本研究採用個案研究法，搭配個案訪談、教室觀察、影片拍攝以及書面文件資料的收集，探討一位高中數學科初任實習輔導教師的輔導歷程。作者以Furlong & Maynard (1995)的輔導階段論作為描述個案學習發展輔導知能過程的架構，透過分析個案在輔導過程中所面對的問題與因應方式，以及輔導、教學和學習三個焦點之間的轉換情況，嘗試了解高中數學科初任實習輔導教師在一年的輔導過程中，所發展的輔導內容與策略以及輔導知能的發展過程。

研究結果顯示，個案的輔導發展過程與實習教師學習數學教學的發展過程類似，在輔導初期懷抱熱忱並積極地想扮演好輔導者的角色，爾後由於輔導經驗的不足，在面對輔導問題與教學問題時，輔導重心慢慢轉移成教學者，到了輔導的後期，可能因為輔導成效不彰與實習教師學習意願降低的影響，個案已經不再主動扮演輔導者角色而是著重於教學者。此外，研究也發現，輔導的內容與策略是一體兩面的關係，並且和輔導問題是相互牽連影響的，同時，輔導內容與策略的施行結果也可能會引發出不同的輔導問題，形成一連串的「問題－內容與策略」這種交互作用的發展過程。

本研究的結果應該有助於：數學師資培育者了解初任數學科實習輔導教師可能有的輔導知能發展過程和所面對的教學與輔導問題，以及對於輔導所可能造成的影響。並且，也提供後續研究者一個發展的方向：如何幫助初任實習輔導教師學習成為稱職的輔導者？以及如何釐清數學輔導教師所應具備的輔導知能？

Case study with interviews, classroom observations, videos, and documents was used to explore the mentoring format and process of one senior high school mathematics teacher who was first time to be a mathematical mentor. The author uses Furlong & Maynard’s (1995) models of mentoring as the theoretical framework to describe the mentor teacher’s model and process of mentoring in mathematics teaching, and try to grasp the contents and strategies developed during the mentoring process and the emerged knowledge while mentoring his probationary teacher by analyzing the approaches used and the problems faced in the mentoring process. The major foci are mathematical mentoring, teaching and learning.

The research results revealed that the development of the process of mentoring were similar to the phases of learning to teach mathematics for probationary teachers that Furlong & Maynard’s suggested. At the initial stages, the case had high zeal and was ambitiously try to play an active mentor, but he gradually changed his mentoring activities while facing the mentoring and teaching problems because of the emerging failure mentoring experiences. The mentor at the latter period was not playing the role of an active mentor, and this maybe resulted by the effects of little achievement and the low learning willingness of the probationary teacher. In addition, the results also showed that the contents and strategies of mentoring were intertwined with the mentoring problems. Furthermore, the implement of the mentoring contents and strategies probably cause different mentoring problems, and this will form an interacting developing process of a series of problems with these contents and strategies.

The research results may contribute to: mathematical teacher educators in understanding the possible mentoring knowledge developing process and the problems that may be emerged and faced for the novice mentoring teachers, and the resulting possible effects that mathematical mentoring might bring about. Moreover, this result can also provide an expanding aspect for how to help the novice mentoring teachers face the new challenge of learning to be effective mentors and the mentoring content knowledge that a mentor should have.

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