The construction and evaluation of a learning environment to develop pre-service elementary mathematics teachers' mathematical modeling performance

The purpose of the study was to examine and to develop pre-service elementary mathematics teachers' mathematical modeling performance. The study was conducted with 24 second-year prospective teachers taking the elective course offered in a public university in Blacksea Region during one semester. The design of the study was mixed approach since quantitative and qualitative data collection and data analysis methods were used together. The quantitative part of the study was conducted by using single group pre-test and post-test design. In this part, the main purpose is to determine whether teaching method by using mathematical modeling has any effect on pre-service teachers' mathematical modeling skills. Pre-service teachers were taught by using mathematical modeling method during one semester. Each week they were given two mathematical modeling problems and were required to solve them by doing group work. After that, self evaluation forms for each problem were given to each group in order to make an evaluation of the mathematical modeling process. The data collection tools of the study consisted of pre and post mathematical modeling performance tests, self evaluation forms, solution papers of the problems which were solved in the class and the researcher's daily notes. The scoring of the mathematical modeling performance tests were made according to the analytical scoring scale which was developed by Özer-Keskin (2008). In data analysis process, SPSS 20 package program was used in order to make paired samples t test and also descriptive statistics was used. Besides, self evalution forms, solution papers and researcher's daily notes were analyzed by the use of descriptive analysis. The results showed that pre-service teachers'post-test scores for the mathematical modeling performance test are significantly higher than the pre-test scores which were collected before the treatment. Hence, it can be inferred that there was a development in modeling skills of the pre-service teachers. According to each modeling step, the scores of the pre-test showed that pre-service teachers had difficulty in "understanding the problem" phase which was the first step of mathematical modeling process. As a result, they could not be successful in further steps. However, there was an increase in the scores of pre-service teachers' scores for each modeling step after the treatment. Though, the difficulties in interpreting the solutions to real life decreased but still observed at the end of the treatment. Besides, it can be concluded that the pre-service teachers had some difficulties within the mathematical modeling process and they explained that the modeling activities were too long and complicated. Until the end of treatment, those difficulties continued but in a decreasing manner.