The Power of Seeing in Problem Solving and Creativity: An Issue Under Discussion

Abstract

This paper discusses some assumptions in the teaching and learning of problem solving, including the particular importance of a problem-solving strategy towards a visual solution, named seeing, which can be a complementary contribution to the approach and development of problem-solving abilities in students and its relation with mathematical creativity. In this path of stressing visual strategies and representations, we present and discuss different potentialities of visualization, as students use it to solve problems, pointing out some appropriate tasks to illustrate them, and we also underline some constraints of the use of visualization. Within problem solving, we make the connection between the use of visual solutions and mathematical creativity, which allows producing new and elegant solutions to a problem, clarifying and deepening the understanding of it, as well as suggesting productive paths for reasoning. Finally, we illustrate the ideas discussed based on examples emerging from some studies that we carried out with elementary pre-service teachers.