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…

A pre- to post-test design was used to evaluate the effects of rule-based instruction on rule observance, copying performance, and discrimination skill. Three ways of imparting rules (demonstration, verbal description, and combined demonstration-verbal description) were examined, and their usefulness was compared to that of copying without…

Two studies demonstrated dissociation between preschoolers' understanding of pictorial and mental representations. Results showed that false picture tasks were significantly easier than false belief tasks. There was no correlation between performance on the two. Children were trained on false belief, false picture, or number conservation tasks;…