Exploring Collective Mathematical Creativity in Elementary School

This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity in elementary school classrooms. Collective learning takes place when mathematical ideas and actions, initially stemming from an individual, are built upon and reworked, producing a solution which is the product of the collective. Referring to characteristics of individual mathematical creativity, such as fluency, flexibility, and originality, this paper examines the possibility that collective mathematical creativity may be similarly characterized. The paper also explores the role of the teacher in fostering collective mathematical creativity and the possible relationship between individual and collective mathematical creativity. Many studies have investigated ways of characterizing, identifying, and promoting mathematical creativity. Haylock (1997), for example, and more recently, Kwon, Park, and Park (2006) assessed students' mathematical creativity by employing open‐ended problems and measuring divergent thinking skills. Leikin (2009) explored the use of multiple solution tasks in evaluating a student's mathematical creativity. These studies focused on an individual's mathematical creativity as it manifests itself in the solving of various problems. Yet students, acting in a classroom community, do not necessarily act on their own. Ideas are interchanged, evaluated, and built‐upon, often with the guidance of the teacher. The resultant mathematical creativity of an individual may be a product of collective community practice. The question which then arises is: Who is being mathematically creative, the individual or the community? This study focuses on the collective, not as the aggregation of a few individuals, but as a unit of study. Although some of the studies mentioned above acknowledged the effect of classroom culture on the development of mathematical creativity, and others considered the creative range of a group of students, those studies did not necessarily investigate mathematical creativity as a collective process or as the product of participating in a collective endeavour. This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity. The notion of collective creativity has been used to investigate creativity in several contexts including the work place (Hargadon & Bechky, 2006) and the global community (Family, 2003). In those cases, collective creativity was considered to occur when the social interactions between individuals yielded new interpretations that the individuals involved, thinking alone, could not have generated. Can the notion of collective creativity also be applied to the classroom community?