The Role of Prior Knowledge and Intelligence in Gaining from a Training on Proportional Reasoning.

We explored the mediating role of prior knowledge on the relation between intelligence and learning proportional reasoning. What students gain from formal instruction may depend on their intelligence, as well as on prior encounters with proportional concepts. We investigated whether a basic curriculum unit on the concept of density promoted students' learning in a training on proportional reasoning. A 2 × 2 design with the factors basic curriculum unit (with, without) and intervention context to introduce proportional reasoning (speed, density) was applied in two consecutive, randomized classroom studies (N1 = 251, N2 = 566 fourth- and fifth-graders; 49%/56% female). We controlled for intelligence and mathematical achievement. We expected the combination of having received the basic curriculum unit on floating and sinking and proportional reasoning introduced via density (a familiar problem-solving context for this group) to be especially favorable. Whereas this hypothesis was not supported, we showed that mathematical achievement mediated the relation between intelligence and proportional reasoning and enabled learners to better exploit the learning opportunities.