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Abstract
Background: Developmental dyscalculia is a heterogeneous disorder with largely dissociable performance profiles. Though our current understanding of the neurofunctional foundations of (adult) numerical cognition has increased considerably during the past two decades, there are still many unanswered questions regarding the developmental pathways of numerical cognition. Most studies on developmental dyscalculia are based upon adult calculation models which may not provide an adequate theoretical framework for understanding and investigating developing calculation systems. Furthermore, the applicability of neuroscience research to pedagogy has, so far, been limited.
Purpose: After providing an overview of current conceptualisations of numerical cognition and developmental dyscalculia, the present paper (1) reviews recent research findings that are suggestive of a neurofunctional link between fingers (finger gnosis, finger-based counting and calculation) and number processing, and (2) takes the latter findings as an example to discuss how neuroscience findings may impact on educational understanding and classroom interventions.
Sources of evidence: Finger-based number representations and finger-based calculation have deep roots in human ontology and phylogeny. Recently, accumulating empirical evidence supporting the hypothesis of a neurofunctional link between fingers and numbers has emerged from both behavioural and brain imaging studies.
Main argument: Preliminary but converging research supports the notion that finger gnosis and finger use seem to be related to calculation proficiency in elementary school children. Finger-based counting and calculation may facilitate the establishment of mental number representations (possibly by fostering the mapping from concrete non-symbolic to abstract symbolic number magnitudes), which in turn seem to be the foundations for successful arithmetic achievement.
Conclusions: Based on the findings illustrated here, it is plausible to assume that finger use might be an important and complementary aid (to more traditional pedagogical methods) to establish mental number representations and/or to facilitate learning to count and calculate. Clearly, future prospective studies are needed to investigate whether the explicit use of fingers in early mathematics teaching might prove to be beneficial for typically developing children and/or might support the mapping from concrete to abstract number representations in children with and without developmental dyscalculia.
Acknowledgement
The author was supported by the Austrian Science Foundation (grant number T286-B05).
Notes
1. A major disadvantage of ‘complex models’ is that they may render the verification and/or falsification of working hypotheses difficult (because they typically encompass many dependent and/or unknown variables). Hence, researchers aiming to assess complex developmental disorders are especially required to (1) formulate very clear-cut hypotheses from the outset; (2) carefully define selection criteria for their study populations; and (3) employ paradigms that have been found previously to be adequate (and testable) for the research questions of interest. Reasons for advocating ‘complex models’ are at least twofold: first, complex models readily acknowledge modulating cognitive abilities (within and outside the numerical domain: Kaufmann and Nuerk Citation2005; Wilson and Dehaene Citation2007); and second, complex models may lead to a better understanding of the link between mind (cognitive), brain (neurofunctional) and pedagogy (behavioural and educational factors) mediating the acquaintance of number processing and calculation skills.
2. Though Benton (Citation1997) seriously questioned the entity of the syndrome by stressing that a substantial proportion of patients exhibit some, but not all four symptoms constituting the full Gerstmann syndrome, the Gerstmann syndrome has received increased interest recently.
3. Stimuli across the three tasks were identical (only instructions varying), thus enabling us to control for domain-general perceptual and response-bound processing mechanisms. The strict control of domain-general processing mechanisms is crucial in brain imaging research as the to-be-interpreted activation patterns should be attributable to task-relevant processing solely (or as far as possible). The latter endeavour is achieved by a subtraction method whereby the cerebral activation patterns obtained in response to a control task (which is preferably identical to the experimental task in all but the variable of interest, in our case, number processing) are subtracted from the activations obtained in response to the experimental task. According to the subtraction logic, only the task-relevant–hence domain-specific–activations should remain. In order to achieve the best possible match between experimental and control tasks, we created stimuli that could be used across all three task conditions. In particular, stimuli consisted of two simultaneously displayed children's hands with coloured thumbs. In half of the trials the palms of the two hands showed in the same direction, while in the other half they did not. The spatial task required participants to judge whether the palms of the two hands were showing in the same direction or not. Likewise, in the colour condition, individuals were asked to state whether the colours of the two thumbs were identical or not. The colour task served as a true control task. The spatial task was incorporated in the study because our main aim was to disentangle spatial and non-symbolic numerical processing (Walsh Citation2003; for a comprehensive review on the neurofunctional overlap between spatial and numerical processing see Hubbard et al. Citation2005).