Patterns generalization processes, preferred strategies, determination of misconceptions of 7th grade students and the effect of problem based learning applications supported by concept cartoons on eliminating the misconceptions

The purpose of this study is to determine the pattern generalization processes, preferred strategies and misconceptions of secondary school seventh grade students and to analyze the effect of concept cartoon supported problem-based learning practices in eliminating these misconceptions. In this study, the qualitative research design was used in the data collection, analysis and interpretation. In the research, firstly, the Pattern Test was applied to 152 seventh grade students selected by simple random sampling method. An experimental application was carried out to eliminate the misconceptions of 31 students selected by criterion sampling method, one of the purposeful sampling methods. The research was carried out in two stages. An experimental study was carried out based on the pre-test post-test single-group weak experimental design model, which is one of the experimental design models. Pattern Test and Interview Form were used. The obtained data were analyzed descriptively. As a result of the study, it is seen that most of the students remained at the level of arithmetic generalization or immature induction, where they could not make algebraic generalizations. It is determined that the students preferred the most iterative and modeling strategies to find the terms in the close step of the pattern, the most preferred strategies in the middle step are iterative and multiplication by difference, and the most preferred strategies in the far step are multiplication and functional strategies. It is concluded that the students generally used different strategies in solving the same problem and did not stick to a single strategy. It has been observed that students have more misconceptions about expressing the amount of increase in the pattern generalization process as the general term of the pattern, mistakes made in choosing the mathematical process, not using the model effectively, and limiting the rule of the pattern with verbal expressions. It is determined that problem-based learning practices supported by concept cartoons have a positive effect on eliminating the misconceptions of secondary school seventh grade students about patterns.