This study investigates pre-service mathematics teachers' concept images of radian and possible sources of such images. A multiple-case study was conducted for this study. Forty-two pre-service mathematics teachers completed a questionnaire, which aims to assess their understanding of radian. Six of them were selected for individual interviews on the basis of theoretical sampling. The data indicated that participants' concept images of radian were dominated by their concept images of degree. As the data in this study suggested, pre-service mathematics teachers were reluctant to accept trigonometric functions with the inputs of real numbers but rather they use value in degrees. More interestingly, they have two distinct images of : as an angle in radian and as an irrational number.

The purposes of this study were to determine preservice physics teachers' instructional beliefs and to investigate the relationship between their beliefs and practices. The theoretical framework was based on the combination Haney & McArthur's (Science Education, 86 (6): [783][784][785][786][787][788][789][790][791][792][793][794][795][796][797][798][799][800][801][802] 2002) research and Ford's (1992) motivation systems theory. A multicase study design was utilized for the research in order to focus on a beliefpractice relationship within several examples. Semistructured interviews, observations, and preservice teachers' written documents were used to collect data. Results showed that most preservice teachers held instructional beliefs aligned with constructivist philosophy. Some of the preservice teachers' beliefs were consistent with their practices while some of them presented different practices from their beliefs in different placements.

In this paper, we examine the development of pre-service mathematics teachers' use of multiple representations during teaching in technology-rich environments. The pre-service teachers took part in a preparation program aimed at integration of technology into teaching mathematics. The program was designed on the basis of Technological Pedagogical Content Knowledge (TPCK) framework; and the mathematical content chosen for the program was the concept of derivative. The pre-service teachers' development was scrutinized in terms of their knowledge of representations, of connections established among the representations, and of the aspects of derivative emphasized by these connections. On the basis of our analyses we argue that any attempt to prepare pre-service teachers for effective use of technology in teaching mathematics needs to explicitly focus on the functions of multiple representations in tandem with the mathematical content under consideration. We discuss the educational implications of the study in designing and conducting of the preparation programs related to the successful integration of technology in teaching mathematics.

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