Pre-Service Elementary Mathematics Teachers’ Generalization Processes of Patterns: Strategies and Justifications

The aim of this study is to investigate the generalizations created by pre-service elementary mathematic teachers, to explore the justifications predicted for their generalizations, and to determine any relationships between generalization and justification. We used phenomenology design from qualitative research methods in the study. The study was conducted by the 4th grade students/pre-service teachers who are studying in a department of Elementary Mathematics Teaching at a university located in the Eastern Black Sea region. Data collection tools are linear and quadratic pattern problems which are prepared with the support of literature and teaching staff and in which different solution strategies and justification types can be produced. Interviews were analyzed using the descriptive analysis technique within the conceptual framework of the research. The results show that the most common type of strategy used by pre-service teachers was functional strategy, contextual, recursive, guess-check and mixed strategies. While many of the pre-service teachers have justified their verification by numerical control, pre-service teachers who have justified through explanation and external knowledge sources have also been identified.