Investigation of 8th grade students' proportional and probability reasoning skills and awareness of their metacognitive self-regulations in the problem solving process

The aim of this study is to determine the proportional reasoning skills, probabilistic reasoning skills and awareness of metacognitive self-regulation in the problem solving process of 8th grade students and to investigate the relationships between them. In addition, it was aimed to examine the proportional reasoning skills, probabilistic reasoning skills and awareness of metacognitive self-regulation in the problem solving process of 8th grade students in terms of gender and perception of mathematical competence variables. In this particular study, causal comparison and correlational approach were used, which are the basis of the descriptive survey model and the relational survey model. The study group of the research consists of 315 students studying in the eighth grade of four secondary schools in the central districts of a province in the Eastern Anatolia Region in the 2021-2022 academic year. Proportional Reasoning Skill Test, Probabilistic Reasoning Skill Test and Metacognitive Self-Regulation Scale were used as data collection tools in the research. While calculating the arithmetic mean and standard deviation values from descriptive statistics in the analysis of the data obtained in the study, the F test was used to determine whether the students' skill and awareness scores differed in terms of these variables. In addition, the Pearson Correlation Coefficient was used to determine whether there was a statistically significant relationship between the proportional reasoning skill levels, probabilistic reasoning skill levels, and awareness levels of metacognitive self-regulation in the problem solving process. As a result of the descriptive analyzes, it was concluded that the proportional reasoning skill scores of the 8th grade students were at a moderate level, their probabilistic reasoning scores were at a low level, and their metacognitive self-regulation awareness scores were at a sufficient level. According to the results of the difference analysis, it was determined that there was no significant difference between the proportional and probabilistic reasoning skill scores of the students and the metacognitive self-regulation awareness scores in terms of gender variable. In terms of the mathematical competence variable, statistically significant differences were found between the proportional and probabilistic reasoning skill scores of the students and the metacognitive self-regulation awareness scores. In addition, a high level of positive correlation was found between proportional reasoning skill levels and probabilistic reasoning skill levels of students, and a moderate positive correlation between proportional reasoning skill levels and awareness levels of metacognitive self-regulation. Similarly, it was concluded that there is a moderately positive relationship between the levels of probabilistic reasoning skills and the awareness of their metacognitive self-regulations. Key Words: Proportional Reasoning, Probabilistic Reasoning, Metacognitive Self-Regulation, Mathematical Competence