Linking Mathematical Creativity to Problem Solving: Views from the Field

Abstract

The purpose of this chapter is to gain an understanding of how mathematics educators view creativity in mathematical problem solving. We are particularly concerned with their opinions as to the role creativity plays in mathematics education, how creativity can be and is promoted, and if the promotion of creativity is valid for all mathematics students. To address these issues, we review the literature on mathematical creativity. Due to its complex and multifaceted nature as a construct, particular attention is given to four different lenses for considering creativity. The first is how creativity is defined, as a product, a process, or an experience (Getzels, Encyclopedia of Educational Research, New York: Macmillan, 1969). The second considers three components of creativity – fluency, flexibility, and novelty (Silver, ZDM 29:75–80, 1997). We then focus on five overarching principles that have been proposed to maximize creativity: gestalt, aesthetic, free market, scholarly, and uncertainty (Sriraman, Prufrock Journal 17:20–36, 2005). Finally, the fourth lens delves into the keys to creating a creativity-friendly classroom (Starko, Creativity in the classroom: Schools of curious delight, New York: Routledge, 2013). In light of what is known in the field of mathematics education, we then report on a particular group and its members’ ideas related to creativity. The group under consideration is comprised of instructors and staff associated with a gifted mathematics program in the United States. The data used for this qualitative analysis includes instructors’ and staff members’ responses to a set of five open-ended survey items related to creativity and problem solving in mathematics. Responses were collected, compiled, and then shared with all participants in order to gain feedback and further insights into their interpretations. The multiple phases of coding (one for each lens being considered) and the variety of coding schemes allowed the research team to develop a more comprehensive understanding of how differing views of creativity impact the way educators consider methods for fostering creativity in mathematics classrooms.