| Summary: | 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.
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