| This study explores mathematics teachers' beliefs about using multiple representations, such as manipulative, pictorial, symbolic, language, and realistic representations that are described the Lesh translation model. Using a qualitative approach, the teachers' beliefs about the helpfulness and hindrances of using each representation described in the Lesh translation model were clarified. Teachers' belief changes were also explored, before and after participating in a yearlong professional development program. Furthermore, this study investigated the teachers' reflections on teaching mathematics based on their beliefs during the program. Results indicated that the teachers' beliefs were mostly in line with the Lesh translation model. Changes in the teachers' beliefs were also observed after participating in the program. These changed beliefs led teachers to change their practices in the classroom. The teachers mostly used pictorial, symbolic, language, and realistic representations during the three observations periods. Using translations within and between these types, especially pictorial and realistic representations, were varied in the three classroom observations. On the other hand, the teachers used few physical and virtual manipulatives, even though they claimed to have positive beliefs about using them in the classroom. That is, the teachers' beliefs concerning the hindrances of using manipulatives prevented them from using these representations in the classroom. Furthermore, changing teachers' practices required more time after their beliefs were changed. In future studies, researchers could focus on a longitudinal study of the interactions between beliefs and practices. In addition, research could explore more effective activities that involve physical manipulatives or virtual manipulatives, which reduce any hindrances that were identified in this study for K-12th grade students. |
