高中數學教師教學專業知識的個案研究

沈湘媛

指導教授 ： 金鈐

國立臺灣師範大學/理學院/數學系/碩士(2012年)

摘要

本研究採用個案研究法，分析並比較兩位資深高中數學教師的教學專業知識。在Ball等（2008）所提出的教學用的數學知識（mathematical knowledge for teaching）的理論架構下，收集並分析兩個案教師各三階段的實徵資料。教學單元包括四領域的數學主題：李師的微積分、邱師的機率、李師和邱師的矩陣（進度教學單元）、李師和邱師的排列組合（複習教學單元）。

資料收集的主要方法是參與觀察和訪談，其中，教學影片和訪談錄音的內容都轉譯成逐字稿。為了在質性取向的研究裡加入量化分析，本研究使用教學觀察系統來分析參與觀察的教學影片資料，它主要是修改自LMT計畫（2007）所設計的「教學中的數學品質（mathematical quality of instruction）」的影片編碼詞彙表。作者在詮釋參與觀察和訪談的內容之前，會參考一些文本證據以提升本研究的品質。

　　作者將參與觀察的研究結果視為教師的顯性知識，而訪談的研究結果則視為教師的隱性知識。在不同的研究階段裡，兩位個案教師顯性知識和隱性知識有許多異同；在教師的顯性知識方面，雖然質性部分有許多相異之處，但是量化部分卻是非常相似的；而在教師的隱性知識方面，穩定的教學表象背後具有複雜多變的教學脈絡。

　　研究結果指出，專門的內容知識（specialized content knowledge）在高中數學教師教學專業知識裡佔有舉足輕重的地位，尤其是對教師專業發展而言。對於以教學工作為志業的高中數學教師來說，本研究在教學實務裡所描述的教學專業知識有許多發人省思之處。對於國內數學教師知識的研究而言，本研究結果指出了數學教學專業知識在不同面向的各種觀點。

關鍵字

教學用的數學知識 ； 教學中的數學品質 ； 個案研究 ； 參與觀察 ； 訪談

並列摘要

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.

並列關鍵字

Mathematical knowledge for teaching ； Mathematical quality of instruction ； Case study ； Participant observation ； Interview.

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