Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving…

The involvement of working memory (WM) was examined in two types of mental calculation tasks: exact and approximate. Specifically, children attending Grades 3 and 4 of primary school were involved in three experiments that examined the role of verbal and visuospatial WM in solving addition problems presented in vertical or horizontal format. For…

The SNARC (spatial-numerical association of response codes) effect refers to the finding that small numbers facilitate left responses, whereas larger numbers facilitate right responses. The development of this spatial association was studied in 7-, 8-, and 9-year-olds, as well as in adults, using a task where number magnitude was essential to…

The aim of this study was to investigate the strategies used by third graders in solving the 81 elementary subtractions that are the inverses of the one-digit additions with addends from 1 to 9 recently studied by Barrouillet and Lepine. Although the pattern of relationship between individual differences in working memory, on the one hand, and…

Three experiments investigated the roles of resource-sharing and intrinsic memory demands in complex working memory span performance in 7- and 9-year-olds. In Experiment 1, the processing complexity of arithmetic operations was varied under conditions in which processing times were equivalent. Memory span did not differ as a function of processing…

Age-related changes in children's performance on simple division problems (e.g., 6 divided by 2, 72 divided by 9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children.…

Two experiments investigated extent to which English- and German-speaking childrens' mental arithmetic was constrained by working memory. Found higher mental addition spans when numbers were visible throughout calculation than when not. Variation in addition span with age and arithmetical operation difficulty approximated to a linear function of…

Speeded performance on simple mental addition problems of 6- and 7-year-olds with and without mild mental retardation was modeled from a person perspective and an item perspective, both inferred from Siegler's work. Models from item response theory were used to test hypotheses. Found that all children follow same developmental path in acquiring…

In one experiment, subjects from third grade through college relied on memory retrieval rather than on counting to solve multiplication problems. An effect of confusing problems on error rates and reaction times indicated the activation of related information. In a second experiment, subjects demonstrated automaticity of fact retrieval on simple…

Understanding of the cardinality principle in children with Williams Syndrome (WS) was compared to that of typically developing children. Findings indicated that such understanding was extremely delayed in WS children and only at the level predicted by their visuo-spatial mental age. Findings suggested that visuo-spatial ability played a greater…

First, fourth, seventh, and tenth graders were timed when solving simple and complex addition problems, then were presented similar problems in untimed interviews. Manipulation of confusion between addition and multiplication, where multiplication answers were given to addition problems (3 + 4 = 12) indicated an interrelatedness of these…

Hypothesized that arithmetic calculating procedures and types of problems that necessitate more subproblems will lead to longer solution times. Data from 36 third grade students who mentally computed problems with sums greater than 20 and less than 100, confirmed both hypotheses. (RH)