Exploring the secondary school students' mathematical modelling processes with Fermi problems

In this research, it was aimed to examine the Mathematical Modeling (MM) processes of sixth and seventh grade students through Fermi Problems (FP) designed from near to far according to their environment. The study was designed with a qualitative approach and is a case study. The sample of the research consists of a total of 37 students, 26 of whom are seventh graders and 11 of whom are sixth graders, from a secondary school studying in the 2021-2022 academic year. In line with the requests of the students, groups of three to five people were formed according to the class size. Thus, there are nine different groups in total. This study was completed with group work and solution presentation in 12 weeks / 24 lesson hours. Data; The worksheets of the student groups were collected with the help of group presentation videos and audio recordings. In the analysis of the data, the "Simplification" and "Mathematicalization" steps of the MM cycle were taken into consideration, and the variables, models and strategies used in these steps were analyzed by the content analysis method. According to the findings, student groups made various assumptions based on their experience and knowledge in the step of simplifying the problem. Sixth and seventh grade students identified different variables regarding FPs. In the strategies for determining the variable value for the simplification stage, it was observed that sixth graders tend to use external resources the most, and seventh graders tend to use digital tools and strategies based on previous knowledge and experience. Looking at the mathematization step, it was seen that all students developed mathematical models expressed verbally or arithmetically. In modeling strategies, it was determined that seventh graders used a different strategy in each question, while sixth graders used the concentration measurement strategy. It was determined that the students used seven different variable value determination strategies in the simplification step and six different model building strategies in the mathematization step. In addition, it has been determined that the context used in problems designed from near to far may affect students' strategies. In line with these results, suggestions were made to teachers and researchers.