leading them to the correct result in a situation, which occasionally leads them to the correct result, will be applicable in any other situations. This conception shows that students tend to use the knowledge that seems appropriate for their logic, their existing knowledge, and their mathematical thinking, even if they notice that what they do in solving problems does not have any mathematical validity. Therefore, this study contributes to the literature in terms of revealing students’ ways of mathematical thinking and addressing the important areas to be covered by teachers in designing learning environments.