Different brain mechanisms mediate two strategies in arithmetic: evidence from Event-Related brain Potentials

Yagoubi, Radouane El; Lemaire, Patrick; Besson, Mireille

doi:10.1016/s0028-3932(02)00180-x

Cited by 89 publications

(90 citation statements)

References 32 publications

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“…For addition problems, this erroneous answer was constructed by adding 1 to or subtracting 1 from the correct answer. Indeed, we know that when a proposed answer is too distant from the correct answer, participants are able to solve that kind of problem by approximation, rather than by calculation (Ashcraft & Battaglia, 1978;Ashcraft & Stazyk, 1981;De Rammelaere, Stuyven, & Vandierendonck, 2001; El Yagoubi, Lemaire, & Besson, 2003;Pesenti, Thioux, Seron, & De Volder, 2000). For comparisons, this number was, in half of the cases, superior to the first operand, which was always the largest one, and, in the other half, inferior to the second operand, the smallest.…”

Section: Experiments 1 Methodsmentioning

confidence: 95%

Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm

2007

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The authors showed that for primary school children, response times (RTs) for simple addition problems (e.g., 4 3) increase linearly with the size of the smaller operand. This result was the first to provide evidence for the use of the min strategy by children. This strategy consists in counting on from the larger of the two operands by the number indicated by the smaller of the operands (Carr & Jessup, 1995;Siegler, 1987;Siegler & Crowley, 1994). Adults also show a significant increase in response latencies as a function of the size of the operands, but this increase is much smaller than that in children. Moreover, unlike in children, adults' RTs form a curvilinear function that is best explained by the square of the sum or the product of the operands than by the size of the operands. These differences between adults and children have been interpreted as evidence that, unlike children, adults use fast and efficient retrieval from memory to solve simple addition problems.However, LeFevre, Sadesky, and Bisanz (1996) stressed that, as has already been mentioned for children (Siegler, 1987(Siegler, , 1989, averaging solution latencies across trials that involve different procedures can result in misleading conclusions about how adults solve problems. These authors note that the researchers who have used the more direct approach of asking participants to report their procedure have challenged the strong assumption that adults always use retrieval for simple addition problems. For example, Svenson (1985) showed that adults were certain that they had used a retrieval strategy on simple addition problems on only 78% of the trials (for similar results, see also Geary, Frensch, & Wiley, 1993;Geary & Wiley, 1991). Then, to address the issue of how the selection of procedures varies across problems and participants, LeFevre et al. collected trial-by-trial reports of procedure, in addition to the classical chronometric data. The authors concluded that the importance of retrieval had been overemphasized in models of adult performance. Indeed, in the case of addition problems, 81% of their participants had used two or more of the counting, retrieval, and decomposition procedures in order to solve simple problems (i.e., both the addend and the augend inferior to 10). In fact, retrieval was the most frequently used procedure for problems with sums lower According to LeFevre, Sadesky, and Bisanz (1996), averaging solution latencies in order to study individuals' arithmetic strategies can result in misleading conclusions. Therefore, in addition to classical chronometric data, they collected verbal reports and challenged the assumption that adults rely systematically on retrieval of arithmetic facts from memory to solve simple addition problems. However, Kirk and Ashcraft (2001) questioned the validity of such a methodology and concluded that a more appropriate method has to be found. Thus, we developed an operand recognition paradigm that does not rely on verbal reports or on solution latencies. In accordance with LeFevre et al.,...

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Section: Experiments 1 Methodsmentioning

confidence: 95%

Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm

2007

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“…First, Duverne and Lemaire (2005) and El Yagoubi et al (2003Yagoubi et al ( , 2005 suggested that two verification strategies are used, depending on the distance between the correct and an incorrect proposed solution. If the distance between the two solutions is large, the arithmetical problem may be verified by means of the fast plausibility-checking strategy.…”

Section: Introductionmentioning

confidence: 99%

“…Event-related brain potentials (ERPs) studies (El Yagoubi et al 2003Núñez-Peña and Escera 2007;Núñez-Peña and Honrubia-Serrano 2004;Csépe 2004, 2005) have shown that the split effect is also evident in brain activity. and reported that incorrect solutions in multiplication problems elicited a negativity starting at about 300 ms, followed by a long-lasting positivity with centro-parietal distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In an inequality verification task in which participants were asked to verify whether complex additions were smaller or larger than 100, El Yagoubi et al (2003Yagoubi et al ( , 2005 found that when the solution was a number far from 100, the LPC showed a larger amplitude than when the solution was a number near 100. These authors interpreted the modulation on the LPC amplitude as an index of different strategies that are used to verify inequalities: an exhaustive verification strategy for small distance problems and a plausibility-checking strategy for large distance problems.…”

Section: Introductionmentioning

confidence: 99%

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Processing false solutions in additions: differences between high- and lower-skilled arithmetic problem-solvers

Peña

Suárez‐Pellicioni

2012

Exp Brain Res

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This paper focuses on the capacity to solve numerical incongruities in high- and lower-skilled arithmetic problem-solvers by investigating event-related brain potentials elicited by incorrect solutions to additions. Fifteen high-skill and fifteen low-skill individuals were presented with simple addition problems in a verification task. The proposed solution was manipulated by presenting correct solutions and incorrect solutions very close to the correct ones. Incorrect solutions elicited a negative component followed by a late positive component (LPC/P3b), whose amplitude was smaller for the low-skill group than for the high-skill group. Because the LPC/P3b amplitude has been taken as an indicator of the plausibility of the stimulus, this result suggests that incorrect solutions close to the correct ones appear more plausible to low-skilled individuals than to their high-skilled counterparts. This result is interpreted in terms of differences in the strength of association between problems and potential solutions depending on arithmetical skill.

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“…Niegeggen et al (2002) reported that the attention modulation of visual motion was reflected in the amplitude of a sensory, motion-evoked component (N200) and in a late positive complex (P300). Yagoubi et al (2003) suggested that the early portion of the ERPs reflected physical identification of the numeral and that a late positive slow wave was functionally related to exact mental arithmetical calculations. In our previous study, we observed that mental calculation elicited a negativity peaking at about 170ms-280ms (N2) and a positivity peaking at about 200-470ms (pSW) in raw ERPs (Dong et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Cognitive Development of Semantic Process and Mental Arithmetic in Childhood: An Event-Related Potential

Dong¹,

Wang²,

Yang³

et al. 2007

Data Sci. J.

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Different brain mechanisms mediate two strategies in arithmetic: evidence from Event-Related brain Potentials

Cited by 89 publications

References 32 publications

Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm

Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm

Processing false solutions in additions: differences between high- and lower-skilled arithmetic problem-solvers

Cognitive Development of Semantic Process and Mental Arithmetic in Childhood: An Event-Related Potential

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