數學文化通識課程對大學生數學信念之影響初探──以醫學大學為例

An Exploratory Study on Influences of a Mathematical Culture Course on University Students' Mathematics Beliefs-the Case in a Medical University

本篇論文旨在描述作者對於一數學文化通識課程如何影響醫學大學學生數學信念之初探。本篇論文敘述的研究使用單一群體前後測的實驗設計，其研究工具包含（1）一門關於數學史與數學文化的大學數學通識課程，以及（2）一份包含20個問題的Likert-scale數學信念問卷。問卷的內容包含兩個向度：數學本質與數學價值。共有100位同學修課並同時參與前後測。教學實驗進行的課程名稱為「多元文化中的數學思維」。課程中學生會接觸到不同文化與歷史場景中的數學知識。學生也會看到古文明中對類似問題的相異解法，例如比較東亞的劉徽對錐體體積的研究與古希臘歐幾理德《幾何原本》中相關命題的證明。學生在課程中也被要求將數學元素融入他們的藝術創作作業中。研究結果顯示，學生部分的數學信念確實有改變。在數學本質向度上，學生更傾向同意「一般化」是數學思考的方法之一。然而，結果也顯示這門課程並沒有幫學生釐清「核證的脈絡」與「發現的脈絡」。至於在數學價值的向度上，學生更傾向同意「數學培養創造力」，以及「數學培養美感」這兩項的價值。

In this paper, we present an exploratory study on how a liberal-arts course about the culture and history of mathematics influenced the mathematics beliefs of medical university students in Taiwan. This study used a single-group pretest-posttest design. The research tools of this study included: (1) a liberal-arts mathematics course with an emphasis on history and culture, and (2) a 20-question Likert-scale questionnaire used in the pre-test and the post-test. The questions were separated into two dimensions, aiming to investigate students' beliefs about the nature and values of mathematics. A total of 100 students took the pre-test, participated in the teaching experiment, and finally took the post-test. In the teaching experiment course, titled ＂Mathematical Thinking in the Multicultural Contexts＂, students were exposed to mathematical topics presented in their historical contexts. There were also examples of distinct approaches to similar problems by scholars in different civilisations, such as comparing Liu Hui's work and Euclid's Elements. Students were also required to make artistic creations related to mathematics. The results showed that part of the students' beliefs did change. In the dimension of the nature of mathematics, after taking the course, the students were more prone to believe that ＂generalisation＂ was a method of thinking in mathematics; however, the results also revealed that the course did not clarify the difference between the ＂context of justification＂ and the ＂context of discovery＂ for students. As for the values of mathematics, students were more prone to believe that ＂sensibility to beauty＂ and ＂creativity＂ were important values of mathematics.