以加強合作學習歷程促進微積分解題之行動研究   免費試閱

Promoting Calculus Problem-solving through Enhancement of Cooperative Learning Processes: An Action Research

本研究的主要目的乃探討在數學系微積分的教學中加強合作學習歷程對數學系學生微積分解題之影響。研究方法採用行動研究的方式，以數學系修讀微積分的30位學生為研究對象，進行一學期的教學行動，並透過微積分解題學習單、學習歷程檔案、學習調查問卷、解題觀察紀錄等工具來蒐集資料。研究結果發現：一、學生在合作解題的過程中遭遇到的最主要困境是，在微積分的學習與解題所需之微積分基本定義、概念、性質及解題方法等先備知識與能力不足，而影響合作解題的進行與效率；二、加強合作學習歷程有助於學生解決微積分問題，包括：能促進微積分的解題思考、解題態度變得較積極主動及對解題更有自信；三、加強合作學習歷程能增強學生在微積分解題的自我監控、自我評鑑與自我修正等自我調整的後設認知；四、合作學習能發揮同儕輔導的功能。最後，依據研究結果，對微積分教學提出一些建議。

This study aimed to explore how enhancing students’ cooperative learning processes in calculus teaching affected mathematics students’ calculus problem-solving performance, using an action research comprised of one semester teaching activities to 30 mathematics students taking a collegelevel calculus course. The data sources included learning logs of calculus problem-solving processes, students’ learning journals, questionnaires on students’ learning, and observation records on problem-solving. The findings were: 1. Students had difficulties solving problems cooperatively due to insufficient prior knowledge and abilities in calculus learning and problem-solving, including the basic definitions, concepts, properties and problem-solving methods of calculus. The operation and efficiency of their cooperative problem-solving was therefore affected. 2. Enhancing the cooperative learning processes was beneficial for students to solve calculus problems. Students improved their thought processes in calculus, developed a more active attitude towards problem-solving, and became more confident in problem-solving. 3. Enhancing the cooperative learning processes augmented students’ metacognitive adjustment in calculus problem-solving, including self-monitoring, self-evaluation, self-correction. 4. Cooperative learning boosted peer-tutoring. In conclusion, we offer some suggestions for calculus teaching methods based on the results of the study.