臺灣與德國中學數學教師專業覺適力跨文化比較研究

The project is a cross-cultural comparison study of Taiwan and Germany regarding teacher noticing. To compare teacher noticing in the two countries, expert norms of researchers and teacher educators were used as a frame of reference. Based on these, this report focused on (1) illustrating how expert norms can be different from a Western and an East Asian perspective and (2) illustrating how the expert norms and the teacher noticing can be different in Taiwan (German teacher data are still in the process of translation, thus the present report can only focus on Taiwan’ situation for this objective). To explore the two objectives, three dimension were chosen: the use of representations, dealing with students’ thinking, and the use of tasks. The participants included 19 and 19 professors from Taiwan and Germany respectively. For the in-service teacher sample, 102 Taiwanese teachers were included. The questionnaire with 18 vignettes (18 norm/noticing questions) were employed and the survey was conducted in the native languages of the experts and teachers via the online tool Unipark. Content analysis was conducted to analyze the expert data and the coding rubric was thus produced. The coding rubric was then used to code the teacher data. Regarding the comparison of expert norms between the two countries, cultural differences revealed. For representations, regarding the situations in which graphical representations are not only means to learn mathematical concepts but also the content to be learnt, the expert from both countries emphasized the connections between the graphical and symbolic representations. For student thinking, the experts from the two countries also revealed cultural differences. Though the two cohorts both indicated the teachers’ insufficiency about dealing with student thinking, the German experts emphasized the value of student thinking and indicated that the teacher should appreciate and encourage it. For tasks, the experts from the two countries presented similar ideas. Regarding the comparison of expert norms and teacher noticing in Taiwan, for representations, a much higher percentage of in-service teachers did not recognize the breaches. They appreciated the use of concrete representations and dynamic representations to support the learning of mathematical concepts.For student thinking, as high as 43% of the in-service teachers did not recognize the breach in the vignette. Instead, 28% of the teachers mentioned about not understanding why students still not know the equation has two solutions and criticize the possible problem of previous instruction. For tasks, comparing to the experts, the in-service teachers emphasized more on the teaching methods than the use of the tasks. They cared more about whether the instruction is too teacher-directed, while the experts criticized more on the teacher’s insufficient use of the tasks for not seizing the opportunity to discuss the pros and cons of the different possibilities of assigning unknown.