Counting on working memory in arithmetic problem solving.
ABSTRACT Mental calculation is an important everyday skill involving access to well-learned procedures, problem solving, and working memory. Although there is an active literature on acquiring concepts and procedures for mental arithmetic, relatively little is known about the role of working memory in this task. This paper reports two experiments in which dual-task methodology is used to study the role of components of working memory in mental addition. In Experiment 1, mental addition of auditorily presented two-digit numbers was significantly disrupted by concurrent random letter generation and, to a lesser extent, by concurrent articulatory suppression, but was unimpaired by concurrent hand movement or by presentation of irrelevant pictures. Although the number of errors increased with two of the dual tasks, the incorrect responses tended to be quite close to the correct answer. In Experiment 2, the numbers for addition were presented visually. Here again, random generation produced the largest disruption of mental arithmetic performance, while a smaller amount of disruption was observed for articulatory suppression, hand movement, and unattended auditorily presented two-digit numbers. The overall levels of performance were better and the absolute size of the disruptive effects shown with visual presentation was very small compared with those found for auditory presentation. This pattern of results is consistent with a role for a central executive component of working memory in performing the calculations required for mental addition and in producing approximately correct answers. Visuospatial resources in working memory may also be involved in approximations. The data support the view that the subvocal rehearsal component of working memory provides a means of maintaining accuracy in mental arithmetic, and this matches a similar conclusion derived from previous work on counting. The general implications for the role of working memory in arithmetic problem solving will be discussed.
Article: Reasoning with Numbers[show abstract] [hide abstract]
ABSTRACT: Could our use of numbers reflect a shared mental model of numbers? If so, heuristics based on a cognitively-inspired treatment of numbers could be used to improve automatic interpretation of numerical data drawn from domains about which little is known.We conjecture that number labels are applied to quantities and to numerousness or counts in different ways, for example, in references to 3 kilograms of apples as opposed to 3 apples. We use the device of a magnitude space to model the treatment of numbers as counts and as quantities, and show how this can be used practically in interpreting numbers. The application area of interest to us is categorization on small sample sets.04/2002;
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ABSTRACT: Semantic memory is thought to consist of category-specific representations of knowledge that may be selectively compromised in patients with neurodegenerative diseases, but this has been difficult to demonstrate reliably across object categories. The authors evaluated performance on several simple measures requiring number representations (including addition and magnitude judgments of single digits), and on a task that requires object representations (an object naming task) in patients with corticobasal degeneration (CBD; n = 13) and semantic dementia (SD; n = 15). They also examined regional cortical atrophy using voxel-based morphometric analyses of high resolution structural MRI in subgroups of five CBD patients and three SD patients. CBD patients were consistently more impaired on simple addition and magnitude judgment tasks requiring number representations compared to object representations. Impaired performance with numbers in CBD was associated with cortical atrophy in right parietal cortex. By comparison, SD patients demonstrated a greater impairment on a naming task requiring object representations relative to their performance on measures involving number representations. This was associated with left anterior temporal cortical atrophy. The cognitive and neuroanatomic dissociations between CBD and SD are consistent with the hypothesis that number and object representations constitute distinct domains in semantic memory, and these domains appear to be associated with distinct neural substrates.Neurology 05/2004; 62(7):1163-9. · 8.31 Impact Factor