Development of cognitive mathematical modeling competencies of elementary school fourth grade students

In this study, the developmental process of fourth grade elementary school students' cognitive mathematical modeling competencies was examined. In this context, this research is a constructivist teaching experiment based on the examination of the developmental process of mathematical modeling competencies developed by Borromeo Ferri (2006) during the model eliciting activities of fourth grade elementary school students. The study group consisted of eight students with low, medium and high mathematical modeling competencies. Among these eight students, three students were selected as the focus participants. The data collection tool of the study was the task-based interview method used in mathematics education qualitative research. In this study, eleven (11) different model eliciting activities were designed for fourth grade elementary school students. Of these eleven (11) model eliciting activities, one was used for identifying the study group and focus participants, and four were used in the pre-clinical, mid-clinical, and final clinical interview process. The remaining six model eliciting activities were applied during the teaching episodes. In this direction, model eliciting activities were given to the students to work on a task and it was tried to determine the modeling competencies and development of the students. In this direction, a process including six teaching episodes and four clinical interviews with fourth grade elementary school students was carried out in which the researcher assumed the role of researcher/teacher and model eliciting activities were implemented in line with cooperative learning techniques (think-talk-write, think-pair-share, timed pair-share). The mathematical modeling processes and competencies of fourth grade elementary school students were analyzed using the Rubric for the Assessment of Modeling Skills created by Tekin Dede and Bukova Güzel (2018) in line with Borromeo Ferri's (2006) modeling competencies. In the first clinical interview and teaching episodes of the research process, it was observed that students proceeded directly to problem solving without understanding and simplifying the problem. In addition, since the students had a result-oriented understanding, they did not interpreting and validating the mathematical result they obtained. However, it was determined that the cooperative learning techniques used (think-talk-write, think-pair-share, timed pair-share) enabled students to demonstrate and improve their cognitive mathematical modeling competencies (understanding the task, simplifying, mathematizing, working mathematically, interpreting, validating). In other words, it was concluded that cooperative learning techniques (think-talk-write, think-pair-share, timed pair-share), which form the basis of the designed learning environments, improved students' cognitive mathematical modeling competencies. It was also concluded that solving mathematical modeling problems, in other words, gaining experience in mathematical modeling by solving problems, improved students' cognitive mathematical modeling competencies. Finally, it was determined that critical thinking, problem solving, collaboration and mathematical communication skills (21st century skills) of students who experienced mathematical modeling process by working with cooperative learning techniques and model eliciting activities developed.