An Analysis of Fraction Operation Units from the Perspective of Semantic Alignment: Focusing on Semantic Relations and Quantity Types

Mathematical concepts are derived from real-world situations, and their construction and application can be facilitated when real-world meanings and mathematical meanings are aligned. According to educational psychology research, the depth of interpretation and use of operations depend on whether the semantic relations between the objects presented in the problem situation and the potential mathematical relations are consistent. This study analyzed the semantic relations between objects in problem situations and the semantic alignment between the quantity types of objects and visual models in the fraction operation units of elementary school mathematics textbooks. The analysis revealed that, in problem situations, symmetric relationships were predominantly presented in fraction addition, subset-set relationships in fraction subtraction, and asymmetric relationships in fraction multiplication and division. Regarding quantity types, continuous quantities were presented more often than discrete ones, and in most cases, the quantity type of the object matched that of the visual model, though a few did not. Based on these findings, implications were drawn for selecting problem situations and instructional models that align with mathematical meanings and support student understanding from the perspective of mathematics learning psychology.