The Effect of Multiple Representations Method on Eliminating Fraction Misconceptions of 4th Grade Students: An Experimental Study Supported by a Two-Tier Diagnostic Test

Abstract

The aim of this study is to investigate the effect of the multiple representations method used in teaching fractions in 4th-grade mathematics on students' academic achievement and their level of eliminating misconceptions. In the study, a quasi-experimental design with a pretest-posttest non-equivalent control group, one of the quantitative research methods, was used. The study group consists of a total of 64 students (32 experimental, 32 control) studying in a public primary school in the 2025-2026 academic year. In the experimental group, lessons were conducted with a multiple representations approach based on concrete materials, visual models, number lines, and transitions between symbols (translation), while the traditional method based on the current curriculum was maintained in the control group. The "Fractions Achievement Test" and the "Two-Tier Fractions Diagnostic Test," developed to deeply analyze students' mental models, were used as data collection tools. Dependent and independent samples t-tests, Analysis of Covariance (ANCOVA), and chi-square tests were used in the analysis of the data. The findings showed that when pretest scores were controlled, the academic achievement posttest scores of the experimental group were statistically significantly higher than those of the control group F(1, 61)=136.45, p<.001. In the effect size analysis, it was determined that the effect of the method on achievement was quite large (η_p^2 = .691). When the results from the two-tier diagnostic test were examined, it was found that students in the control group continued to have faulty mental models such as "Natural Number Bias" (34.4%) and "Adding Denominators Error" (40.6%) even after instruction, whereas these rates dropped below 10% in the experimental group. In conclusion, it was determined that instruction supported by multiple representations is more effective than the traditional method in increasing students' fraction achievement and eliminating misconceptions, and the use of the number line model is specifically recommended for practitioners.