Mental abacus (MA) is a technique of performing fast, accurate arithmetic using a mental image of an abacus; experts exhibit astonishing calculation abilities. Over 3 years, 204 elementary school students (age range at outset: 5-7 years old) participated in a randomized, controlled trial to test whether MA expertise (a) can be acquired in standard…

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…

Presents a stochastic model for distinguishing mental arithmetic errors according to causes of failure. A series of experiments (1) studied questions of goodness of fit and model validity among four and five year olds and (2) used the model to measure the relative contributions of developmental improvements in short-term memory and arithmetical…