Book Chapter10.1016/S0166-4115(08)60890-0
Working memory, automaticity, and problem difficulty.
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TL;DR: In this paper, the authors review the existing research that bears on these issues and present two experiments, one focused on the deployment of working memory resources during arithmetic processing, using a standard dual-task method, and the other focused on automatic and conscious processing as revealed by a priming task.
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Abstract: Summary Two complimentary topics are of special interest in the study of cognitive skills, first the involvement of working memory resources in successful performance, and second the role of automaticity in the component processes of such performance. While these questions figure prominently in contemporary cognitive research, they have only recently begun to receive direct investigation in the area of mental arithmetic. In this chapter, we review the existing research that bears on these issues, then present two experiments. Experiment 1 focused on the deployment of working memory resources during arithmetic processing, using a standard dual-task method. Experiment 2 investigated automatic and conscious processing as revealed by a priming task. The results of both experiments are viewed in terms of the basic problem difficulty variable, and the relationship between this variable and manipulations that tap automatic and effortful aspects of performance. The chapter concludes with some remarks on the central construct of problem difficulty.
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Citations
Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches.
TL;DR: The authors reviewed four approaches that address the relation between working memory and math: dual task studies establishing the role of working memory during on-line math performance; individual difference studies examining working memory in children with math difficulties; studies of working attention as a predictor of mathematical outcomes; and longitudinal studies of the relationship between working attention and math.
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The development of arithmetical abilities.
TL;DR: The evidence broadly supports the idea of an innate specific capacity for acquiring arithmetical skills, but the effects of the content of learning, and the timing of learning in the course of development, requires further investigation.
Working Memory Impairments in Children with Specific Arithmetic Learning Difficulties
Janet F. McLean,Graham J. Hitch +1 more
TL;DR: Children with poor arithmetic had normal phonological working memory but were impaired on spatial working memory and some aspects of executive processing, which seem likely to be important factors in poor arithmetical attainment.
684
The role of working memory in mental arithmetic
Diana DeStefano,Jo-Anne LeFevre +1 more
TL;DR: This paper reviewed the literature on the role of working memory in the solution of arithmetic problems such as 3 + 4 or 345 + 29 and concluded that mental arithmetic requires central executive resources, even for single-digit problems.
518
Counting on working memory in arithmetic problem solving.
TL;DR: 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.
References
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TL;DR: Tested the 2-process theory of detection, search, and attention presented by the current authors (1977) in a series of experiments and demonstrated the qualitative difference between 2 modes of information processing: automatic detection and controlled search.
7.4K
Processing Data for Outliers
TL;DR: In this paper, the authors discussed the problem of whether certain observations properly belong in the presentation of measurements obtained by an experimenter and suggested that a consideration of this sort is more properly made at the recording stage or perhaps at the stage of preliminary processing.
Cognitive arithmetic: a review of data and theory.
TL;DR: This article provides a tutorial review of the area of cognitive arithmetic, discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of problem size or difficulty, errors, relatedness, and strategies of processing.
752
Cross-linguistic regularities in the frequency of number words.
Stanislas Dehaene,Jacques Mehler +1 more
TL;DR: The most striking is a decrease of frequency with numerical magnitude, with local increases for reference numerals such as 10, 12, 15, 20, 50 or 100, which reveals the frequent confound of two experimental variables: numerical magnitude and numeral frequency.
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