Visualization in pattern generalization: potential and challenges

Abstract

This study tries to understand how pre-service teachers, for basic education, solve problems involving the generalization of visual patterns, identifying: the strategies used; the difficulties presented; the role of visualization in their reasoning; the factors that influence their generalizations. We followed a qualitative methodology. The participants were 80 pre-service teachers. During the classes of a Didactics of Mathematics unit course, they solved a sequence of tasks involving growing visual patterns. Results showed that students were able to use different strategies, but also that some dimensions of the tasks can have impact in their reasoning, provoking, sometimes, a shift on the strategies used and the emergence of difficulties of different kind.