Categorical and continuous - disentangling the neural correlates of the carry effect in multi-digit addition

Klein, Elise; Willmes, Klaus; Dressel, Kerstin; Domahs, Frank; Wood, Guilherme; Nuerk, Hans Christoph; Moeller, Korbinian

doi:10.1186/1744-9081-6-70

Cited by 27 publications

(62 citation statements)

References 52 publications

(100 reference statements)

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“…Anderson et al [18] reviewed the evidence that the ANG, particularly the right, is associated with reasoning about intentions. Also the MTG is involved in deductive reasoning [28], [29], reasoning about intentions [30], and arithmetic competence [31], [32].…”

Section: Resultsmentioning

confidence: 99%

Brain Networks Supporting Execution of Mathematical Skills versus Acquisition of New Mathematical Competence

Wintermute

Betts²,

Ferris³

et al. 2012

PLoS ONE

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This fMRI study examines how students extend their mathematical competence. Students solved a set of algebra-like problems. These problems included Regular Problems that have a known solution technique and Exception Problems that but did not have a known technique. Two distinct networks of activity were uncovered. There was a Cognitive Network that was mainly active during the solution of problems and showed little difference between Regular Problems and Exception Problems. There was also a Metacognitive Network that was more engaged during a reflection period after the solution and was much more engaged for Exception Problems than Regular Problems. The Cognitive Network overlaps with prefrontal and parietal regions identified in the ACT-R theory of algebra problem solving and regions identified in the triple-code theory as involved in basic mathematical cognition. The Metacognitive Network included angular gyrus, middle temporal gyrus, and anterior prefrontal regions. This network is mainly engaged by the need to modify the solution procedure and not by the difficulty of the problem. Only the Metacognitive Network decreased with practice on the Exception Problems. Activity in the Cognitive Network during the solution of an Exception Problem predicted both success on that problem and future mastery. Activity in the angular gyrus and middle temporal gyrus during feedback on errors predicted future mastery.

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Section: Resultsmentioning

confidence: 99%

Brain Networks Supporting Execution of Mathematical Skills versus Acquisition of New Mathematical Competence

Wintermute

Betts²,

Ferris³

et al. 2012

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…This means that magnitude-related processing will be the most probable solution strategy the larger the unit and decade sum, respectively. Indeed, with increasing values of unit and decade sum Klein and colleagues [34] observed activation in brain areas associated with magnitude-related processing. By contrast, with decreasing unit and decade sum, addition problems get easier (e.g., 2+3) and may even be solved relying on arithmetic fact retrieval.…”

Section: Introductionmentioning

confidence: 98%

“…For instance, recent studies indicated a shift in brain activation from frontal to parietal regions with arithmetic training [21], [29]–[31] and age [32]. Moreover, first evidence for a flexible interplay of different numerical representations in one and the same task came from fMRI studies using a parametric modeling approach to a number bisection task [33] and to mental addition [34]. The method of parametric modeling seems to be particularly suited to investigate contributions of different representations, because it allows for defining parametric regressors representing several dimensions of complex stimuli.…”

Section: Introductionmentioning

confidence: 99%

“…Following this approach, Wood and colleagues [33] were able to differentiate the influence of number magnitude, fact retrieval, and parity in a number bisection task. Moreover, Klein et al [34] identified different effects of number magnitude processing and fact retrieval in mental addition.…”

Section: Introductionmentioning

confidence: 99%

“…In the latter study [34], participants had to indicate the correct result of single- and two-digit addition problems. The impact of number magnitude and arithmetic fact representations could be isolated by analyzing factors characterizing the stimulus set parametrically.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Processing Pathways in Mental Arithmetic—Evidence from Probabilistic Fiber Tracking

Moeller²,

et al. 2013

Self Cite

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Numerical cognition is a case of multi-modular and distributed cerebral processing. So far neither the anatomo-functional connections between the cortex areas involved nor their integration into established frameworks such as the differentiation between dorsal and ventral processing streams have been specified. The current study addressed this issue combining a re-analysis of previously published fMRI data with probabilistic fiber tracking data from an independent sample. We aimed at differentiating neural correlates and connectivity for relatively easy and more difficult addition problems in healthy adults and their association with either rather verbally mediated fact retrieval or magnitude manipulations, respectively. The present data suggest that magnitude- and fact retrieval-related processing seem to be subserved by two largely separate networks, both of them comprising dorsal and ventral connections. Importantly, these networks not only differ in localization of activation but also in the connections between the cortical areas involved. However, it has to be noted that even though seemingly distinct anatomically, these networks operate as a functionally integrated circuit for mental calculation as revealed by a parametric analysis of brain activation.

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The functional architectures of addition and subtraction: Network discovery using fMRI and DCM

Yang

Friston

Imamura

et al. 2017

Human Brain Mapping

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The neuronal mechanisms underlying arithmetic calculations are not well understood but the differences between mental addition and subtraction could be particularly revealing. Using fMRI and dynamic causal modeling (DCM), this study aimed to identify the distinct neuronal architectures engaged by the cognitive processes of simple addition and subtraction. Our results revealed significantly greater activation during subtraction in regions along the dorsal pathway, including the left inferior frontal gyrus (IFG), middle portion of dorsolateral prefrontal cortex (mDLPFC), and supplementary motor area (SMA), compared with addition. Subsequent analysis of the underlying changes in connectivity - with DCM - revealed a common circuit processing basic (numeric) attributes and the retrieval of arithmetic facts. However, DCM showed that addition was more likely to engage (numeric) retrieval-based circuits in the left hemisphere, while subtraction tended to draw on (magnitude) processing in bilateral parietal cortex, especially the right intraparietal sulcus (IPS). Our findings endorse previous hypotheses about the differences in strategic implementation, dominant hemisphere, and the neuronal circuits underlying addition and subtraction. Moreover, for simple arithmetic, our connectivity results suggest that subtraction calls on more complex processing than addition: auxiliary phonological, visual, and motor processes, for representing numbers, were engaged by subtraction, relative to addition. Hum Brain Mapp 38:3210-3225, 2017. © 2017 Wiley Periodicals, Inc.

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Categorical and continuous - disentangling the neural correlates of the carry effect in multi-digit addition

Cited by 27 publications

References 52 publications

Brain Networks Supporting Execution of Mathematical Skills versus Acquisition of New Mathematical Competence

Brain Networks Supporting Execution of Mathematical Skills versus Acquisition of New Mathematical Competence

Processing Pathways in Mental Arithmetic—Evidence from Probabilistic Fiber Tracking

The functional architectures of addition and subtraction: Network discovery using fMRI and DCM

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