A study on fourth and fifth grade students' levels of fraction conceptualization and modeling

The aim of this research is to determine the levels of fourth and fifth grade students in conceptualizing fractions and modeling fractions, and to examine the consistency between the levels of conceptualizing and modeling fractions among fourth grade students and their classroom teachers, as well as fifth grade students and their mathematics teachers. This research was conducted during the 2022-2023 academic year at a public school in the Adapazarı district of Sakarya province. A mixed-method approach was used in this study, and data were collected using both quantitative and qualitative data collection tools. Both the quantitative and qualitative data collection tools were developed by the researcher based on the literature and expert opinions. To collect quantitative data, the "Fraction Achievement Test" was administered to 66 fourth grade students and 60 fifth grade students. Based on the quantitative data obtained, a qualitative data collection tool, the "Test on the Meanings of Fractions and Fraction Models," was administered to four fourth grade students (two with low performance and two with high performance on the achievement test), four fifth grade students (similarly selected), the fourth grade classroom teacher, and the fifth grade mathematics teacher. Semi-structured interviews were also conducted. In the analysis of the data, the Mann-Whitney U test was applied to the quantitative data using a statistical software, and descriptive analysis was applied to the qualitative data. As a result of the quantitative data, a significant difference in favor of the fourth grade students was found. Based on the qualitative data, it was observed that both teachers and students predominantly used the part-whole meaning of fractions and the area model as the most common fraction model. None of the students expressed any conceptualization of the operational, measurement, or division meanings of fractions, and none used the number line model.