science education
M. Nadjafikhah; N. Yaftian; S. Bakhshalizadeh
Abstract
Mathematical creativity is often considered as a mysterious phenomenon. Most mathematicians seem to be not interested in analyzing their own thinking processes and do not describe how they work or conceive their theories. One of the goals of this paper, which is based on research findings from contemporary ...
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Mathematical creativity is often considered as a mysterious phenomenon. Most mathematicians seem to be not interested in analyzing their own thinking processes and do not describe how they work or conceive their theories. One of the goals of this paper, which is based on research findings from contemporary literature, presents some definitions and characteristics of mathematical creativity and also describes and analyzes mathematicians’ thinking processes during creating mathematics. For this purpose, a four-stage model is considered consisting of: preparation, incubation, illumination and verification. Referring to literature, it is evident that there is not a specific conventional definition of mathematical creativity. According to some of definitions, a creative act in mathematics could consist of: creating a new fruitful mathematical concept; discovering an unknown relation; and reorganizing the structure of a mathematical theory. The challenges in the identification and development of mathematical creativity are due to the large variety in definitions and characteristics of mathematical creativity. Understanding, intuition, insight and generalization are some of moving powers of mathematical creativity. Fallibility is one of the characteristics of creative mathematical activities which should be appreciated since this existing chance of fallibility could lead to major success achievements of human. Hence, considering all above mentioned, learning-teaching mathematics should be so that it provides environment that fosters ability to make connections among concepts and processes and also provides opportunities to generalize.
