The relationship between number sense and problem solving success in fractions of 4th and 5th grade students

Mathematics is not only composed of formulas and operations. Mathematics is a discipline that gains meaning by going beyond rules. In the solution of mathematical problems, noticing the relationships between numbers and using these relationships effectively is quite important. At this point, the concept of number sense takes place at the center of mathematical thinking. Determining and developing number sense in fractions has great importance for eliminating the difficulties that students experience with fractions. In this study, it was aimed to examine the number sense skills of 4th and 5th grade students in fractions and at the same time to determine their number sense skills in fractions and their success in solving problems with fractions. The research was carried out in the 2024–2025 academic year on a total of 380 students in one primary school and one secondary school located in the central district of Bolu. In this research, a mixed method was used and the data were obtained with both quantitative and qualitative data collection tools. These tools were developed by the researcher in line with the literature review and expert opinions. Quantitative data were collected through the 17-item "Number Sense in Fractions Scale (NSFS)" and the 16-item "Problem Solving in Fractions Achievement Test (PSFAT)." In line with the quantitative findings, semi-structured interviews were conducted in the qualitative data collection process. As a result of the data analyses, the number sense in fractions and problem-solving success in fractions of 4th and 5th grade students were examined, and as a result of the analyses, it was determined that there was a significant difference between grade levels in terms of problem-solving success in fractions. The research findings revealed that the average number sense of 5 th grade students was higher than that of 4 th grade students; however, it was found that this difference was not statistically significant. The interview findings show that students primarily preferred rule-based solution strategies, but when an alternative solution method was requested, they turned to number sense strategies.