本研究的目的是想探討數學教學案例討論對教師數學教學的基礎知識影響為何，採質性研究的方式，研究者在校內成立數學教學案例討論小組，透過三位國小老師參與五次數學教學案例討論，並在案例討論前後，對個案教師進行數學教學觀察與訪談等，蒐集相關資料。本研究發現透過數學教學案例討論，個案教師數學教學的基礎知識變化如下:(1)注意過程知識，由著重程序性知識轉變為關注學生的理解和思維;(2)遵循教科書知識，由仰賴教科書轉變為以情境題來複習舊經驗;(3)數學術語的使用知識，由使用生活語言轉變為使用”倍”的數學術語來建立數學概念;(4)公開的學科知識，由數學運算操作轉變為使用教具和數學知識的縱(橫)向連結幫助學生理解數學;(5)識別學生錯誤知識，由訂正錯誤轉變為能分辨學生的錯誤類型，並試著用其他學生的解題來引導學生澄清錯誤或建立新概念。此外，研究結果也發現，數學教學案例討論，可以提升個案教師數學教學的基礎知識。

This study aimed to realize the influence of discussions on mathematics teaching cases among schoolteachers to their foundation of mathematics teaching. This study used the qualitative research method. First off, this study followed 3 elementary schoolteachers by forming “The Team for Discussions on Mathematics Teaching Cases” and having them participated in Discussions on Mathematics Teaching Cases for 5 times, next administered observation on their mathematics teaching and interviews with them before and after the discussions on the cases, and then collected the related information. This study led to the results - the change in the foundation of mathematics teaching among the schoolteachers having participated in discussions on mathematics teaching cases – as the follows in particular: (1) In concentration on procedures – changed from former emphasis on procedures to currently focusing on students’ comprehension and thinking; (2) In adhering to textbook – changed from formerly relying on textbooks to currently brushing up and reviewing the existing experiences with situational questions; (3) In use of mathematical terminology – changed from formerly using living plain talk words to currently using mathematical terminology such as “times” etc to currently building mathematical concepts; (4) In overt display of subject knowledge – changed from former emphasis on operation of math computation skills to currently facilitating students to comprehend mathematics by using teaching aids and math knowledge as vertical (transverse) links; (5) In identifying errors - changed from correcting the errors to being able to analyze the student's error pattern and trying to make use of other students' solutions to direct and guide students in clarifying the causes of errors and developing the new concepts. In addition, the results of this study also led to the clear picture that by administering discussions on mathematics teaching cases it is likely to promote the mathematics teaching foundation of the schoolteachers performing mathematics teaching.

目 錄

第一章 緒論 ………………………………………………………………………… 1
第一節 研究動機 …………………………………………………………… 1
第二節 研究目的與研究問題 ……………………………………………… 3
第三節 名詞釋義 …………………………………………………………… 3
第四節 研究限制 …………………………………………………………… 4

第二章 文獻探討 ………………………………………………………………… 6
第一節 教師數學教學的基礎知識 ………………………………………… 6
第二節 數學教學案例討論 ………………………………………………… 22

第三章 研究方法 ………………………………………………………………… 29
第一節 研究架構 …………………………………………………………… 30
第二節 研究對象和研究者角色……………………………………………… 31
第三節 研究情境 …………………………………………………………… 34
第四節 研究流程與資料處理 ……………………………………………… 41
第五節 本研究的品質 ……………………………………………………… 46

第四章 研究結果 ………………………………………………………………… 48
第一節 怡怡老師在注意過程之基礎知識的變化 ………………………… 48
第二節 怡怡老師在遵循教科書之基礎知識的變化………………………… 60
第三節 怡怡老師在數學術語的使用之基礎知識的變化…………………… 72
第四節 怡怡老師在公開的學科知識之基礎知識的變化…………………… 82
第五節 怡怡老師在識別學生錯誤之基礎知識的變化……………………… 94

第五章 結論與建議 …………………………………………………………………103
第一節 結論 …………………………………………………………………103
第二節 建議 …………………………………………………………………106

參考文獻
中文部份 …………………………………………………………………………108
西文部份 …………………………………………………………………………112

附錄
附錄一 參與數學教學案例討論成員背景資料訪談 ……………………………117
附錄二 數學教學案例討論後訪談 ………………………………………………118
附錄三 個案教師數學教學後訪談 ………………………………………………119
附錄四 五次數學教學案例討論結束後省思單……………………………………120

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