臆測是數學思考的骨幹，學生參與臆測活動有助於數學能力的養成，教師學習設計臆測活動是落實臆測於課室教學的主要手段，而師培師規劃與實施臆測活動設計工作坊便是協助教師學習的關鍵支撐，因此，師培師如何規劃、如何實施及如何反思調整臆測活動設計工作坊是重要的研究問題。本篇研究探討一位參與教育部中央輔導團亮點基地計畫的生手師培師，如何透過行動研究法探索自己輔導學校數學教師設計臆測活動的專業成長，特別是聚焦在促進策略的演化。本研究的師培師透過行動研究探究輔導實作的成果便是專業學習，包含：(1)建構臆測活動設計工作坊的課程內容與實施方式；(2)察覺設計為本工作坊所容易引發師培師與教師張力並形成輔導問題；(3)因應輔導問題調整課程內容與實施方式並促成促進策略的演化：由內容學習為取向到學生學習為取在再到教師學習為取向；(4)認識教師參與設計為本工作坊的表現，包含設計臆測活動的能力、對學生學習的敏感度及學校專業學習社群的營造等；(5)反思設計為本專業發展工作坊規劃與實施的原則，包含設計為本的入口活動、進擊活動和回顧活動等。最後，研究者根據本行動研究結果，提出初任師培師的局部發展和設計為本教師專業發展兩方面的實作和研究之建議。

Conjecturing is viewed as backbone of mathematical thinking, which suggests that students should engage in conjecturing activities for enhancing their mathematical competence in a comprehensive way. The key to enactment of conjecturing activities in classrooms is Mathematics Teachers’ (MTs) competence in designing such kinds of instructional activities. In this regard, how Mathematics Teacher Educator-Researchers (MTE-Rs) arrange, implement, and refine professional development programs to facilitate MTs in designing conjecturing tasks is of concern. This study reports professional growth of a novice mathematics teacher educator-researcher(MTE-R) evolved through mentoring in-service MTs in designing conjecturing activities. In particular, the study focuses on the evolution process of mentoring strategies that the novice MTE-R adopted and refined. By means of action research approach, professional growth of the novice MTE-R can be identified from five perspectives including (1) developing the program for facilitating in-service MTs in designing conjecturing tasks; (2) being aware of tensions and challenges encountered when facilitating the learning of MTs in the program; (3) refining the program and the strategies to facilitate the learning of MTs based on the tensions and challenged noticed, which can be generally described as the evolution from content-oriented to both student-centered and teacher-centered; (4) knowing how MTs learn from participating in design-based program in terms of MTs’ competence in designing conjecturing tasks, MTs’ sensitivity to student learning, and how MTs build up professional learning communities on school basis; (5) eliciting principles involving entry phase, attack phase and review phase for arranging and implementing design-based programs. On the basis of the results derived from the action research, this study further provides suggestions to research on professional growth of MTE-Rs, and to the implementation of design-based professional development programs for facilitating MTs’ learning.

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