Automatic Activation of Addition and Multiplication Facts in Elementary School Children

Lemaire, Patrick; Barrett, Susan E.; Fayol, Michael; Abdi, Hervé

doi:10.1006/jecp.1994.1011

Cited by 78 publications

(59 citation statements)

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“…Since De Brauwer et al (2006) observed that the problemsize eVect remains equally large from sixth grade on till adulthood; we might conclude that children from fourth grade on have developed a memory network that strongly resembles the adult memory network. This conclusion is in agreement with previous studies which maintain that mental-arithmetic networks might be completely operational from third grade on (e.g., Ashcraft & Fierman, 1982;Koshmider & Ashcraft, 1991;Lemaire, Barrett, Fayol, & Abdi, 1994).…”

Section: Discussionsupporting

confidence: 93%

Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?

Imbo

Vandierendonck

2007

Psychological Research

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Adult's simple-arithmetic strategy use depends on problem-related characteristics, such as problem size and operation, and on individual-diVerence variables, such as working-memory span. The current study investigates (a) whether the eVects of problem size, operation, and working-memory span on children's simple-arithmetic strategy use are equal to those observed in adults, and (b) how these eVects emerge and change across age. To this end, simple-arithmetic performance measures and a working-memory span measure were obtained from 8-year-old, 10-year-old, and 12-year-old children. Results showed that the problem-size eVect in children results from the same strategic performance diVerences as in adults (i.e., sizerelated diVerences in strategy selection, retrieval eYciency, and procedural eYciency). Operation-related eVects in children were equal to those observed in adults as well, with more frequent retrieval use on multiplication, more eYcient strategy execution in addition, and more pronounced changes in multiplication. Finally, the advantage of having a large working-memory span was also present in children. The diVerences and similarities across children's and adult's strategic performance and the relevance of arithmetic models are discussed.

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Section: Discussionsupporting

confidence: 93%

Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?

Imbo

Vandierendonck

2007

Psychological Research

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“…The associative-confusion/interference eect is a third observation. When a presented false answer matches a correct answer under another arithmetic operation, error rates are higher and latencies are longer (e.g., 7 5 35 and 7 Â 5 12; e.g., Le Fevre & Kulak, 1994;Lemaire, Barrett, Fayol, & Abdi, 1994). Finally, there is the odd-even eect.…”

Section: Introductionmentioning

confidence: 96%

The contribution of working memory resources in the verification of simple mental arithmetic sums

Rammelaere

Stuyven

Vandierendonck

1999

Psychological Research

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The present study replicated the investigations of Lemaire, Abdi, and Fayol with some modi®cations: the random time interval generation (RIG) task was used and the stimuli were created in another way. The results provide additional evidence for the crucial role of the central executive in the speed of solving both true and false sums and for the role of the phonological loop in solving false sums. However, the ®ndings concerning the role of this slave system in solving true sums were dierent. Possible explanations and limitations of these results are discussed.

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“…One explanation for people's use of multiple strategies is that they may be invoked flexibly, depending on the inherent characteristics of the task (such as problem difficulty) or on transitory situational demands (such as the need to answer quickly or accurately in particular contexts). Recently, explorations of strategy use have been concerned with people's ability to fine-tune their control over strategy selection while performing cognitive tasks (e.g., Lemaire, Barrett, Fayol, & Abdi, 1994;Lemaire & Siegler, 1995; Lovett & Anderson, 1996;Reder, 1982Reder, , 1987Reder, , 1988Reder & Ritter, 1992; Reder & Schunn, 1996, in press;Schunn, Reder, Nhouyvanisvong, Richards, & Stroffolino, 1997;Siegler, 1988;Siegler & Lemaire, 1997). These explorations have demonstrated that people are flexible in their use of a set of strategies.…”

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confidence: 99%

What affects strategy selection in arithmetic? The example of parity and five effects on product verification

1999

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The parity effect in arithmetic problem verification tasks refers to faster and more accurate judgments for false equations when the odd/even status of the proposed answer mismatches that of the correct answer. In two experiments, we examined whether the proportion of incorrect answers that violated parity or the number of even operands in the problem affected the magnitude of these effects. Experiment 1 showed larger parity effects for problems with two even operands and larger parity effects during the second half of the experiment. Experiment 2 replicated the results of Experiment 1 and varied the proportion of problems violating parity. Larger parity effects were obtained when more of the false problems violated parity. Moreover, all three effects combined to show the greatest parity effects in conditions with a high proportion of parity violations in problems containing two even operands that were solved during the second half of the experiment. Experiment 3 generalized the findings to the case of five rule (i.e., checking whether a false product ends in 5 or 0), another procedure for solving and verifying multiplication problems quickly. These results (1) delineate further constraints for inclusion in models of arithmetic processing when thinking about how people select among verification strategies, (2) show combined effects of variables that traditionally have been shown to have separate effects on people's strategy selection, and (3) are consistent with a view of strategy selection that suggests a bias either in the allocation of cognitive resources in the execution of strategies or in the order of execution of these strategies; they argue against a simple, unbiased competition among strategies.A very striking feature of human cognition is that people use multiple strategies to accomplish most cognitive tasks. In domains as diverse as arithmetic, serial recall, question answering, sentence verification, reading, and naive physics, people know and use multiple strategies (see, e.g., Ashcraft, 1992;Collins, 1978;Donley & Ashcraft, 1992;Glucksberg & McCloskey, 1981; Hasher & Zacks, 1979;Jacoby & Dallas, 1981;Lemaire, Abdi, & Fayol, 1996;Lemaire, Fayol, & Abdi, 1991;Lemaire & Siegler, 1995;Mandler, 1980, Norman, 1973Reder, 1982Reder, , 1987Reder & Anderson, 1980;Reder & Ritter, 1992;Siegler & Shrager, 1984;Smith, Shoben, & Rips, 1974; Stone & This research was supported in part by the French National Science Foundation Centre National de la Recherche Scientifique (CNRS), and by the U.S. Office ofNaval Research, Contract No. NOOO 14-95-1-0223, by NIMH Grant IROI MH52808-01, and by AFOSR Grant F49620-97-0054. We thank Jason Wyse for collecting the data for Experiments I and 2 and Alison Clark for assistance in many phases of manuscript preparation. We also thank Mark Ashcraft, Jamie Campbell, Jason Carr, James Dixon, David Geary, and Jane Zbrodofffor especially useful comments on previous drafts. Correspondence concerning this article should be sent to P. Lemaire, University of Provence, Departement de Psyc...

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Automatic Activation of Addition and Multiplication Facts in Elementary School Children

Cited by 78 publications

References 0 publications

Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?

Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?

The contribution of working memory resources in the verification of simple mental arithmetic sums

What affects strategy selection in arithmetic? The example of parity and five effects on product verification

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