Mathematical Creativity and Mathematics Education

Mathematical Creativity and Mathematics Education Narges Yaftian1, Mehdi Nadjafikhah2, Shahrnaz Bakhshalizadeh 3 Iran University of Science and Technology - Shahid Rajaee Teacher Training University, Iran

Abstract Creativity plays an essential role in mathematics. It helps to make plausible conjectures in developing mathematical theories. It is an essential factor when new ideas are formulated or when an idea is presented in a new way. 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. Only a few (such as Poincaré and Hadamard) made effort to describe ideas related to mathematical creativity. Mathematical creativity can not occur in vacuum and needs a context in which the individual moves forward based on previous experiences. The purpose of this paper is to provide an overview of effective characteristics of mathematical creativity which briefly describe how creativity in mathematical developments could be occurred. In addition, it describes moving power of mathematical creativity. Keywords: mathematics education, creativity, mathematical creativity, creative process 1 Introduction When one thinks of the term "creativity", one may use it interchangeably instead of discovery. What would one mean, while (s)he uses the term “creativity”? What is the difference between creativity and discovery? Discovery is when something already existed but it is not known to one. For instance, America already existed and Christopher Columbus discovered it. However, when one talks about creativity, one may think of something which was not existed before and is being created. Some of distinctions between these terms have roots in philosophy, but from Hadamard’s point of view, psychological conditions of both terms are quite the same [1]. Referring to literature, a number of definitions for creativity could be found. In this paper, we emphasize on those which are closely related to mathematics and solving problem in mathematics. There is not a certain conventional definition of mathematical creativity [2]. In that regards, some questions come to the mind. For instance, when students solve a problem that its solution is known previously if this action is considered as a creative work? Does creativity occur in a mathematical activity when students solve an old problem in a new way? Or, does creativity refer to just finding an authentic, new idea? The challenges in the identification and development of mathematical creativity and answering these questions are due to the large variety in definitions and characteristics of mathematical creativity. Since describing structure of mathematical creativity and its characteristics is vague and difficult, the majority of available definitions has been introduced which created challenges found in mathematics and mathematics education literature. For instance: 1

- PhD student and member of academic board - Member of academic board - Iran University of Science and Technology 3 -Ministry of Education, Organization for Educational Research and Planning, Iran