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This study examined whether the quality of first graders’ (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children’s pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be predictive of their learning of answers to unfamiliar arithmetic problems. The relation to learning of unfamiliar problems remained after controlling for prior arithmetic knowledge, short-term memory for numbers, and math achievement test scores. Moreover, presenting randomly chosen children with accurate visual representations of the magnitudes of addends and sums improved their learning of the answers to the problems. Thus, representations of numerical magnitude are both correlationally and causally related to arithmetic learning.
