An investigation of cognitive and meta-cognitive mathematical modelling competencies of 7th grade middle school students

The purpose of this thesis study is to investigate cognitive and meta-cogniteve mathematical modelling competencies of 7th grade middle school students. Besides, it is aimed to determine how modelling competencies are in low achievement and high achievement groups. The study was conducted with 7th grade students enrolled in a public school having low socio-economic level of students. The pilot study was done by implementing model eliciting activities to the 24 students in one classroom in the form of group work for three weeks. After the pilot study, 8 students were selected from those 24 students for the main study and two groups of four students were formed with the mathematics achievement level being "low" and "high" considering their previous year final report card grade for mathematics course and the performances they had shown in the pilot study through criterion sampling. The two groups that were formed were asked to work on a total of three model eliciting activities for six weeks and all work processes were recorded with video. After that, the modelling competencies and the written documents that the students performed during the modelling processes were analyzed qualitatively in the domain of cognitive and meta-cognitive competences using the "Modelling Competencies Evaluation Rubric" adapted from the study of Biccard (2010). In line with the findings obtained from the groups as a result of the study, it was determined that 7th grade middle school students had difficulty in the modeling process, usually in the context of the competency of interpretation and validating of both groups. In addition to these, it was determined that the low achievement group had also difficulty and could not demonstrate adequate approaches in the understanding, working mathematically and mathematising competencies. Moreover, an increase was seen in the levels of the competencies of arguing, mathematising, planning and monitoring, and a sense of direction of the low achievement group throughout the working process. In general, it was determined that the cognitive and meta-cognitive competencies levels of the high achievement group were high; it was determined that the levels of meta-cognitive competencies increased at the end of the implementation period. One of the most important results obtained in the study was that an increase was determined in the levels of some competencies of the low achievement group at least as in the high achievement group. One of the most important results about the groups' views on mathematics was that especially for the low achievement group the view that mathematics can be made by reasoning and mathematics is rather funny than difficult as a course, became evident. As a result of this study, it is suggested that long-term mathematical modelling studies should be carried out and MEAs should be included in classroom practices in order to provide a steady increase in the levels of cognitive and meta-cognitive competencies of students. Keywords: Middle school students, modelling competencies, mathematical modelling, model eliciting activities.