數學教師專業發展的一個面向：數學史融入數學教學之實作與研究

• Main Author: 蘇意雯
• Other Authors: 洪萬生
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/gg528v

博士 === 國立臺灣師範大學 === 數學系 === 93 === Abstract There has been a growing interest in adopting the historical approach in mathematics teaching since the 1970s. How can history play an effective role in improving the teaching and learning of mathematics? Teachers who are concerned about HPM would have regarded this as a primary goal. If we extend the pedagogical concern to initiating more mathematics teachers in applying the history of mathematics into their teaching, we believe that this would be beneficial not only to students but to teachers themselves as well. Teachers’ education is very important. So we must know well what the impact of the history of mathematics is on the development of mathematics teachers. In order to deal with the above questions, we undertook one school-based research during a two-year period, from August of 2002 to July of 2004. A community of teaching practices in terms of HPM was developed in one of the Taipei municipal senior high school. By way of collaborative action research, we observed participating teachers’ process of transformation in which they adjusted and melt the history of mathematics and mathematics knowledge by means of interpretation and teaching. Therefore, in this thesis, I attempt to answer the following two questions: 1. What are the strategies for teacher's professional development on HPM approach on the school-centered base? 2. And what are the changes of these participating mathematics teachers under this HPM approach? The research was conducted in a partnership among three teachers, T1, T2, T3 and the researcher herself (hereafter abbreviated participants). In the light of the HPM, the participants went through three phases of professional development. They learned to search for primary sources, to read related articles and to engage in critical discussions, which includes practices from both Western and Eastern methods of teaching in order to design and create HPM worksheets. They were encouraged to write down their reflections to make public their private ideas. Apparently their reflective narration could fortify knowledge, make their innovative works accessible to others, and go on to enhance their professional knowledge. We believe that, through this kind of professional practice, the participants can increase their personal and professional knowledge, which in turn contribute to their teaching. The strategies the participants adopted are: reading a lot of articles about mathematics teaching, designing HPM worksheets including the logical aspect of mathematical knowledge, the historical aspect of mathematical knowledge and theaspect of student’s cognition. Finally, the researcher suggests a Teacher’s Model for Professional Development in terms of HPM, which can explain the practices of these teachers through the process. In this model, teachers enter the hermeneutic circle, say C1, to look into the ideas of the editors of textbooks, the mathematics knowledge and the contents of textbooks. Then they enter another hermeneutic circle, say C2, to learn the ancient mathematicians’ ideas, mathematical objects, and mathematical theories. After the teachers interpret the essence of C1 and C2 by themselves they then start to teach. In practice, we can characterize in six different manners, the teachers’ use of the history of mathematics in the classroom: isolation, addition, introduction, execution, integration, and decision-making. In the end, the researcher suggests that “optimization” to be the goal for future development of the teachers. By the end of the two-year project, it is obviously that the participants have enhanced their professional expertise in terms of the HPM in following ways, namely, 1) they can begin to write popular mathematics articles; 2) they are more reflective into their teaching than ever; 3) they are able to integrate their mathematics knowledge into a broad picture; and 4) they start to care about the students' thinking. As a conclusion, this thesis suggests that an HPM approach can do to help mathematics teacher’s professional development in an efficient way.