數學創造力的文獻回顧與探究

Abstract

數學創造力的描述至今尚未明確，本文將從四個不同的觀點回顧數學創造力。數學創造產出的新穎與一般創造力無中生有的新穎性不同，且數學創造力的「新穎」並非全然的無中生有而是將重點放在舊知識的「再結合」。使用創造力量表測量學童的創造力可能窄化了創造力的豐富內涵，部分學者改以「多元解題」的方法分析數學上的創造力指標。從創造力階段理論學童在數學創造的醞釀過程中藉由重組過去的知識與比對題目的條件，在反覆的組合和比對的過程中對學童對於舊知識產生新的認識。創造力的貢獻分為歷史上和心理上的貢獻，學校層次的研究焦點在國小孩童是否具備「心理上的數學創造力」。數學知識與數學創造力同等重要，提供學童發散性思考和連結舊經驗的環境有助於提升學童的數學創造力。

Specific descriptions of mathematical creativity have not been proposed. This article reviews mathematical creativity from four aspects: products, indicators, processes, and contributions. A description of novelty in mathematical creativity is different from that of original creativity; novelty focuses on the recombination of ＂old＂ knowledge in mathematical creativity. The use of creativity tests for measuring creativity indicators may lead the field into a narrow and limited conception of creativity. Recently, scholars have begun to use the multiple-solution task to analyze indicators of mathematical creativity. Regarding creative processes, students recombine mathematical knowledge and compare the recombinations by using the requirements of problems during the incubation period. Through these recombination processes, students obtain new understanding regarding the old knowledge. Creative contributions exist in two forms: historical creativity and psychological creativity. At the school level, the concept of psychological creativity has been adapted for researching the mathematical creativity of elementary school students. Mathematical knowledge and mathematical creativity are both critical. Fostering an environment that encourages divergent thinking and connects to related mathematical knowledge assists in nurturing a student's mathematical creativity abilities.