Developing mathematical modeling activities in science education and investigating mathematical modeling competencies of science teachers and teacher candidates

This study on the use of mathematical modeling (MM) in science education has three main aims. The first of these aims is to develop mathematical modeling activities (MMA) for use in science education, the second is to examine the mathematical modeling competencies (MMCs) of pre-service science teachers and teachers, and the third is to obtain the views of pre-service science teachers and teachers who have experienced MM. A qualitative research was conducted with 4 academicians and 12 science teacher candidates in line with the first purpose, with 12 science teacher candidates and teachers in line with the second purpose, and with 9 science teacher candidates and teachers in line with the third purpose. In the research, design-based research, case study and phenomenology patterns were used. The data of the research were obtained by document analysis methods, interview and observation techniques. 6 video-based MMAs designed on 2 physics, 2 chemistry, and 2 biology topics were analyzed with descriptive analysis by means of Erbaş et al. (2013)'s evaluation criteria in accordance of principles of Model Eliciting Activity (MEA) (Lesh et al.,2000). In order to determine MMCs, descriptive analysis was used by considering the competencies of Borromeo Ferri (2006) and subcompetencies revised by Çakmak (2018). Content analysis was used to obtain views on MM. As a result of the analysis of the data obtained, it was determined that all six of the MMAs were fully compatible with 5 principles and partially compatible with 1 principle. As a result of MMCs' examination, MMCs develop in the process, the most successful competence is understanding, and the most unsuccessful competence is simplification and structuring. Contrary to the literature, it has been determined that there is no problem in reaching real results from mathematical results. While it is seen that newly graduated science teachers and experienced science teachers have an equal level of MMC, it is seen that science teacher candidates have less MMC. In the process, MMCs were performed in biology and chemistry at least, and in physics at most. As a result of the interviews, it is concluded that the participants did not have MM knowledge before the application, and then their perceptions about MM were formed. It is recommended to increase MEAs studies for science, to give MM courses at minimum undergraduate level.