Investigating students’ reasoning in generalization of deconstructive figural patterns

Different types of reasoning, such as intuitive, inductive, and deductive, are used in the generalization of figural patterns, as an important part of patterns in school mathematics. It is difficult to demarcate the constructive patterns where the regularity observed in the first few sentences is generalizable to the other sentences and each reasoning can lead to the correct answer. To examine the types of reasoning used by students and related factors, this study focuses on the deconstructive figural patterns through the design of three targeted tasks. The participants were 33 female students randomly selected from three 10th grade classes in one school. The data collected showed that a consistent reasoning is not used in tasks by the same participant and various factors, such as the appearance of the figures and the concepts used in the tasks, are involved in employing a reasoning. Moreover, the intuitive reasoning under the influence of a salient irrelevant variable was more prevalent than the others in the incorrect answers.