Cognitive and Non-Cognitive Processes: Students’ Perceptions about and Employment of Approaches to Novel Mathematics Problem Solving

The role of creativity in the education of young people is increasingly becoming viewed as an issue of critical importance. Famous introspective accounts from notable mathematicians and scientists such as Albert Einstein, Henri Poincare, and Barbara McClintock, have revealed that their discoveries have been based on the premise of utilising elements of creativity and ingenuity. Therefore, it would be beneficial to further investigate the creative process in the context of teaching and learning in Australian schools. The concept of creativity is one that has been explored in many different fields of research. With much contentious debate in the area, the creative process has been defined in numerous different ways, giving rise to confusion over how the concept should be applied to differing fields of inquiry. There is limited published research on creative problem solving in the classroom, with a particular emphasis on both the cognitive and non-cognitive elements involved. The lack of research on this topic is likely due to a lack of coherence surrounding the role of non-cognitive elements in reasoning, decision making, and problem solving, resulting in a flow on effect for creativity. The current qualitative study involved six participants from a school which specialises in mathematics and science that were selected based on their abilities in mathematics and their likelihood to be willing to share their thoughts on the subject matter. Through semi-structured interviews and verbal protocols of a novel mathematics problem solving event, a snapshot of the participants’ perceptions about and employment of different approaches to reasoning (both cognitive and non-cognitive) in novel mathematics problem solving was gained. A cross-case analysis was then undertaken to elicit themes relating to what constituted a successful novel mathematics problem solver. The five identified approaches to reasoning, used in providing a tool for analysis of the data, were taken to be critical in the process of reasoning in gaining a successful solution; however, the distinguishing factor was the Feeling (intuition) approach to reasoning. The current study contributes to the constantly growing breadth of literature examining the role of creativity and what impact it has for the future of education and society as a whole. Also, this study provides a basis for possible future research to extend upon or draw from; helping to provide a clearer picture of the process of creativity and the impact it may have for future generations.