Summary: | 碩士 === 國立臺灣師範大學 === 數學系 === 100 === This study applies case study research to analyze and compare the professional knowledge of teaching of two high school experienced mathematics teachers. On the
theory of mathematical knowledge for teaching presented by Ball et al.(2008), the author collected and analyzed empirical data in the three phases of each teacher.
These mathematical topics cover four areas: calculus by Mr. Li, probability by Mr.
Chiu, matrix by Mr. Li and Mr. Chiu, and permutation and combination by Mr. Li and
Mr. Chiu.
Major methods of the data collection were participant observation and interview,
and the content of instruction films and interview recording was translated into a
transcript. In order to acquire quantitative analysis in the qualitative-oriented study,
this study used observation system to analyze the data of instruction films of
participant observation. The observation system was modified from mathematical
quality of instruction video coding glossary, which was designed by LMT project
(2007). Before the author interpreted the content of participant observation and
interview, she referred to some text for evidence in order to enhance the quality of this
study.
While the research result of participant observation is regarded as explicit
knowledge of the teacher, the research result of interview is regarded as implicit
knowledge of the teacher. In the various research phases, there are many similarities
and dissimilarities between explicit knowledge and implicit knowledge of the teachers.
In the dimension of the teachers’ explicit knowledge, there are many differences on
the qualitative part, but they are similar on the quantitative part. However, in the
dimension of the teachers’ implicit knowledge, there are complex and changeful
contexts of instruction behind the presentation of stable instruction.
The research result implies that specialized content knowledge plays a vital role
in the professional knowledge of teaching of high school mathematics teachers,
especially in the professional development of teachers. For high school mathematics
teachers who have ambition to engage in teaching, there are many points to stimulate
deep thought in the professional knowledge of teaching described in the teaching
practice of our study. For investigating domestic mathematic teachers’ knowledge, the
result of this study points out the various views of the professional knowledge of
teaching mathematics in different aspects.
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