Working memory and literacy as predictors of performance on algebraic word problems

Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient (IQ), and reading ability. Regression results were consistent with findings from the arithmetic literature showing that a literacy composite measure provided greater contribution than did executive function capacity. However, a series of path analyses showed that the overall contribution of executive function was comparable to that of literacy; the effect of executive function was mediated by that of literacy. Both the phonological loop and the visual spatial sketchpad failed to contribute directly; they contributed only indirectly by way of literacy and performance IQ, respectively.     

A microgenetic study of insightful problem solving

An eight-session microgenetic study of acquisition of an insightful problem-solving strategy was conducted. A total of 35 second graders who did not use this insightful strategy initially were assigned to two groups that differed in the frequency of problems likely to facilitate discovery and generalization of the strategy. Children in the facilitative problems group discovered the insightful strategy earlier, used it more often subsequently, and transferred it more often to novel problems than did those in the nonfacilitative problems group. Children generally discovered the insightful strategy on the most facilitative items and extended it progressively to items on which its advantages were smaller but still substantial. The results indicate that experience outside the experimental situation, as well as experience inside the experimental situation, influences use of new strategies.     

Use of the mathematical principle of inversion in young children

An important issue in the development of mathematical cognition is the extent to which children use and understand fundamental mathematical concepts. We examined whether young children successfully use the principle of inversion and, if so, whether they do so based on qualitative identity, length, or quantity. Twenty-four preschool children and 24 children in Grade 1 were presented with three-term inversion problems (e.g., 3+2-2) and standard problems of similar magnitude (e.g., 2+4-3). Problems were presented in three conditions to determine whether children used inversion at all and, if so, whether their decisions were based on quantitative or nonquantitative features of the problems. Both preschool and Grade 1 children showed evidence of using inversion in a fully quantitative manner, indicating that this principle is available in some form prior to extensive formal instruction in arithmetic.     

Acquiring an understanding of design: evidence from children's insight problem solving

The human ability to make tools and use them to solve problems may not be zoologically unique, but it is certainly extraordinary. Yet little is known about the conceptual machinery that makes humans so competent at making and using tools. Do adults and children have concepts specialized for understanding human-made artifacts? If so, are these concepts deployed in attempts to solve novel problems? Here we present new data, derived from problem-solving experiments, which support the following. (i) The structure of the child's concept of artifact function changes profoundly between ages 5 and 7. At age 5, the child's conceptual machinery defines the function of an artifact as any goal a user might have; by age 7, its function is defined by the artifact's typical or intended use. (ii) This conceptual shift has a striking effect on problem-solving performance, i.e. the child's concept of artifact function appears to be deployed in problem solving. (iii) This effect on problem solving is not caused by differences in the amount of knowledge that children have about the typical use of a particular tool; it is mediated by the structure of the child's artifact concept (which organizes and deploys the child's knowledge). In two studies, children between 5 and 7 years of age were matched for their knowledge of what a particular artifact "is for", and then given a problem that can only be solved if that tool is used for an atypical purpose. All children performed well in a baseline condition. But when they were primed by a demonstration of the artifact's typical function, 5-year-old children solved the problem much faster than 6-7-year-old children. Because all children knew what the tools were for, differences in knowledge alone cannot explain the results. We argue that the older children were slower to solve the problem when the typical function was primed because (i) their artifact concept plays a role in problem solving, and (ii) intended purpose is central to their concept of artifact function, but not to that of the younger children.     

An investigation of the interaction between cognitive style and context reinstatement on the memory performance of eyewitnesses

The power of context reinstatement to improve recall is well established, but the degree of effect obtained varies widely between studies. Exploring possible causes for this variation, this paper examines the relationship between cognitive style and the efficacy of context reinstatement in improving free and cued recall in an eyewitness paradigm. Experiment 1, using a live staged event and a 1 week delay, indicated a significant improvement in free recall with the reinstatement of context and, as expected, no such improvement in cued recall. However, analysis of the data according to field dependency, as measured by Witkin, Oltman, Raskin, and Karp's [A manual for the Embedded Figures Test (1971) Palo Alto, CA: Consulting Psychologists Press] Group Embedded Figures Test (GEFT) revealed that, in free recall, field dependent witnesses' scores improved significantly with context reinstatement, whilst the scores of field independent witnesses did not. In cued recall, however, the field independent witnesses scored significantly higher overall than field dependent witnesses. Experiment 2 sought replication of these findings again utilised the GEFT and the Riding [Cognitive Styles analysis (1991) Birmingham: Learning and Training Technology] Cognitive Styles Analysis (CSA). Analysis of the data according to the Wholist-Analytic (W-A) dimension of the CSA, indicated no interaction with either context reinstatement or memorial performance. However the GEFT analysis produced similar results to that obtained in Experiment 1. The meaning of the interaction between the GEFT and both free and cued recall, and the failure of the CSA to similarly interact are discussed, together with the implication of these findings for establishing the value of reinstating context for individual eyewitnesses.