From algorithmic computing to direct retrieval: Evidence from number and alphabetic arithmetic in children and adults

Barrouillet, Pierre; Fayol, Michel

doi:10.3758/bf03201146

Cited by 73 publications

(51 citation statements)

References 60 publications

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“…Developmental research in additive problem solving suggests that this kind of strategy is available in childhood, and even in adulthood, for simple two-operand additions only (operands from 1 to 9; Siegler, 1996). The other problems require algorithmic strategies, the use of which is demanding (Barrouillet & Fayol, 1998). The solution times recorded in both age groups (about 10 s) testified to the use of algorithmic strategies by our participants.…”

Section: Discussionmentioning

confidence: 69%

Developmental Increase in Working Memory Span: Resource Sharing or Temporal Decay?

Barrouillet

Camos

2001

Journal of Memory and Language

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126

143

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Working memory span tasks require participants to maintain items in short-term memory while performing some concurrent processing (e.g., reading, counting, and problem solving). It has been suggested that the difficulty of these tasks results either from the necessity of sharing a limited resource pool between processing and storage (Case's cognitive space hypothesis) or from the fact that the memory traces suffer from a temporal decay while the concurrent task is being performed (Towse and Hitch's memory decay hypothesis). We tested these two hypotheses by comparing children's performance in tasks in which the processing component always had the same duration but varied in cognitive cost (counting or problem solving vs repeatedly saying "baba"). The results indicate that both time and limitation of resources constrain performance in working memory tasks. We discuss their implications regarding current models of working memory.

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Section: Discussionmentioning

confidence: 69%

Developmental Increase in Working Memory Span: Resource Sharing or Temporal Decay?

Barrouillet

Camos

2001

Journal of Memory and Language

Self Cite

126

143

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“…In the slowpaced condition, participants had 2 s to process each sign-operand pair, but only 1 s in the fastpaced condition. Many studies in cognitive arithmetic have established that adding or subtracting one to small numbers just involves direct retrievals of the answer from memory, retrievals that have been described as automatic (Aschcraft and Battaglia 1978;Barrouillet and Fayol 1998;LeFevre, Bisanz and Mrkonjic 1988). The authors were thus not surprised to observe that the slow-paced condition resulted in higher spans than the traditional operation span task (3.65 and 2.30 respectively).…”

Section: The Time-based Resource-sharing Model Of Working Memorymentioning

confidence: 98%

The time-based resource-sharing model of working memory

Barrouillet¹,

Camos²

2007

The Cognitive Neuroscience of Working Memory

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Since Baddeley and Hitch's (1974) seminal proposal to distinguish between short-term and working memory, several influential models and theories have been put forward to account for the structure and functioning of a working memory thought of as the core system of cognition devoted to the maintenance and processing of relevant information. As Engle and Oransky (1999) suggested, deas about temporary storage in memory during the previous decades have moved from multi-store models and structural approaches championed by Baddeley and Hitch (1974;Baddeley and Logie 1999) to more dynamic or process-oriented models of working memory (Cowan 1995(Cowan 1999Engle, Cantor and Carullo 1992;Engle, Kane and Tuholski 1999; Lovett, Reder and Lebiere 1999; Schneider and Detweiller 1987). By conceiving working memory as the activated part of long-term memory rather than as a structure or a set of cognitive structures, these theories have emphasized functional aspects of cognition related to the way activation is produced, maintained or even inhibited, and to the way cognitive processes use the activated items of knowledge. The main question, which seemed to be 'How is working memory organized?' has progressively become 'How does working memory work?'. We do not claim to know how working memory works and admit that the reader will not find the final answer in this chapter. However, we hope to provide some elements to shed light on questions such as 'How is the relevant information maintained active during concurrent processing?', 'What is the nature of the resource to be shared between maintenance and processing?', 'How is this sharing achieved?' , and thus 'What are the limiting factors of working memory functioning?' .Retracing the history of the literature on short-term and working memory, Engle and Oransky (1999) noted that models have become more complex and more flexible. Whereas the first descriptions of working memory functioning mainly concerned the articulatory loop, which is closest in character to the original concept of a short-term store, further models provided thorough descriptions of the relationships between short-and long-term memory, of processes devoted to the activation and maintenance of information, as well as of the role of attention in selecting relevant information and monitoring working memory functioning. Several complex span tasks designed to evaluate working memory capacity proved to be reliable and predictive of high level cognition, and the relations between working memory capacity, controlled attention and general intelligence have been investigated extensively. However, these models might have overlooked an important factor in accounting for cognition, namely time.Many models of working memory mentioned time as an important factor, but almost exclusively to account for forgetting from short-term memory. For example, Baddeley (1990Baddeley ( , 2000 suggested that the traces within the articulatory or phonological loop decay within about 2 s unless they are maintained by a process of subvocal arti...

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“…Several other studies have reported a mix of algorithmic and retrieval strategies in children when solving elementary subtractions (Ilg & Ames, 1951;Lankford, 1974;Starkey & Gelman, 1982). Accordingly, studies on subtraction in adults have also reported frequent use of retrieval (Barrouillet & Fayol, 1998;Geary, Frensh, & Wiley, 1993).…”

Section: Mental Subtraction and Additionmentioning

confidence: 99%

Strategies in subtraction problem solving in children

Barrouillet

Mignon

Thévenot

2008

Journal of Experimental Child Psychology

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112

111

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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 Lépine. Although the pattern of relationship between individual differences in working memory, on the one hand, and strategy choices and response times, on the other, was the same in both operations, subtraction and addition differed in two important ways. First, the strategy of direct retrieval was less frequent in subtraction than in addition and was even less frequent in subtraction solving than the recourse to the corresponding additive fact. Second, contrary to addition, the retrieval of subtractive answers is confined to some peculiar problems involving 1 as the subtrahend or the remainder. The implications of these findings for developmental theories of mental arithmetic are discussed.

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From algorithmic computing to direct retrieval: Evidence from number and alphabetic arithmetic in children and adults

Cited by 73 publications

References 60 publications

Developmental Increase in Working Memory Span: Resource Sharing or Temporal Decay?

Developmental Increase in Working Memory Span: Resource Sharing or Temporal Decay?

The time-based resource-sharing model of working memory

Strategies in subtraction problem solving in children

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