探討高中數學教學融入建模活動的支撐策略及促進參與教師反思的潛在機制

Exploring the Scaffolding Strategies of Inserting Mathematical Modeling into Teaching of Secondary Mathematics and the Latent Mechanism of Promoting Teachers' Reflection

楊凱琳(Kai-Lin Yang) ； 林福來(Fou-Lai Lin)

《科學教育學刊》 14卷5期 (2006/12) Pp. 517-543

https://doi.org/10.6173/CJSE.2006.1405.02

摘要

在台灣不利於數學建模教學的環境中，透過參與協同行動研究的過程，本文分析可支撐高中數學教師在既有的上課時間與教材內容中融入數學建模教學活動的策略，由參與教師的改變評估支撐策略可能的成效，並進一步探討可促進教師反思的潛在機制。一年半的研究過程中，由一位研究者先以參與的研究者之角色和參與教師共同討論，設法解決在協同行動研究過程中所面臨的障礙。之後，再由兩位研究者分別以參與和觀察研究者的角度來詮釋此行動研究的歷程。研究發現參與教師所顯現的成長，包含對教材設計的考量從課本教材的相關性、問題情境的多元性與子活動順序的流暢性已逐漸擴充至關心學生既有經驗的聯結性與教材是否引動學生發展多樣的建模策略；教學方法的使用從主導者、旁觀提示者、經營管理者逐漸展現有預謀的參與討論者；對學生建模思維的瞭解，也從數學解題的觀點轉化成數學建模的思維模式。檢視參與教師在各學習脈絡中的成長後，也驗證了提供教材資源有助於建立參與教師實作的信心，利用一次觀摩其他教師的教學可突破其反思的侷限，而開放討論數學建模思維的分析模式也激發參與教師設計新的教學活動。此外，透過「解惑」的觀點來分析參與教師與研究者的互動歷程後，「雙重體驗爲憑的交流」、「同理心的投射」和「不確定感的激發」被認定爲促進教師反思成長可能的潛在機制。本文在實作上可提供師資培育者或教師進行專業發展時一些新的支撐策略，在理論上則基於「解惑」觀點來探討可促進參與教師反思的潛在機制，此探討可以讓教育學者更有效地掌握教師專業發展的歷程，也希望未來的研究可以從本文所探討的潛在機制來擬定適合不同特質教師的支撐策略。

關鍵字

反思機制 ； 教師專業成長 ； 數學建模

並列摘要

This paper reports on how the researchers assisted a senior high school teacher to insert mathematical modeling into his teaching in the context of time and content constraints. The paper examines the effects of the teaching strategies as well as the latent mechanism of promoting teachers' reflection in terms of the ”solving doubt” theory. During the research process of one and half years, one researcher collaborated with the participating teacher with aim of helping this teacher overcome obstacles in teaching mathematical modeling. Subsequently, both researchers interpreted the data from this process. The teacher's growth during the participating process was demonstrated by (a) teaching materials: consideration of the relevance of textbooks, the diversity of problem situations, movement from the fluency of sequential activities to consideration for the association with students' experience and the variety of students' modeling strategies initiated by the teaching material; (b) teaching method: playing the leading role in the beginning, the hinting and observing role, the managing role followed by the premeditating and discussing role; (c) students' modeling thought: changing the perspective from problem solving to mathematical modeling. After examining the teacher's growth under each learning context, it is confirmed that providing the source of teaching material is helpful in establishing the teachers' confidence, inspecting and learning from another teacher's teaching can break through the limitation of teachers' reflection, and openly discussing the analysis framework of students' modeling thought encourages teachers to design new activities. This paper provides educators or teachers with new strategies for professional development in practice. This analysis of the latent mechanism underlying this teacher’s reflection may help educators elaborate the process of professional development.

並列關鍵字

Mathematical Modeling ； Teachers' Professional Development ； Mechanism of Reflection

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