數學美感教育之行動研究

Abstract

本研究以橫向連結藝術與數學領域，從古希臘時期希臘哲學家所提倡的美是「和諧與比例」之美學觀點，讓學生從「覺察」、「探索」、「印證」與「實踐」，探討「美感構面」中「比例」的美感經驗，引發學生去觀察、探索相關知識，運用資訊軟體實際描繪出精準的數學幾何圖型，讓「美感課程」的課程具體實踐，藉由跨科跨領域的學習，具體進行「以生活為題，美感探索為歷程」的學習。本方案規畫的目的包括規劃與藝術跨領域的統整課程、探討提升數學學習興趣的原因、調查數學美感課程結合科技工具之學生看法。研究方法以行動研究法為主，研究對象為八年級資優班學生為主。研究歷程從109學年進行第一次的美感課程，深受學生肯定，110學年再將美感課程續深化與精緻化。資料收集內容包含社群定期研討紀錄，以及學生問卷及學生訪談回饋單。研究結果顯示數學美感課程能引發學生學習興趣，從觸發興趣、維持興趣、新興個人興趣以致發展良好的個人興趣，在使用科技工具時，運用「鷹架指導」及任務的結構化的教學概念，讓學習的效果更完美，對美感體會更深刻。期待本研究課程能提供數學教師跨領域課程的參考，而使用科技工具的心得與成效能提供教師使用科技工具時少走許多彎路。

The purpose of this study is to integrate the two learning areas, art and mathematics. Based on the aesthetic point of view advocated by Greek philosophers in ancient Greece, beauty is"harmony and proportion", the curriculum inspired students to “observe”, “explore”, “verify”, and “practice”. Accordingly, the current study aims to investigate the students’ aesthetic experience of "proportion" in the "aesthetic dimension". Meanwhile, students are expected to observe and explore relevant knowledge as well as use information software to actually depict accurate mathematical geometric figures in order to actually practice "Aesthetics Course". Through the interdisciplinary learning, we will specifically carry out the learning of"taking life as the topic and aesthetic exploration as the course". The purpose of this study is to plan an art interdisciplinary curriculum, explore the reasons for increasing interest in math learning, and investigate students' perceptions of mathematical aesthetics curriculum assisted with technological tools. The teacher/researcher used the action research method to conduct the current study and the participants were students from an eighth-grade math-gifted class. The study began with the first aesthetic course in the 109th academic year, which was highly praised by the students. In the 110th academic year, the aesthetic course was further deepened and refined. The data consisted of regular community discussions, student questionnaires, and student interview feedback sheets. The results showed that the math-aesthetics interdisciplinary curriculum aroused students' interest in learning in terms of triggering interest, maintaining interest, as well as emerging personal interest to well-developed personal interest. Furthermore, when using technological tools, the “scaffolding” and task-based teaching concepts helped develop the learning effects and experience the aesthetics more profoundly. It is hoped that the course in this study can provide an example for math teachers to design an interdisciplinary curriculum. Additionally, the experience and effectiveness of using technology tools can help teachers avoid many detours when using them.