數學人文教案培養數學文化素養之理論探討與反思

A Theoretical and Reflexive Study on Cultivating Literacy of Mathematical Culture by Using Lesson Plans from Humanistic Mathematics

數學文化是理解數學知識本質的重要途徑之一，但長期以來在傳統教學中幾乎都被忽視。本研究嘗試從理論論述和實務教學兩方面初探並反思數學文化如何應用於實際教學之中。在理論方面，本文定義數學文化並說明其中之「文化中的數學」與「數學中的文化」雙構面，再定義何謂數學文化素養，以進一步論述數學文化素養在教育上的意涵。在教學實務方方面，本研究基於數學人文精神發展「費波納西數列」和「霍爾遊戲」兩份教案，並實際針對國中生和高中生實施素養教學。初步觀察結果發現，學生對於這兩份數學文化教案均表現出高度肯定，也能從教學活動中掌握所與傳達的數學精神。惟學生在「費波納西數列」的教學中沒能深入體認與自然界的關聯，而在「霍爾遊戲」教案中也發現大約半數參與的高中生對於將條件機率概念推廣到一般情形仍有困難。

Mathematical culture a crucial approach to understanding the nature of mathematical knowledge, but it has been mostly ignored in traditional teaching for a long time. This research was a theoretical and reflexive study on how mathematical culture can be conducted in practical teaching in terms of theoretical and practical aspects. In terms of theory, this research provided a definition of mathematical culture and explained the dual dimensions of mathematical culture, that is “mathematical culture literacy” to explore the meaning of mathematical culture literacy in education. For the practical aspect, by referring to the humanistic spirit of mathematics, this research focused on two lesson plans–the Fibonacci Sequence and the Monty Hall Problem. Furthermore, two lesson plans were implemented for middle school and high school students. The findings indicated that, although the students were highly appreciative of the lesson plan content, they failed to be impressed by the connection between mathematics and natural world in teaching the Fibonacci sequence, For the Monty Hall problem lesson plan, results also demonstrated that approximately half of the participating high school students still had difficulties in generalizing the concept of conditional probability.