Investigation of processes about modeling that mathematics teachers and preservice teachers designed and applied

The purpose of this study is to explore development and utilization of modeling tactics by in-service and pre-service teachers. The modeling tactics are a type of demonstration strategies which are an important element of pedagogic content knowledge.In order to determine how in-service and pre-service teachers develop and utilize the modeling tactics, qualitative research methodology was used. The data of the study were analyzed using grounded theory techniques. Three in-service and three pre-service secondary school mathematics teachers were the participants of this study. Each in-service and pre-service teacher prepared lesson plans for two mathematical concepts; trigonometry and circle. Total of twelve lesson plans were prepared. Then these lesson plans were reviewed and one plan for each teacher was observed in classroom while they teach the concept. Using the data from these lesson plans and observations, modeling tactics used by the teachers were extracted. Finally, teacher interviews were conducted on preparation and utilization process of these modeling tactics.In the light of findings from this analysis, the process that pre-service and in-service teachers use determining modeling tactics was put forward. Findings indicate that pre-service teachers first determine the utilization purpose of the model, then based on this purpose they decide on the type of modeling they use, and finally, based on their purpose they start searching for and selecting modeling aligned with their instructional purposes in different resources. Findings also indicated that some factors affect this modeling selection process. These factors were mainly grouped under learning and teaching styles of teachers and levels of knowledge for other elements of pedagogic content knowledge. Moreover, a schema was provided for each step in the modeling process and factors affecting it. This schema presents all possible situations related to types of modeling, the purposes of modeling and utilization stages of modeling, resources utilized for searching/developing modeling, and factors impacting modeling selection process.