Modulating Neuronal Activity Produces Specific and Long-Lasting Changes in Numerical Competence

Transcranial direct current stimulation (tDCS) is a noninvasive, low-cost and easy-to-use technique that can be applied to modify cerebral excitability. This is achieved by weak direct currents to shift the resting potential of cortical neurons. These currents are applied by attaching two electrodes (usually one anode and one cathode) to distinct areas of the skull. Galvanic Vestibular Stimulation (GVS) is a variant of tDCS where the electrodes are attached to the mastoids behind the ears in order to stimulate the vestibular system. tDCS and GVS are safe when standard procedures are used. We describe the basic physiological mechanisms and application of these procedures. We also review current data on the effects of tDCS and GVS in healthy subjects as well as clinical populations. Significant effects of such stimulation have been reported for motor, visual, somatosensory, attentional, vestibular and cognitive/emotional function as well as for a range of neurological and psychiatric disorders. Moreover, both techniques may induce neuroplastic changes which make them promising techniques in the field of neurorehabilitation. A number of open research questions that could be addressed with tDCS or GVS are formulated in the domains of sensory and motor processing, spatial and nonspatial attention including neglect, spatial cognition and body cognition disorders, as well as novel treatments for various neuropsychological disorders. We conclude that the literature suggests that tDCS and GVS are exciting and easily applicable research tools for neuropsychological as well as clinical-therapeutic investigations. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitudes with scalar variability. Instead, the data indicated that individual children possess multiple numerical representations; that with increasing age and numerical experience, they rely on appropriate representations increasingly often; and that the numerical context influences their choice of representation. The results, obtained with second graders, fourth graders, sixth graders, and adults who performed two estimation tasks in two numerical contexts, strongly suggest that one cause of children's difficulties with estimation is reliance on logarithmic representations of numerical magnitudes in situations in which accurate estimation requires reliance on linear representations.

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education.