校內數學教師專業發展的互動模式

An Interaction Model of Professional Development of Mathematics Teachers Within a School

在一學校內有三位數學教師組成一個討論小組，利用課餘時間，討論、解決自己有興趣的數學問題。教學問題是聚焦在關心學生的學習，而解決教學問題的中心想法是營造數學感的教學和診斷教學。本文探討這種小組的互動方式為何能促進教師的專業發展。本研究採人種誌研究法，參與研究的兩位數學教師與研究者任教於同一學校。收集的資料包括教師互動錄音、教師教學錄影與錄音、教學札記、教師深度訪談、以及教學講義。資料信度採三角校正，除將研究者所轉錄原案內容拿給參與教師確認外，資料分析的編碼並與第三者達成一致性。資料效度分析除採教學錄影的生態效度之外，並參照教師的言談、教學行為相互印證。研究發現，同事間互動的方式引動教師在教室內進行師生互動，而師生互動的經驗又為同事互動引入活水。同事互動與師生互動就像是引動教師內在專業發展的一個外部循環系統，它的運轉引動了教師本身對教學問題的反覆察覺、解決與反思所組成的內在循環，外循環與內循環間又相互連動，形成了教師專業發展的互動模式。這種在學校內的互動模式扮演著教師長期專業發展的一種機制。

A discussion group of three mathematics teachers within a school was organized to discuss their teaching issues during their out-of class time regularly. Their discussion very often focused on the learning difficulties of their students. In order to improve students' mathematics understanding, the group tried to implement two fundamental ideas about mathematics teaching into their classes, namely mathematics sense-making and diagnostic teaching. Can the interaction of this group enhance teachers' professional development? If it does, why and how does this happen? This is an ethnography study. Two mathematics teachers and the researcher teach in the same school. Data collecting includes tape recording of group interaction, video-audio tape recording of each teacher's teaching, teaching notes, and profound interviews with teachers. The reliability of data analysis triangulates with the two teachers and the third party. Except both of two teachers confirm the content transcribed by the researcher, the encoding of data analysis reaches consistency with a third party. The validity of data analysis not only takes the ecological validity of the videotape of teaching, but also verifies with teachers' everyday talks and their teaching behavior. The research has found out that the way the colleagues interact makes their interaction with students in procession in the class, and the experience of interaction in between leads into the interaction between colleagues. The interaction between the colleagues and that between the teachers and the students are like an external circulatory system. Its circulation leads into the internal circulatory system formed by teachers' consistent awaring, solving, and reflecting towards their teaching problems. The external and internal circulatory systems interact with each other, and jointly create the interaction model of professional development of mathematics teachers. Therefore, the interaction model within a school induces a mechanism of teachers' long-term professional development.