Pre-service Elementary Teachers’ Reasoning Types of Generalization and Justification on a Figural Pattern Task

Abstract

The purpose of this study is to examine how pre-service elementary teachers generalize a non-linear figural pattern task and justify their generalizations. More specifically, this study focuses on strategies and reasoning types employed by pre-service elementary teachers throughout generalization and justification processes. Data were collected from 32 pre-service elementary teachers who were enrolled in the Elementary Teacher Education program of a university, Turkey. During the data collection process, these pre-service teachers were first asked to generalize a non-linear figural pattern task and were then asked to justify their generalizations. To analyze the pre-service elementary teachers’ written answers for the task considering reasoning types for both generalization and justification, data reduction and constant comparative methodologies were used (Miles, Huberman, & Saldana, 2014). The findings indicated that the pre-service teachers were better able to find a rule for the pattern using the explicit strategy. It was also found that although these pre-service teachers used different types of reasoning which were numerical reasoning, figural reasoning, and pragmatic reasoning, figural reasoning was the most frequent one throughout the generalization process. Reasoning types for justification by the pre-service teachers fell into two categories: inductive and deductive. Most pre-service teachers resorted to inductive reasoning; however, there were a few pre-service teachers who referred to deductive reasoning. In addition, the pre-service teachers who articulated figural reasoning to generalize appeared to be more successful in justifying their developed rules deductively.