Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents (original) (raw)

2014, Learning and Instruction

Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The integrated theory of numerical development posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of the magnitudes to which they refer, and this magnitude understanding is central to general mathematical competence. We investigated relations among fraction magnitude understanding, arithmetic and general mathematical abilities in countries differing in educational practices: U.S., China and Belgium. Despite country-specific differences in absolute level of fraction knowledge, 6th and 8th graders' fraction magnitude understanding was positively related to their general mathematical achievement in all countries, and this relation remained significant after controlling for fraction arithmetic knowledge in almost all combinations of country and age group. These findings suggest that instructional interventions should target learners' interpretation of fractions as magnitudes, e.g., by practicing translating fractions into positions on number lines. (J. Torbeyns). 1 It should be noted that knowledge acquisition, instruction, and cognitive development are closely intertwined both in real life and in the integrated theory of numerical development. Therefore, the word development in the latter theory's name should be understood in its broadest meaning, i.e., as integrating e rather than excluding e knowledge acquisition and instruction as important influences on people's numerical development. However, for readability reasons, the authors decided not to include all three sources of competence growth in the theory's name and refer to the, in the learning sciences, well-known and frequently used term development.