Preservice Mathematics Teachers' Knowledge of Generalization and Justification about Patterns

Abstract

The purpose of this study is to examine preservice elementary school mathematics teachers' knowledge of generalization within the context of patterns, to elaborate their justifications for generalizations and to identify the relationships between the generalizations and justifications. In this study, which was conducted with eight preservice teachers using the basic qualitative research design, the research data were collected with the clinical interview technique. As the data collection tool, linear and non-linear pattern tasks were used. The data coming from clinical interview were analyzed through thematic analysis method. The research findings revealed that the preservice teachers used explicit and implicit reasoning in the process of generalizing the patterns, and applied deductive and inductive methods in the process of justifying their reasoning. In the study, the preservice teachers who prefer explicit reasoning generally used deductive and inductive methods in the justification process, while those also used implicit reasoning applied only the inductive method. It was also found that some of the preservice teachers' justifications were limited to using empirical evidence and taking support from external authority. One important result obtained in the study was that the given figural pattern tasks supported the processes of generalization and justification. In addition, another important result was that justification contributed to generalization. Preservice teachers could be provided with the opportunity to develop a more in-depth understanding of the processes of generalization and justification in the profession-related courses in the field of teacher training.