Learning by strategies and learning by drill—evidence from an fMRI study

Delazer, Margarete; Ischebeck, Anja; Domahs, Frank; Zamarian, Laura; Koppelstaetter, Florian; Siedentopf, Christian; Kaufmann, Liane; Benke, Thomas; Felber, Stefan

doi:10.1016/j.neuroimage.2004.12.009

Cited by 198 publications

(168 citation statements)

References 82 publications

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“…Even its activation by backward recitation could be explained by task demand on visual-spatial processing or working memory load. The activation of left angular gyrus has been found in previous research on arithmetic, which has been assumed as a result of verbal or phonological processing (Chochon et al, 1999;Dehaene et al, 1999;Lee, 2000;Delazer et al, 2005). That finding was not replicated in other related studies (Kawashima et al, 2004) as well as our study.…”

Section: Neural Network For Reciting Number and Alphabet Sequencescontrasting

confidence: 79%

Neural substrates for forward and backward recitation of numbers and the alphabet: A close examination of the role of intraparietal sulcus and perisylvian areas

et al. 2006

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Section: Neural Network For Reciting Number and Alphabet Sequencescontrasting

confidence: 79%

Neural substrates for forward and backward recitation of numbers and the alphabet: A close examination of the role of intraparietal sulcus and perisylvian areas

et al. 2006

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“…Despite strong correlations across the math tests themselves (SI Text), performance on elementary (and speeded) arithmetic problems (WJ-math fluency), knowledge of math-related concepts (WJ-quantitative concepts), and competence with word problems (WJ-applied problems) were not reliably related to number or cumulative area precision, suggesting that nonsymbolic magnitude representations may not interact evenly across different types of symbolic math and that individual differences in other cognitive abilities may contribute additional variance to performance on these tests. A wealth of studies using behavioral and neuroimaging techniques suggest that people sample from an assortment of strategies when solving math problems, with different strategies recruiting at least partially distinct neural circuits (42,66). For example, highly routinized arithmetic problems, as in WJ-math fluency, show greater reliance on rote visuoverbal memory than explicit computations of magnitude (41,42).…”

Section: Discussionmentioning

confidence: 99%

“…A wealth of studies using behavioral and neuroimaging techniques suggest that people sample from an assortment of strategies when solving math problems, with different strategies recruiting at least partially distinct neural circuits (42,66). For example, highly routinized arithmetic problems, as in WJ-math fluency, show greater reliance on rote visuoverbal memory than explicit computations of magnitude (41,42). Because simple arithmetic problems can be memorized rather than explicitly computed, nonsymbolic magnitudes may contribute minimally (if at all) to their maintenance in memory or their speeded recall.…”

Section: Discussionmentioning

confidence: 99%

“…Psychometric studies report strong correlations across standardized math tests (38,39), but the extent to which different types of math may be grounded in nonsymbolic magnitudes has yet to be systematically investigated. Studies using neuroimaging techniques suggest that the neural circuitry recruited for solving different math problems can vary depending on the type of problem; whereas over-rehearsed arithmetic facts have been shown to recruit left angular gyrus (41,42), word problems activate prefrontal cortex (43,44). Such differences in brain activation raise the possibility that not all aspects of mathematical competence will interface similarly with nonsymbolic magnitudes, which have been shown to primarily recruit the IPS (13,37).…”

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confidence: 99%

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Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

Lourenco

Bonny

Fernandez

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

186

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Humans and nonhuman animals share the capacity to estimate, without counting, the number of objects in a set by relying on an approximate number system (ANS). Only humans, however, learn the concepts and operations of symbolic mathematics. Despite vast differences between these two systems of quantification, neural and behavioral findings suggest functional connections. Another line of research suggests that the ANS is part of a larger, more general system of magnitude representation. Reports of cognitive interactions and common neural coding for number and other magnitudes such as spatial extent led us to ask whether, and how, nonnumerical magnitude interfaces with mathematical competence. On two magnitude comparison tasks, college students estimated (without counting or explicit calculation) which of two arrays was greater in number or cumulative area. They also completed a battery of standardized math tests. Individual differences in both number and cumulative area precision (measured by accuracy on the magnitude comparison tasks) correlated with interindividual variability in math competence, particularly advanced arithmetic and geometry, even after accounting for general aspects of intelligence. Moreover, analyses revealed that whereas number precision contributed unique variance to advanced arithmetic, cumulative area precision contributed unique variance to geometry. Taken together, these results provide evidence for shared and unique contributions of nonsymbolic number and cumulative area representations to formally taught mathematics. More broadly, they suggest that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system, which includes partially overlapping representations of numerical and nonnumerical magnitude.analog magnitude | Weber's law | estimation | nonsymbolic magnitude precision | mathematical cognition H ow do humans come to understand mathematics? A common view is that the mental capacity for formal mathwhich includes access to symbolic notations of number, knowledge of quantitative concepts, and the implementation of computational operations-builds on a set of core abilities such as an intuitive, nonverbal sense of numerosity (1-5). Also known as the approximate number system (ANS), this nonsymbolic sense of numerical magnitude is shared with nonhuman animals (6) and is widespread across cultures (7). Unlike the acquisition of symbolic number (e.g., Arabic digits) and formal math concepts, which are learned via explicit instruction and allow for exact quantification, the ANS may be innate (8) and is characteristically "noisy," with variance increasing linearly as a function of the absolute numerical value (9). This imprecision can be modeled as overlapping Gaussian distributions along an internal continuum (10) and is captured by Weber's law, which holds that subjective differences in intensity are proportional to the objective ratios between values. When people compare numerical values under conditions that prevent counting or that do not...

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“…intraparietal sulcus activity (Delazer et al, 2005). Although not an arithmetic task, algebra problems solved with a verbal strategy had strong prefrontal activity but little parietal activity, whereas the same problems that were solved using an equation-based strategy showed the opposite pattern (Sohn et al, 2004).…”

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confidence: 94%