A design, implementation and evaluation of the teaching of algebraic concepts and generalisations in accordance with the abstraction process

The use of abstraction analysis in the teaching of mathematical concepts and generalizations has led to an increasing interest in abstraction. Those who investigate students' abstraction processes; They trained personal research, which increased the importance of examining classroom analysis. The aim of this study is to examine the processes of creating algebraic concepts and generalizations and abstraction processes of 6th and 7th grade students starting from the 6th grade and determining the contribution of the design of encryption method to the abstraction process by experimenting. The research is in mixed method research model and consists of two stages. The design-based research model was used in the first stage, and the case study model was used in the second stage, and it is a semi-longitudinal study. The study was conducted for two years between 2017 and 2018 in Bursa Setbaşı Secondary School with a total of 64 students in two groups, one of which was determined as the experimental group and the other as the control group. Chelsea Algebra Diagnostic Test (CCTT) was applied before the application to measure the students' knowledge of algebra concepts and generalizations. By determining the concepts and generalizations of algebra in the curriculum in the sixth and seventh grades, an instructional design was prepared that would allow to examine the abstraction processes of these concepts and generalizations, and the deficiencies were identified and eliminated through a pilot study, and the instructional design was applied to the experimental group students. After the application, CCTT, SBT1 (Abstraction Skills Test), SBT and SBT3 tests were performed, the results were analyzed, and the abstraction processes of the students were examined in detail with the RBC + C model. The development between the pre and posttests was determined by quantitative analysis. In order to analyze the abstraction processes of the students in depth, the activity papers of the focus group students with 2 low, 3 medium and 4 high achievement levels selected from the experimental group, and the qualitative analysis of the pre and post tests were carried out within the framework of the determined thematic abstraction indicators. Some of the situations when the indicators are taken as in the RBC + C model do not allow for detailed analysis, so they are detailed. Considering the quantitative analysis results of the SBT2, SBT3 and CCTT pre and post tests used in the study, it was seen that significant differences were obtained in the development of abstraction skills of the students after the applications in 6th and 7th grade. It was observed that abstraction skills developed in the qualitative analysis of the activity papers and tests obtained from the focus group students selected for detailed analysis. It has been observed that students with medium and high achievement levels have reached the stages of formation and reinforcement. It has been observed that students with low level of success may have false positional forms or achieved partial correct constructions with helpful recognition. In the second stage of the study, when the qualitative data obtained from the focus group students were analyzed, it was concluded that the students with high success level and middle students could reach the reinforcement step, while the students with low achievement level could not reinforce it because they remained at the partial correct formation step. It was concluded that the instructional design prepared at the end of the study improved the abstraction skills of the students. It was concluded that the RBC + C model can be used as an informative and design tool as well as a diagnostic tool. According to these results, suggestions were made for teaching and future studies in the process of developing abstraction skills.