Middle school students' mathematical modeling skills and their representation usage in the modeling process

Mathematics and everyday life cannot be treated separately in today's education systems, and mathematics should not be a lesson taught only in classrooms. Mathematical modeling activities may serve as a bridge between mathematics and real life and highlights the importance of mathematics in daily experiences. Thus, the study aimed to examine middle school students' competencies in the mathematical modeling process and their usage of representations in the modeling process. Twelve students were chosen among middle school students enrolled in a public school in the Southeast Anatolia Region and were divided into three groups to engage in modeling activities. This study used a case study methodology to examine the development of students' modeling skills and their use of representation in the process. The students participated in four different mathematical modeling activities. The data collected from their written work, audio and video recordings, and notebooks were examined in detail within two stages focusing on the modeling process and their representation usage. In the first data analysis stage, the modeling processes were analyzed based on the modeling rubric. In the second stage, content analysis was conducted in the context of the representations used in the modeling steps. The results revealed that the primary purpose of the students was to digitize the question by attending numeric values, aim to make calculations directly, and mathematize it excessively instead of discussing the appropriate solution without internalizing the problem in the modeling processes. The students were the most successful in understanding the problem and mathematization steps, and the most unsuccessful was the verification step. In the interpretation step, they were unsuccessful in the first activities, but as they got used to the structure of the modeling activities in the following modeling tasks, their interpretation skills increased in parallel. The results also showed that the students used verbal, figural, graphical, and table representations throughout the modeling process. The students mostly used verbal and figural representations in modeling activities. They failed to use representation in the interpretation and validation step. The results of this study suggest that if the students have more opportunities for mathematical modeling tasks in their mathematics classrooms, they will better associate and interpret mathematics with daily life and increase their ability to use different representations. For these reasons, students need more opportunities to engage in mathematical modeling activities. Keywords: Mathematical modeling, modeling process, mathematical representations