Children's (N = 275) use of retrieval, decomposition (e.g., 7 = 4+3 and thus 6+7 = 6+4+3), and counting to solve additional problems was longitudinally assessed from first grade to fourth grade, and intelligence, working memory, and in-class attentive behavior was assessed in one or several grades. The goal was to assess the relation between…

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…

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…

Two experiments with third to sixth grade children were undertaken to test three predictions derived from the assumption that children may fail to solve union problems because addition of classes is not implied when classes to be combined overlap. (SB)

Examined the relationship between counting knowledge and computational skills for 13 mathematically disabled (MD) first graders who showed a delay in acquiring mathematical skills and 24 nondisabled first graders. MD children's immature counting knowledge and poor skills at detecting counting errors underlay their poor computational skills on an…

Examined whether 5- and 6-year-olds understand that addition and subtraction cancel each other and whether this understanding is based on identity or quantity of addend and subtrahend. Found that children used inversion principle. Six- to eight-year-olds also used inversion and decomposition to solve a + b - (B+1) problems. Concluded that…

Three experiments examined whether children, like adults, can surpress interference effects when retrieving from long-term memory to solve arithmetic problems. Found that the associations between a number pair and its sum or product are of sufficient strength during the elementary school years to produce interference effects, depending on the age…

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…

Suggested that strategy choices for solving addition problems were related to numerical and spatial ability domains, while the speed of executing the component process of fact retrieval was related to arithmetic ability only. Findings supported the convergent validity of the strategy choice model and its discriminant validity. (RH)

Two experiments examined developmental changes in reasoning about intensive quantities--predicting mixture intensity of pairs of liquids with different intensities of red color. Results showed that cognitive averaging in this domain developed late and slowly. Predominating up to 12 years was an extensivity bias, a strong tendency to use rules that…

Validated models of mental addition processing by testing children and adults in a production task paradigm. Examined individual-difference relations between strategy choice parameters and criterion-related measures of ability. Found that individual differences in the apparently calculative processes that underlie numerical facility are highly…

Five- to six-year-old children estimated the size of Euclidian objects using an addition rule of Height plus Width, rather than a multiplying rule. Within the framework of information integration theory, tested whether intensive handling of objects would facilitate shift from addition rule to multiplication rule. Found that following handling,…

Compared young mathematically disabled and academically normal children in terms of the distribution of strategies and solution times involved with simple addition problems. Performance characteristics of normal students and disabled students who improved were essentially the same, whereas those of disabled students who did not change were…