The Double Triangle Diagram —A Unified Diagrammatic Representation for Multiplication and Division Word Problems and Its Evaluation in Classroom Practice—

Abstract

The Double Triangle Diagram (DTD) is a novel and integrated visualization method to represent proportional relationships in multiplication and division word problems. The DTD illustrates the proportional relationships between two quantities by incorporating six possible operations: multiplications and divisions involving two existential quantities and two relational quantities. This study investigated its application in a classroom setting with fifth-grade students in elementary school. Through pre-tests, post-tests, and delayed retention tests, the study found that students achieved a deeper understanding of relational quantities in multiplication and division problems. The results suggest that the DTD effectively aids students in visualizing and understanding complex relationships between quantities. Teachers also assessed the approach as both practical and highly beneficial for elementary education. Future studies are recommended to expand this research across different grade levels and educational contexts to further validate the diagram’s effectiveness and explore its potential to enhance mathematical reasoning skills longitudinally.