Preservice teachers' knowledge of linear functions within multiple representation modes

Abstract

This study examines preservice teachers’ knowledge in the case of linear functions. Teachers’ knowledge in general consists of their subject matter knowledge and their pedagogical content knowledge. In this study, teachers’ subject matter knowledge is examined by looking at their ability to adapt to different representation modes. The framework for subject matter content knowledge consists of five components: (1) flexibility across formal mathematical symbolisms; (2) flexibility between visual and algebraic representations; (3) flexibility within visual representations; (4) flexibility with real-life situations, and (5) procedural skills. In terms of pedagogical content knowledge, two aspects were examined across five corresponding components. These two aspects were knowledge of students’ conceptions and misconceptions, and teachers’ teaching strategies. The primary source of data for the study was from two tests and six interviews. The results showed preservice teachers performed poorly in terms of representation flexibility. Furthermore, most of the preservice teachers had limited knowledge of the nature and sources of students’ mistakes as well as effective teaching strategies to help students with their misconceptions. In terms of knowledge structure, representation flexibility was found to be significant in both CK and PCK compared to procedural skills. Moreover, the representational flexibility in terms of CK seemed to strongly predict the overall PCK performance. Representational flexibility seemed to be related to the use of instructional representations. Overall, there was a strong relationship between various components of CK and PCK.