Patterning process of middle students in free and semi-free generalization tasks

The aim of this study is to examine partonomic structures that middle school sixth grade students formed in the context of generalizing semi-free and free patterns during teaching experiment process and the effect of these structures on the function-based generalization process. Qualitative research management was adopted in the collection, analysis and interpretation of data in the research and the study was designed as a teaching experiment. The research was carried out in the Osmanbey Middle School in Simav district of Kütahya province, in the 2018-2019 academic year. The teaching experiment was carried out as a nine-week classroom practices with a middle school sixth grade group consisting of three low, three middle and three high-level students. The data in the study were collected with clinical interview videos, classroom teaching lecture videos and student documents. At the end of the study, while it was observed that students mostly formed a figural pattern based on number pattern in the pre-clinical interviews, the majority of the students created patterns based on partonomic relationships in the last clinical interviews, and generalized patterns they formed based on standard or non-standard functions. In this process, it was determined that most of the students used table representation, verbal representation, semi-symbolic and symbolic representations and were able to switch between representations. In addition, it was among the observed results that the students used the representations meaningfully in themselves.