探究歷史導向微積分課程與發展學生數學觀點之關係

Exploring the Relationship between a History Oriented Calculus and the Development of Students' Views on Mathematics

劉柏宏(Po-Hung Liu)

《科學教育學刊》 15卷6期 (2007/12) Pp. 703-723

https://doi.org/10.6173/CJSE.2007.1506.05

摘要

本探究之主要目的在探討以歷史進展為導向的微積分課程，對於培養學生的數學觀點有何種關聯。本研究採取單一群體前後測研究法，研究工具包括開放式問卷、數學自傳、歷史導向的微積分課程、隨堂報告、與半結構式一對一訪談。研究結果顯示，大部份受測者在學前表示數學思考是一種牽涉到數字計算與套用公式的求解過程，但到學期末絕大部份的學生對於數學思考都有另一番論述，並且對數學家解題情境的想像投射到對於數學思考的認知上。在數學知識的認知方面，大部份學生對於數學知識始終抱持著強烈的工具化觀點。不過，學生於學期末的論述增加了兩方面的覺察：(1)數學知識承先啟後的概念；(2)數學家所扮演的角色。本研究最後不僅分析歷史導向課程與發展學生數學觀點之間的關係，也探討了學生對數學本質的瞭解在數學學習中的重要性。

關鍵字

微積分 ； 數學史 ； 數學觀點 ； 數學本質

並列摘要

To explore the relationship, between a historical calculus course and students' views on mathematics, the one-group pretest-posttest design was adopted in which an open-ended questionnaire, students' mathematics biographies, a history oriented teaching material of calculus, students' self-reports, and the follow-up semi-structured interviews were served as the tools. The results indicated that most of the students considered mathematics thinking as the processes involved calculation and formula at the very beginning, nonetheless expressing different viewpoints after finishing the course. They attempted to connect the context of mathematicians' problem solving with the characteristics of mathematics thinking. On mathematics knowledge, students strongly held a consistent instrumentalist view on mathematics, before and after the course. However, at the end of the course, they were more likely to recognize mathematics as the continuity and in-heritance knowledge and the role of mathematicians on its development. Furthermore, this study also emphasizes the importance of students' understanding of the nature of mathematics.

並列關鍵字

Calculus ； History of Mathematics ； View on Mathematics ； Nature of Mathematics

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