Visualization and visual representation in problem solving

This research aims to investigate the effect of teaching through visualization and representation-based activities in math problem-solving processes on the problem-solving success of students of 8th grade, their attitude towards problem-solving and mathematics lessons. In the research, students' general problem-solving behaviors and visual representation behaviors were also examined in detail. In the research, the descriptive pattern of the mixed method with quantitative and qualitative data was used. The study group of the study consisted of 54 eighth grade students who took the Mathematics Practice course at a public school in a district in the West Black Sea in the 2018-2019 academic year. The quantitative dimension of the research was performed with a single group pretest-posttest experimental design and the qualitative dimension was performed with case study design. In the study, the Problem Solving Achievement Test, developed by the researcher to examine the change in students' problem-solving achievements, and the Math Problem Solving Attitude Scale and Math Attitude Scale, as well as the records of the interviews with the students were used to examine the change in the attitude towards the problem solving and mathematics lesson. As the data analysis in the quantitative dimension of the research, the descriptive analysis was used in the qualitative dimension while Wilcoxon Signed Rank Test, Mann Whitney U- test, Kruskal Wallis Test, Dependent Sample t-Test, Independent Sample t-Test and ANOVA Test were used. While teaching using visualization and representation had a statistically significant effect on students' problem-solving success, it was observed that there was no significant difference regarding the gender of the students and there was no significant difference in the education status of the parents. While the attitudes of 8th-grade students towards problem-solving did not make any difference in terms of the "teaching" dimension, they made a difference in favor of pre-testing in the "liking" dimension. In the attitude towards problem-solving, there is no significant difference in pre-test and post-test scores according to gender, while there is a difference in the education status of parents in favor of fathers who are high school graduates. There is a significant difference between the pre-test and post-test scores of the 8th-grade students' attitude towards mathematics course in favor of the pre-test. There is no significant difference between students' gender, education level of parents'. As a result of the interviews with the students, it was seen that the students were able to create correct visuals by using the factual knowledge and strategy knowledge correctly and in place. However, it is seen that students with low problem solving success need more education in using this type of knowledge. Although some problems are lacking in the context of conceptual or procedural knowledge, it has been observed that they can solve the problem correctly and meaningfully with the right strategy knowledge.