本研究探討學生教師數學教學概念的學習歷程與發展機制,研究對象為台灣師大數學系的四位學生教師,以培育課程中所學的「概念啟蒙例」這個教學概念作為研究的核心。所謂啟蒙例是指學習抽象數學概念時,用以引動學習的具體例子,本研究認為啟蒙例教學概念應包含有代表性、發展性、易學性、樂學性等四個屬性,也就是說,一個好的啟蒙例應能正確表達欲教的數學概念、能接續在相關概念的學習時所用、能讓學生容易操作、能引起學生的學習動機等。 本研究為一個詮釋性研究,研究設計上採用人種誌研究的精神,從研究對象大三起便進入培育課堂進行參與觀察,直到大四畢業,紀錄研究對象在此期間於培育課程中進行的學習活動資訊,並配合訪談、文件分析等方法收集資料。所收集的資料以Vygosky(1934)所提出抽象概念的社會內化理論作為詮釋的理論基礎。 研究的主要結果為: 一、啟蒙例教學的科學性概念屬性因場域張力的批判反思使學生教師感受到認知衝擊而察覺。 二、已察覺的啟蒙例屬性因現實教學功能的認同而與自發性概念聯結,其間教學概念的意叢思維經歷群組、鏈結、擴散等發展階段。 三、引導教學思維的試教輔導有助於學生教師實作啟蒙例教學。 根據這些結果,數學教學概念的學習乃是一種社會內化的歷程,並據此詮釋提出教學概念的學習模式。
ABSTRACT This interpretive research investigates how the student teachers learning pedagogical concept by the case of generic example for learning mathematics. The pedagogical concept of generic example, with four features: representative, expansibility, painless, and motivational, is one key point of mathematics teaching. A good generic example creates a familiar and concept-embedded situation, which is helpful in concept formation and sense making.features of generic example, . A group of 4 student teachers was formed and researched by ethnographic approach. The learning process, dialogue between members in this group, commention on the teaching narrations, and pedagogical practice in the educating-lessons, were recorded and analyzed during the teacher education program in the university and the data were interpreted on the theoretical base of internalization of abstract concept in the social context(Vygosky,1934). The main findings are: 1.The feature of generic example was aware of because of the cognitive impact on student teachers’ spontaneous conceptions of teaching mathematics which was inspired by the critical and reflective tension in the education class. 2.The student teachers internalized the aware features because they recognized that the features are advantageous to teaching mathematics. 3.The “guidance of practical thinking” is an effective strategy for practical mentoring. 4.The learning and developing of the pedagogical concept of generic example is a process of social internalization. According to these findings, this research proposed an learning model of learning pedagogical concept.