A cognitive analysis of number-series problems: Sources of individual differences in performance

LeFevre, Jo‐Anne; Bisanz, Jeffrey

doi:10.3758/bf03202506

Cited by 65 publications

(77 citation statements)

References 18 publications

(17 reference statements)

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“…This observation is not very surprising, however, as both our primary task (solving simple arithmetic problems) and the French Kit are speeded performance tests. Hence, correlations between arithmetic skill and strategy efficiency have been observed previously (see, e.g., Campbell & Xue, 2001;Imbo et al, in press;LeFevre & Bisanz, 1986). Arithmetic skill correlated with strategy selection only in the multiplication experiment: High-skill participants used retrieval more frequently than did low-skill participants, an observation that is in agreement with previous studies (see, e.g., Imbo et al, in press;.…”

Section: The Impact Of Individual Differencessupporting

confidence: 81%

“…For each participant, several individualdifference measures were obtained-namely, arithmetic skill, math experience, gender, calculator use, math anxiety, and associative strength. Effects of arithmetic skill have already been reported (see, e.g., Campbell & Xue, 2001;Gilles, Masse, & Lemaire, 2001;LeFevre & Bisanz, 1986;. Generally, strategy use is more efficient (i.e., faster) in high-skill participants than in low-skill participants.…”

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confidence: 73%

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Do multiplication and division strategies rely on executive and phonological working memory resources?

Imbo

Vandierendonck

2007

Memory & Cognition

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Working memory is a system devoted to short-term storage and processing and is used in various cognitive tasks, such as reading, reasoning, and mental arithmetic. Throughout the past decennium, research into the role of working memory in mental arithmetic has flourished (for a review, see DeStefano & LeFevre, 2004) and has shown that solving both simple arithmetic problems (e.g., 8 5, 3 9) and complex arithmetic problems (e.g., 23 98, 12 35) relies on working memory resources. The present study further investigates the role of working memory in simple-arithmetic strategies, on the basis of the multicomponent working memory model of Baddeley and Hitch (1974). In this model, there is an attentional system (the central executive) that supervises a phonological subsystem and a visuospatial subsystem. The phonological subsystem guarantees short-term maintenance of phonological information, and the visuospatial subsystem guarantees short-term maintenance of visuospatial information.The role of executive working memory resources in simple arithmetic has been shown extensively (see, e.g., Ashcraft, 1995;De Rammelaere, Stuyven, & Vandierendonck, 1999Deschuyteneer & Vandierendonck, 2005a, 2005bDeschuyteneer, Vandierendonck, & Muyllaert, 2006;Hecht, 2002;Lemaire, Abdi, & Fayol, 1996;Seitz & Schumann-Hengsteler, 2000. The role of phonological working memory resources in simple arithmetic is less clear. In some studies, an effect of phonological load on simple-arithmetic problem solving was observed (see, e.g., Lee & Kang, 2002;Lemaire et al., 1996;Seitz & Schumann-Hengsteler, 2002), whereas, in other studies, it was not (see, e.g., De Rammelaere et al., 1999Seitz & Schumann-Hengsteler, 2000). Investigations of the role of the visuospatial "sketch pad" in simple arithmetic are scarce (but see Lee & Kang, 2002;Seitz & Schumann-Hengsteler, 2000), and the findings in the few studies conducted are equivocal.A drawback of all the studies mentioned above, however, is that none of them showed any distinction between retrieval and nonretrieval trials. Yet it has been shown that adults use several strategies to solve even the simplest arithmetic problems (see, e.g., Hecht, 1999;. For instance, although direct memory retrieval (i.e., knowing that 3 4 12) is the most frequently used strategy, nonretrieval strategies (or procedural strategies) are used as well. Examples of such procedural strategies are transformation (e.g., 96 (10 6) 6 60 6 54) and counting (e.g., 4 7 7 . . . 14 . . . 21 . . . 28). The studies mentioned above notwithstanding, it is impossible to discern the specific simple-arithmetic strategies in which executive and phonological working memory resources are needed.Investigations of the roles of executive and phonological working memory across different simple-arithmetic strategies have only very recently been conducted, beginning with Hecht (2002). In his study, simple addition equa- 1759Copyright 2007 Psychonomic Society, Inc. Do multiplication and division strategies rely on executive and phonological working memory...

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Section: The Impact Of Individual Differencessupporting

confidence: 81%

mentioning

confidence: 73%

Do multiplication and division strategies rely on executive and phonological working memory resources?

Imbo

Vandierendonck

2007

Memory & Cognition

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“…Each trial consisted of an initial digit cue (e.g., 2+3) and a subsequent digit target (e.g., 7). Excluded were combinations of digit cues and targets that might have elicited activation on the basis of some relation among the elements other than addition, such as multiplication (e.g., 2+4 = 8; see Campbell & Graham, 1985;Miller & Paredes, 1990;Winkelman & Schmidt, 1974), or number series relations (e.g., 2+4 = 6; LeFevre & Bisanz, 1986).…”

Section: Methodsmentioning

confidence: 99%

Individual differences in the obligatory activation of addition facts

LeFevre

Kulak

1994

Memory & Cognition

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In two experiments, we found evidence for individual differences in the obligatory activation of addition facts. Subjects were required to verify the presence of a target digit (e.g., 4) in a previously presented pair (e.g., 5 +4). Subjects rejected targets that formed the sum of the initial pair (e.g., 5+4 and 9) more slowly than they rejected unrelated targets (e.g., 5+4 and 7). This interference of the sum was largest for subjects who were relatively skilled at multidigit arithmetic. Less skilled subjects did not show statistically significant effects of obligatory activation. In comparison with less skilled subjects, skilled subjects showed differential interference on plus-one (e.g., 3 + 1) and standard (e.g., 2 +3) problems when the plus sign was presented, and on ties (e.g., 2 2) when the plus sign was omitted. These results suggest that network models of arithmetic fact retrieval are appropriate for skilled subjects, but that alternative models need to be considered for less skilled individuals.

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“…LeFevre and Bisanz (1986), for example, found that low-skill people used less efficient and slower mental calculation processes than highskill people. Therefore, the difference between low-and high-skill subjects was greater on items that required calculations than on items that could be solved without calculations.…”

Section: Individual Differencesmentioning

confidence: 99%

The influence of problem features and individual differences on strategic performance in simple arithmetic

2007

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454Strategic performance of adults on cognitive problems consists of two main components. To solve a cognitive problem, people first have to choose the most appropriate strategy to solve it (i.e., strategy selection). Next, they have to execute the chosen strategy with reasonable speed and accuracy (i.e., strategy efficiency). For a long time, researchers studying mental arithmetic assumed that adults used only memory retrieval to solve simple arithmetic problems such as 8 3 or 5 4 (see, e.g., Ashcraft, 1987Ashcraft, , 1992Ashcraft, , 1995Campbell, 1987aCampbell, , 1995Campbell & Oliphant, 1992;Lebiere & Anderson, 1998;McCloskey, 1992;Siegler, 1989;Widaman & Little, 1992). Fairly recently however, LeFevre and colleagues ; see also Baroody, 1994;Geary, Frensch, & Wiley, 1993;Geary & Wiley, 1991) showed that even skilled adults still make substantial use of procedures such as counting (e.g., 6 3 6 1 1 1) and transformation (e.g., 7 5 7 3 2) when solving simple arithmetic problems. It is clear that retrieval and nonretrieval (i.e., procedural) strategies differ in their efficiency, since retrieval is generally much faster (i.e., more efficient) than any procedural strategy. Although people may adopt other strategies to solve arithmetic problems (such as using a calculator), the present study investigated mental arithmetic and thus focused on the two broad kinds of strategy mentioned above-retrieval and procedural.Both strategy selection and strategy efficiency may depend on factors such as problem features (e.g., operation, problem size) and individual differences 1 (e.g., arithmetic skill, arithmetic practice). Although models have been proposed in which such experiential factors are the main determinants of mental representation, acquisition, and performance (see, e.g., Ashcraft, 1987;Campbell & Graham, 1985;Siegler, 1988;Siegler & Shipley, 1995), there are very few direct comparisons of the simple arithmetic performance of adults who differ in their mathematical education, arithmetic skill, or arithmetic practice (see also LeFevre & Liu, 1997). Moreover, up until now, no study has investigated the effects of these factors in strategy selection and strategy efficiency separately. The present study therefore examined the effects of features that differed across problems and across individuals on strategic performance of simple arithmetic. Problem FeaturesAlthough adults rely on both retrieval and procedural strategies for the entire domain of elementary arithmetic (i.e., the four basic operations; see, e.g., Campbell & Xue, 2001), they adjust their strategy selection according to the operation involved. In solving subtraction and division problems, for example, adults rely more heavily on procedural strategies than they do when solving either addition or multiplication problems, for which retrieval strategies are predominantly used (Campbell & Xue, 2001;Seyler, Kirk, & Ashcraft, 2003). Furthermore, adults use direct retrieval to solve multiplication problems even more frequently than they do to solve addition prob...

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A cognitive analysis of number-series problems: Sources of individual differences in performance

Cited by 65 publications

References 18 publications

Do multiplication and division strategies rely on executive and phonological working memory resources?

Do multiplication and division strategies rely on executive and phonological working memory resources?

Individual differences in the obligatory activation of addition facts

The influence of problem features and individual differences on strategic performance in simple arithmetic

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