Metacognitive and cognitive processes utilized by fifth grade students in solving problems designed free of numbers

Mathematical problem-solving ability is closely related to various skills and individual characteristics. Higher cognitive skills are also important factors that affect problem-solving ability. This research is a case study that examines the metacognitive and cognitive processes utilized by fifth grade students in solving problems designed free of numbers. The study group consists of six students at the 5th-grade level. Two of these students have high, two have medium, and two have low levels of mathematical achievement. The two students with high levels of mathematical achievement are also identified as gifted. The research process lasted for seven weeks. Each week, students solved two problems designed free of numbers using the think-aloud method. Audio recordings of students' thoughts and video recordings of their worksheets were taken. The collected data were analyzed using qualitative methods to reach the findings of the research. According to the research findings, when solving problems designed free of numbers, students mostly used metacognitive strategies during the reading-comprehension stage. It was observed that students, especially those with medium levels of mathematical achievement, frequently used strategies such as rereading the problem and expressing it in their own words. In tasks requiring comparison, ordering, or determining the ratio, students with high levels of mathematical achievement were able to reason without using numbers, whereas other students faced difficulties in this regard. Another finding of the research is that during the control stage of problem-solving, students with high levels of mathematical achievement applied appropriate metacognitive strategies to ensure control, students with medium levels of mathematical achievement used metacognitive strategies but still encountered difficulties in the control stage, and students with low levels of mathematical achievement generally failed to use effective control strategies and often did not notice the errors in their solutions. The results of the research in the context of giftedness are parallel to the relevant literature. When examining the data obtained from gifted students, it is observed that these students use effective metacognitive strategies in their problem-solving processes, and this situation does not show significant variations depending on the problem. Based on the results of the research, it is anticipated that including problems designed free of numbers in lessons and textbooks can be beneficial, especially for students with medium levels of mathematical achievement, and recommendations have been made for the use of such problems in mathematics lessons.