數學史融入數學教學─以高中第三冊第一章「三角」為例

本研究目的在了解「數學史融入數學教育」是否有助於提升學生數學學習態度。配合高中課綱第三冊第一章「三角」的內容，研究者設計三份主題式單元的HPM 教案，並透過行動研究的方式，在過程中利用課堂觀察、學生的學習單回饋與學生訪談等方式，不斷地反思與修正教案的方向，以達到研究目的。本研究採行動研究法，以研究者任教學校的高二兩個任課班級共83 名學生為研究對象，進行三個主題式共六節課關於HPM 加深加廣的教學活動。研究工具包含數學態度量表、教學活動學習單以及學生訪談紀錄，進行量化的分析與質性的詮釋。研究結果發現，透過HPM 的教學活動，對學生數學學習態度上的改變，不僅在情意部分有所提升，另外也發現，在設計教案時，若能呈現數學家創造理論的過程，學生亦能在認知的層次有所提升。研究者亦在過程中得到重要的反省，由於任教的兩個班的程度差異很大，得到的回饋差異也很大，透過行動研究的反思，發現即使是HPM 的教案設計，仍須考量學生的起點行為，而調整教學活動的內容，以達到認知與情意部分皆能提升的效果。

關鍵字

HPM ；行動研究；數學學習態度

並列摘要

The present study aims to investigate whetherintegrating history of mathematics into math pedagogy can promote students’ learning attitudes of learning mathematics. Based on the contents of triangleof teaching syllabus which is in Chapter One, Book Three of Senior High Mathematics, the researcher designed three History and Pedagogy of Mathematics (HPM) teaching plans that were presented in thematic units. In order to achieve the research goals, this study applied active research, completed class observation, collected students’ feedback through learning sheets, interviewed the participants, took teacher’s reflection and constantly adjusted the direction of teaching plans. The subjects (N = 83) were the researcher’s 11-grade students who were divided into 2 classes. The researcher deeply and broadly integrated 3 HPM thematic units into six-hour teaching activities. The research tools included Mathematics Attitude Scale, Learning Sheet of Teaching Activities, and the records of student interview. The researcher statistically analyzed and quantitatively interpreted the collected data. The results reveal that integrating HPM into teaching activities do not only change the participants’ mathematics-learning attitudes, but encourage their learning affection. In addition, if the instructors can present the processes mathematicians create theories when they design teaching plans, they can increase participants’ levels of recognition. In this study, the researcher learns 2 important reflections. Since the different math achievement between the students of two classes is very huge, the difference between students’ feedback is also very great. Through the reflection of active research, the researcher finds that even applying HPM into teaching activities, the instructors should take students’ start-behavior into their consideration. Meanwhile, they have to adjust the content of their teaching activities to promote students’ learning effects of both recognition and affection aspects. Key words: HPM. Active research, attitudes of mathematics learning