The development of mathematical modeling activities for the middle school 7th grade students and determination of students' modeling competences

The study was carried out as a qualitative study in two different public schools in Bolu province. One of these schools was piloted and the missing parts of the designed activities were arranged and then the actual implementation was started in the other school. Students were selected by purposeful sampling method. The study lasted for 6 weeks with the students who chose the course titled "Mathematics Applications". There were nine students in pilot application,12 students were employed in the actual application and 3 groups were formed in both applications. In this study, two different mathematical modeling activities for Mathematics Applications for middle school 7th grade students were developed and the modeling competencies of the students were tried to be determined during the implementation of these activities. The first one was based on the "coordinate system" and the second was based on "translation and reflection". This study is a qualitative action research examining the mathematical modeling competencies of the groups. The modeling competencies of the groups were analyzed on the basis of Ludwig and Xu's (2010) modeling competencies and each level was divided into 5 different sub-levels. The findings of the study showed that in both activities, the groups reached Level 5 at the level of modeling competency, but remained lower in Level 5 in the first activity and Level 5 in the second activity. In both activities, the groups understood the basic questions, answered the questions, understood the real situation and related them to the mathematical idea As a result of this connections, they were able to develop models and work clearly on mathematical ideas. The groups were able to experience the mathematical modeling process by going through all these processes in the first activity, but they had difficulty in establishing the coordinate system mathematically. To sum up, it was seen that the levels of the groups were close to each other in both activities and thus the activities could be used in mathematics classes. As a result of the interviews with the students, it was revealed that modeling activities required a long time but a pleasant and enjoyable process was passed, their attitudes towards mathematics course has been changed positively, and other subjects of mathematics could be done with the activity. It has been suggested that mathematics teachers will be able to design modeling activities specific to learning attainments and it will be beneficial for students to work regularly with these activities in Mathematics Applications course. Key Words: Mathematical Modeling, Modeling Activities, Modeling Competencies, Secondary School Students