Assessment of primary school students' modeling competencies and reasoning processes in the context of mathematical modeling: An action research study

This research was conducted to examine the mathematical modeling competencies and mathematical reasoning processes of fourth-grade elementary school students. In this context, the students' reasoning skills were evaluated according to their tendencies toward rote, algorithmic, and creative reasoning. The research was designed as an action research study in line with the qualitative paradigm. The action research implementation process consisted of a total of three cycles, with the first cycle being a pilot application. The first cycle, which was the pilot application, lasted four weeks, the second cycle lasted four weeks, and the third cycle lasted three weeks. Thus, in the second and third cycles, which were the main application part of the research, mathematical modeling activities were given to students for seven weeks, and during this process, both their mathematical modeling competencies and mathematical reasoning processes were evaluated. The data for the research were collected through three focus groups. Data collection tools used in the study included mathematical modeling activity solution sheets, video and audio recordings, reflective journals, and semi-structured interview forms. Content analysis and evaluation rubrics were used to analyze the data obtained from the study. Within this scope, it was determined that students had high mathematical modeling competencies. Students achieved high success particularly in competency areas such as understanding the problem, simplifying it, and mathematizing it. Students can achieve successful results in terms of modeling competencies when provided with the right group dynamics and guidance and when working with modeling activities appropriate to their levels. Throughout the mathematical modeling activities, when students' reasoning processes were examined, all three types of reasoning—rote, algorithmic, and creative—were observed. However, when action research is evaluated in general, it has been observed that creativity-based reasoning comes to the fore. When the action research process was completed, students began to use creativity-based reasoning predominantly while solving problems. The mathematical modeling cycle provided opportunities for students to naturally use their creativity. In the process, students' group work, exchange of ideas, and proper teacher guidance supported creativity-based reasoning. When students' opinions on mathematical modeling activities were gathered, they generally gave positive evaluations and expressed a desire for these activities to be implemented in their lessons. Students stated that they found the modeling activities most challenging due to their complex structure and length.