Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

339 children aged 6 and 7 at Oxford primary schools took part in a study of arithmetic. 204 of the children had been selected by their teachers as having mathematical difficulties and the other 135 children were unselected. They were assigned to an Addition Performance Level on the basis of a calculation pretest, and then given Dowker's (1998)…

The present study concerns redundant data problems, defined as problems in which irrelevant data is provided. This type of problem provides a misleading context [Pascual-Leone, J. (1987). Organismic process for neo-Piagetian theories: A dialectical causal account of cognitive development. "International Journal of Psychology," 22, 531-570] similar…

Using the ''between-grade levels'' regression discontinuity design, this study examined the hypothesized differential sensitivity of logico-mathematical (LM) and infralogical (IL) operational tasks to the effects of chronological age and first grade schooling in a sample of 580 1st and 2nd grade Israeli children. The results indicate that the…

Arithmetic algorithms include two types of rules: conventional rules that may be changed by authority, and may legitimately vary from one classroom or country to another (e.g. putting the sum below, rather than above, the numbers added) and logical rules that involve the logic of the algorithm. Changes in the logical rules produce incorrect…