Ad. Schliemann et al., USE OF MULTIPLICATIVE COMMUTATIVITY BY SCHOOL-CHILDREN AND STREET SELLERS, Journal for research in mathematics education, 29(4), 1998, pp. 422-435
We analyzed use of the commutative property for solving multiplication
problems by children who learn about multiplication in schools and by
street vendors who solve multiplication problems through repeated add
ition. Subjects were Brazilian street vendors with irregular school at
tendance, who had received no, or very little, school instruction on m
ultiplication, and 1st- to 3rd-grade Brazilian school children. Result
s from 2 studies show that use of commutativity to solve multiplicatio
n problems is closely related to use of multiplication. Street sellers
who rely exclusively on repeated addition to solve such problems may,
however, use multiplicative commutativity if it represents a clear re
duction in the number of computational steps needed to reach a solutio
n. But their justifications for its use are often based on knowledge a
bout multiplication.