本研究是探究三位學生教師在師資培育後兩年中，數學教學概念的狀態及其轉變的歷程。研究設計採用問卷調查法、選樣晤談法、及教室觀察法，研究的取樣對象為國立台灣師範大學數學系三年級的一班24位學生教師。問卷調查的結果透過因子分析顯示，這群學生教師有六個共通的主要因子。以這六個因子所表徵的教學認同空間，篩選出小凱、小龍、和小宗三個個案。他們呈現出兩種不同思考數學教學的觀點。其一認同由教師講授數學內容的「知識傳遞者」，另一則認同以學生活動為主的「知識引動者」。接著，依據這兩個向度的相對位置，分析這三個個案在大三和大四兩年間教學概念的起始狀態、過程狀態、和目標狀態。同時，也以互動、反思、教學功力、和數學功力作為研究者介入的取向，嘗試引動他們教學概念的轉變。
結果顯示具補習班教學經驗的小凱，他的模擬教學和試教活動大半是補習班教學的翻版，採用「教師概念解說—教師精選範例演示—學生反覆練習」的教學步驟。由於長期的補教經驗和格式化的教學模式，使得小凱沒能察覺數學教學的問題，且持有強烈知識傳遞者的教學概念。原先認為「老師教得多，學生才會收穫多」、且堅持數學知識應完整教授的小龍，由於修讀研究所高等數學課程的受挫經驗，而察覺到學生學習動機的重要，其教學概念呈現由知識傳遞者轉向知識引動者的跡象。至於小宗，雖然有意圖以生活實例或操作活動啟動教學並透過師生對話激發學生的思考，但是，這樣的觀念並未在課堂的教學中實踐。他的模擬教學和試教活動的步驟乃依據「教師概念解說—教師課本例題演示—學生上台演練」的模式。其原因可能是師資培育者輔導介入的不足，或是缺乏實際教學經驗，導致小宗無法察覺教學問題所在。
這三位個案教師即將進入教學實習的階段，他們目前的教學概念狀態和九年一貫課程對數學教師和教學活動的期待有很大的落差。本研究的結果有助於師資培育者，掌握學生數學教師階段性教學概念學習的狀態和內涵；並可用於設計相關數學師資培育的課程，促進其教學專業的發展，以縮短學生教師教學概念和數學課程期待之間的落差。

This paper describes the states and progress of a group of three student teachers’ conceptions of mathematics teaching within a two-year period in the secondary mathematics teacher education programme. It was carried out through questionnaire survey, interview and classroom observation. The student participants were a group of 24 pre-service mathematics teachers. The first year results revealed six salient conceptions of mathematics teaching from the group, in particular with two different states of conceptions of mathematics teaching derived from the three cases. Two student teachers identify themselves with the roles of ‘a knowledge transmitter’, and the other sees himself as ‘a knowledge initiator’. In the light of this, their conceptions of mathematics teaching related to these two teacher roles and the possibility of introducing an scaffolding for learning consisting of the notions of interaction, reflection, and mathematical and pedagogical power, are examined in terms of the second year data.
One of the three students, ST1, taught consistently the procedures of solving mathematical problems as in a cram school. ST2 thought that students’ abilities of solving mathematical problems are more important than understand them at the initial stage. But due to the frustrated experiences gained in learning advanced mathematics course, he came to see the importance of student inner motivation which should be the major focus of his classroom teaching. For ST3, he intended to teach mathematics using manipulative and communication with students, however not being observed in classroom practices.
As a result, “felt problematic” and “felt relevant” seem to be the two starting points of facilitating the transition of conceptions of mathematics teaching for these three student teachers. Understanding of the different states of learning about student teachers’ conceptions of mathematics and teaching might be useful for mathematics teacher educators in designing relevant educational programs to facilitate the professional development of student teachers.

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