Pre-Service Mathematics Teachers' Generalization Processes of Visual Patterns

Abstract

The aim of this study is to investigate pre-service mathematics teachers\" generalization processes and models used in these processes. 145 elementary pre-service mathematics teachers were asked four openended problems which requires to generalize linear and non-linear pictorial patterns. Pre-service teachers\" written responses were analyzed to investigate their generalization processes and how they used pictorial models in these processes. Radford\"s (2006) framework is used for the analysis. The analysis of data indicated that pre-service teachers used pictorial models more effectively for linear patterns when compared to non-linear patterns. It was also found that they tend to represent pictorial patterns numerically first and then generalize the numerical pattern. In addition to that it was observed that the way they discovered the commonalities among the terms of the patterns were not helpful in generalization process since they looked for commonalities by focusing on the consecutive terms of the patterns.