Virtual Learning Communities of Problem Solvers: A Potential for Developing Creativity in Mathematics?

Abstract

Mathematics is viewed as a school subject that can develop creativity in students (Liljedahl and Sriraman in Learn Math 26: 17-19, 2006; Sheffield in Creativity in mathematics and the education of gifted students. Sense Publishers, Rotterdam, The Netherlands, pp. 87-100, 2009; Sriraman in ZDM: Int J Math Educ 41: 13-27, 2009). However, many authors have mentioned that mathematics learning is still based on applying routine procedures and already prescribed algorithms (Chan Chun Ming in The use of mathematical modeling tasks to develop creativity, 2008). Yet, studies have shown that open-ended problems can create opportunities for students to face more cognitive challenges and to develop different and original problem solving strategies, thus leading to more creative solutions (Leikin in Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks, pp. 2330-2339, 2007). Some researchers have also mentioned that virtual learning communities may support the development of creativity, but this does not seem to have been proved (Piggot in Math Teach 202: 3-6, 2007). This study thus focuses on the richness of mathematical problems posted and the creativity of solutions submitted by members of the CAMI website, a virtual community of problem solving designed for Francophone students from New Brunswick, Canada, and elsewhere. I have developed a conceptual framework to: analyze the richness of the problems posted on the website; assess the mathematical creativity of the solutions submitted; and determine whether a link exists between these two variables. I created two grids to analyze the richness of the problems and the creativity of the solutions for 50 randomly selected problems. Then, using the Likelihood ratio, I determined whether there was a link between the two variables. Results show that, in general, richer problems seem to bring different correct answers and more original solutions.