How does learning mathematics in a spatial format affect children's understanding of number, and the basic cognitive processes that support it? The proposed project will explore this question by investigating users of 'mental abacus' a system of mental arithmetic practiced by children throughout the world. Children who use mental abacus first learn to do arithmetic on a physical device, and then internalize these computations by creating a mental image of an abacus. By moving beads in their mental representation, children perform computations like addition, subtraction, multiplication, and division, all with astonishing speed and accuracy. In three sets of experiments, we will explore how visualizing beads on an abacus to do arithmetic affects abilities such as estimation and comparison of amount, visual attention and working memory, and children's understanding of early numerical concepts, such as addition, place value, and commutativity. Participants will include children in Gujarat Province, India, who are highly trained in abacus, as well as children and adults in the US. Our hypothesis is that learning to do math in a spatial format facilitates not only early understanding of number, but also lays the groundwork for learning advanced mathematics, by training the underlying cognitive processes that support numerical reasoning.
