負數史與負數教學中的美感意涵

The Aesthetic Value Embedded in the Negative Number History and the Negative Number Instruction

陳淑娟(Shu-Chuan Chen)

《教育實踐與研究》 26卷2期 (2013/12) Pp. 133-159

摘要

本文從四方面說明負數史與負數教學中的美感意義和價值。首先，說明從美感角度看負數教學的理由；其次，說明什麼條件下容易產生美感；其三，從負數史及東西方處理負數特質的對比看負數之美；最後，說明以美感觀點開拓負數教學的視野，分析負數美的內涵。負數教學的視野與美感內涵包括：一、以同理寬容負數困頓的美感態度，化解負數學習的不安；二、藉美感態度欣賞負數的曲折發展，幫助學生重視負數；三、藉圖像所蘊含的直覺，促進負數運算的理解，本文以兩個圖像直觀的例子，說明：「減一負數等於加上它的相反數」及「兩個負數相乘，得到一正數」的便捷之道；四、藉負數史中前人的經驗，幫助學生面對並跨越負數學習的困難。本文認為引導學生體會負數在數學中的美感價值，是值得嘗試的教學方式。

關鍵字

負數教學 ； 負數算則 ； 數學美學

並列摘要

The purpose of this article is to interpret the meaning and the aesthetics value in the history of negative numbers and the instruction of negative numbers. The argument begins with explaining the reasons why the aesthetic approach can be recommended to inspire the instruction of negative numbers. The aesthetic contents of negative numbers are then analyzed and presented. The author further explicates the beauty embedded in negative numbers can be demonstrated through their developmental history. This article ends up with emphasizing the 4 merits of aesthetic viewpoints in broadening the visions of the negative number instruction; they are as follows: (1) to calm the restlessness of negative number learning; (2) to inspire student to pay more attention to number learning; (3) to better the understanding of negative number algorithm through the aesthetic intuition afforded by two examples of figure images showing that ”subtracting a negative number by adding its opposite” and that ”the multiplication of two negative numbers being positive”; (4) to assist student in facing and overcoming the problems in learning negative numbers. The teachers are encouraged to facilitate students to embrace the aesthetic value of negative numbers and to tackle students' problems in advanced mathematics learning by taking into consideration of their cognitive abilities and mathematic performance.

並列關鍵字

mathematics aesthetics ； negative number algorithm ； negative number instruction

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