Visualizing Fractions: Enhancing Problem-Solving Performance Through Diagrammatic Reasoning in Elementary Mathematics

This study explores the effectiveness of diagram construction activities, including area proportional and number line representations, in enhancing conceptual understanding and problem-solving performance in fractions among fifth-grade elementary students. Despite the established benefits of visual models, their systematic application in problem-solving contexts remains underexplored. Many elementary students struggle to integrate symbolic and visual representations in fraction problem-solving meaningfully. Using a quasi-experimental design involving 120 students from four public schools in Makassar, the findings reveal that students who participated in diagrammatic reasoning training significantly outperformed those in the control group in both post-test scores and short-term retention. Specifically, the intervention engaged students in constructing area diagrams and number lines to actively visualize fractions. The integration of spatial visualizations through a dual-coding approach proved effective in strengthening symbolic-spatial connections and reducing extraneous cognitive load, with area-proportional strategies emerging as the strongest predictor of accuracy. These results underscore the importance of routinely integrating diagrammatic activities into elementary mathematics curricula and open new avenues for future research using technologies such as eye-tracking and artificial intelligence to support personalized visual learning.