title: The relationship between non-symbolic multiplication and division in childhood.
abstract: Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b - b = a). The current study examines children's ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and were then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8*4/4) or did not (e.g., 8*4/2). Children's performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a*b/b structure, suggesting that they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems.
authors.affiliation: a Psychology Department , Barnard College, Columbia University , New York , NY , USA.
authors.forename: Koleen
authors.initials: K
authors.lastname: McCrink
authors.affiliation: b Department of Mathematics and Computer Science , Rutgers University , Newark , NJ , USA.
authors.forename: Patrick
authors.initials: P
authors.lastname: Shafto
authors.affiliation: c Psychology Department , Wesleyan University , Middletown , CT , USA.
authors.forename: Hilary
authors.initials: H
authors.lastname: Barth
mesh_terms: D002648:Child; D003210:Concept Formation / Q000502:physiology*; D005260:Female; D006801:Humans; D007858:Learning / Q000502:physiology*; D008297:Male; D008433:Mathematics; D010775:Photic Stimulation; D011340:Problem Solving / Q000502:physiology*; D012923:Social Class
keywords: Cognitive development; Division; Inversion; Memory; Multiplication; Number; Quantity