本研究旨在探討數學臆測活動中教師角色的內涵。本研究的數學臆測是數學課堂中學生造例子、提出猜想、效化猜想、一般化及證明的過程，數學臆測活動能培養學生的論證能力，教師是其中影響的重要因素。然而有關於臆測教學中的教師角色相關研究較少，故本研究試由教師的行為表現和身分地位來分析數學臆測活動中教師角色內涵。研究方法採用個案研究法，觀察一位個案教師將臆測融入六年級的數學課堂教學。蒐集資料包括課堂的錄影及錄音逐字稿、學生解題紀錄。教師角色分析以Chen, Hand與 Norton-Meier（2017）的論證課堂教師角色分析架構為基礎，從八種行為表現的編碼來歸納四種具代表性的身分地位－引導者、主持人、教練及參與者。研究初步發現：在不同的臆測教學階段，教師會有不同的角色分布。造例階段中教師的角色最單一，當進入提出猜想階段時，教師會充分運用多種角色，而學生在教師的角色切換後能產出更多且品質更佳的猜想。一般化階段教師則以教練的角色為主，來刺激學生思考猜想的適用範圍，達到一般化的效果。效化及證明階段任務難度較高，教師經常扮演引導者角色，維持學生高度的專注力來意義化抽象的數學性質，此外教師經常輔以參與者的角色，在學生對話中提出關鍵的問題，有助於提高效化和證明的效率。臆測教學活動中教師角色會因應階段的性質而有不同的樣態使各個階段的效果最佳化。

In the context of conjecturing, argumentation to be initiated is a form of discourse that goes beyond conversation or interaction. Argumentation in mathematics classrooms is involved with supporting conjectures by data or warrants and rebutting by a counterexample. In this regard, a teacher cannot simply play one single role. The purpose of this study was to investigate teacher’s roles playing in students engaging in the activities of mathematically conjecturing that argumentation took place. An experienced elementary school teachers was the case of the study. The data collection in the study mainly consisted of the transcripts of videos of teaching and students’ worksheets. The analytical framework of teacher roles was based on the framework of Chen, Hand and Norton-Meier (2017). The finding of the study indicates that there were different roles and each role playing in different stages of conjecturing activities. In the stage of constructing cases, teacher played a single role, but when entering the stage of formulating conjectures, the teacher played multiple roles. Students formulated rich and high-quality conjectures as the teacher played multiple roles in different situations of conjecturing. In the stage of generalization, the teacher played a coach as a main role to stimulate the students. It is difficult for students engaging in the stage of validation and justification, thus the teacher often played the role of dispenser for students concentrating to the meaning of mathematics. This study made a contribution that the role of a teacher supporting students’ engaging in mathematical argumentation was varied by the nature of the stage of conjecturing and the roles optimized the effects of each stage of conjecturing activities.

第一章 緒論--------------------------------1
第一節 研究背景與動機-----------------------1
第二節 研究目的與待答問題-------------------4
第三節 名詞釋義----------------------------4
第四節 研究限制----------------------------5
第二章 文獻探討----------------------------6
第一節 教師角色----------------------------6
第二節數學臆測----------------------------16
第三節教師角色的分析架構-------------------32
第三章 研究方法與設計----------------------40
第一節 研究方法---------------------------40
第二節 研究架構---------------------------42
第三節 研究情境與研究對象------------------44
第四節 資料蒐集及資料分析------------------45
第五節 研究流程---------------------------55
第四章 研究結果---------------------------57
第一節 臆測教學中教師的角色分布-----------57
第二節 數學臆測五個階段中教師的角色分布-----106
第五章 討論與建議-------------------------112
第一節 討論------------------------------112
第二節 建議------------------------------116
參考文獻 --------------------------------118
中文部份 --------------------------------118
英文部審閱部份----------------------------120

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