Semantic Domains of Rational Numbers and the Acquisition of Fraction Equivalence

This study examined how the semantic meanings of rational numbers embodied in graphical representations pose a constraint on children's construction of the concept of fraction equivalence. A test consisting of graphical representations representing the part–whole and measuring semantic meaning was given to 205 fifth-graders and 208 sixth-graders from China. Results showed that the fifth-graders' overall performance on equivalent fraction items was poor across the semantic domains of rational numbers. The sixth-graders showed significantly improved performance on the equivalent fraction items representing the part–whole relation but not on those representing the measure aspect of rational number. The results provide evidence that semantic meanings of fractional numbers in different relevant contexts also constitute a source of difficulty in children's constructing the concept of fraction equivalence, in addition to the multiplicative nature of the concept.