Examining the effects of different multiple representational systems in learning primary mathematics

Multi-representational learning environments are now commonplace in schools and homes. Research that has evaluated the effectiveness of such environments shows that learners can benefit from multiple representations once they have mastered a number of complex tasks. One of the key tasks for learning with multiple representations is successful translation between representations. In order to explore the factors that influence learners' translation between representations, this article presents 2 experiments with a multi-representational environment where the difficulty of translating between representations was manipulated. Pairs of pictorial, mathematical, or mixed pictorial and mathematical representations were used to teach children in 1 of 3 experimental conditions aspects of computational estimation. In Experiment 1, all children learned to become more accurate estimators. Children in the pictorial and the mathematical conditions improved in their ability to judge the accuracy of their estimates, but children in the mixed condition did not. Experiment 2 explored if the mixed condition's difficulties with translation were temporary by requiring additional time to be spent on the system. It was found that children in all the experimental conditions improved in their judgments of estimation accuracy. It is argued that the mixed condition's failure to improve in Experiment I was due to the difficulties they experienced in translating information between disparate types of representation. Their success in Experiment 2 was explained not by learning to translate between representations, but through the adoption of a single representation that contained all the necessary information. This strategy was only effective because of the way that information was distributed across representations.