Generalization Strategies about Linear Figural Patterns: Effect of Figural and Numerical Clues

Abstract

Generalization is one of the fundamental building structures of algebra and an important component of development of algebraic thinking. The pattern in mathematical process is a basic step for structuring the generalization and is crucial to reach generalization. In this study, pre-service teachers' strategies to generalize linear shape patterns were investigated. Sixteen pre-service teachers participated in the treatment. For data collection, clinical interview technique was used and the interviews were recorded. The obtained data was analyzed qualitatively. It was found that while determining the rule of pattern and extending the linear shape pattern to next/far step, some pre-service teachers adapted the numerical approach through which the visual and figural patterns that focus on only shape are conveyed into numerical pattern. Under these approaches, they used 26 strategies in total. While generalizing the patterns under the numerical approach, pre-service teachers applied recursive strategies in which only the relationship between the terms were examined. On the other hand, under the figural approach, they used the functional strategies which were both recursive in examining the relationship between the variables.