The impact of visualization on functional reasoning: the ability to generalize
Keywords:
Functional Reasoning, Patterns, Generalization, Visualization, LearningAbstract
With this study we try to understand how pre-service teachers, from basic education (for 3 to 12-year-old students), solve problems involving the generalization of patterns in visual contexts, identifying: the strategies they use; the difficulties they present; the role of visualization in their reasoning; and the factors that influence their generalizations. Considering the aims of this study, we followed a qualitative methodology. The participants were 80 pre-service teachers. During the classes of a Mathematics unit course, these students solved a sequence of tasks involving pattern generalization in figurative contexts. Our results showed that students were able to use different types of generalization strategies, but also that some dimensions of the tasks (e.g. type of pattern, nature of the figures) can have impact in students’ reasoning, causing, in some cases, a shift on the strategies used and the emergence of difficulties of different kind.
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