RESUMEN

There is evidence that early variations in the development of an approximate number system (ANS) and symbolic number understanding are both influences on the later development of formal arithmetic skills. We report a large-scale (N = 552) longitudinal study of the predictors of arithmetic spanning a critical developmental period (the first 3 years of formal education). Variations in early knowledge of symbolic representations of number and the ordinal associations between them are direct predictors of later arithmetic skills. The development of number ordering ability is in turn predicted by earlier variations in arithmetic, the ANS (numerosity judgments), and rapid automatized naming (RAN). These findings have important implications for theories of numerical and arithmetical development and potentially for the teaching of these skills.

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RESUMEN

Vision of the body has been reported to improve tactile acuity even when vision is not informative about the actual tactile stimulation. However, it is currently unclear whether this effect is limited to body parts such as hand, forearm or foot that can be normally viewed, or it also generalizes to body locations, such as the shoulder, that are rarely before our own eyes. In this study, subjects consecutively performed a detection threshold task and a numerosity judgment task of tactile stimuli on the shoulder. Meanwhile, they watched either a real-time video showing their shoulder or simply a fixation cross as control condition. We show that non-informative vision improves tactile numerosity judgment which might involve tactile acuity, but not tactile sensitivity. Furthermore, the improvement in tactile accuracy modulated by vision seems to be due to an enhanced ability in discriminating the number of adjacent active electrodes. These results are consistent with the view that bimodal visuotactile neurons sharp tactile receptive fields in an early somatosensory map, probably via top-down modulation of lateral inhibition.

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Stroke patients suffer from impairments of both motor and somatosensory functions. The functional recovery of upper extremities is one of the primary goals of rehabilitation programs. Additional somatosensory deficits limit sensorimotor function and significantly affect its recovery after the neuromotor injury. Sensory substitution systems, providing tactile feedback, might facilitate manipulation capability, and improve patient's dexterity during grasping movements. As a first step toward this aim, we evaluated the ability of healthy subjects in exploiting electrotactile feedback on the shoulder to determine the number of perceived stimuli in numerosity judgment tasks. During the experiment, we compared four different stimulation patterns (two simultaneous: short and long, intermittent and sequential) differing in total duration, total energy, or temporal synchrony. The experiment confirmed that the subject ability to enumerate electrotactile stimuli decreased with increasing the number of active electrodes. Furthermore, we found that, in electrotactile stimulation, the temporal coding schemes, and not total energy or duration modulated the accuracy in numerosity judgment. More precisely, the sequential condition resulted in significantly better numerosity discrimination than intermittent and simultaneous stimulation. These findings, together with the fact that the shoulder appeared to be a feasible stimulation site to communicate tactile information via electrotactile feedback, can serve as a guide to deliver tactile feedback to proximal areas in stroke survivors who lack sensory integrity in distal areas of their affected arm, but retain motor skills.

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We report novel findings from experiments on the enumeration of canonical patterns under attentional load. While previous studies have shown that the process of enumerating randomized arrangements can be disrupted by attentional load, the effect of attentional load on canonical patterns has been unexplored. To investigate this case, we adapted a spatial dual-task paradigm previously used to study attentional disruption during the enumeration of randomized arrangements. We begin by replicating previous findings for randomized arrangements, with enumeration error increasing with cluster numerosity and attentional load. For dice patterns, enumeration error also increased under attentional load. However, contrary to findings from studies on single-task enumeration of dice patterns, we observed conflation of patterns with similar outlines. In subsequent experiments, we manipulated the spatial location of the enumeration task, placing the dot cluster in the center. With centrally located, canonical patterns that remained in the same location across trials, enumeration accuracy was more consistent with results from single-task studies. We hypothesize that participants may be using shape cues to inform guessing during enumeration tasks when unable to both localize and fully attend to target patterns.

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Participants consisted of 496 children (mean age = 6 years; 9 months) recruited from 11 schools in Brisbane, Australia. Children were assessed on the addition and subtraction subtests of the Test of Basic Arithmetic and Number Skills (TOBANS), an adapted version of the Head-Toes-Knees-Shoulders task to measure inhibition, numerosity discrimination using eight subtests varying ratio (2:3 or 5:6) and congruency, and non-verbal cognitive ability using an adapted version of Raven's Coloured Progressive Matrices. Information on children's demographics (gender, English as an additional language, and learning difficulty status) is also provided. All assessments were administered during the second year of formal schooling (i.e. Grade 1). Findings regarding the impact of inhibition on the relation between numerosity discrimination and arithmetic are reported elsewhere [1].

RESUMEN

Numerosity discrimination tasks (judging which of two random dotarrays contains the larger number) have been widely used as a measure of the efficiency of an approximate number system (ANS) and are a correlate of early arithmetic skills. Recently, it has been suggested that the relationship between numerosity discrimination and arithmeticis explained by inhibition rather than the ANS. We assessed this hypothesis in astudy of 496 children (mean age = 81.23 months) using numerosity discrimination tasks that manipulated the congruency between surface area and numerosity. Numerosity discrimination for incongruent arrays (which are postulated to require inhibition due to a conflict between judgments based on surface area rather than numerosity) was more difficult than that for congruent arrays. However, all numerosity discrimination tasks showed substantial correlations with each other and correlated with arithmetic. A latent variable path model showed that a general numerosity judgment factorcorrelated witharithmetic even after controlling for a measure of response inhibition. In contrast, numerosity discrimination for incongruent arrays showed no unique relationship with arithmetic ability. Our results do not support the view that the relationship between numerosity discrimination and arithmetic is largely attributable to inhibition; rather, theyare consistent withthe view that numerosity discrimination tasks tap the operation of an ANS.

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Researchers investigating numerosity processing manipulate the visual stimulus properties (e.g., surface). This is done to control for the confound between numerosity and its visual properties and should allow the examination of pure number processes. Nevertheless, several studies have shown that, despite different visual controls, visual cues remained to exert their influence on numerosity judgments. This study, therefore, investigated whether the impact of the visual stimulus manipulations on numerosity judgments is dependent on the task at hand (comparison task vs. same-different task) and whether this impact changes throughout development. In addition, we examined whether the influence of visual stimulus manipulations on numerosity judgments plays a role in the relation between performance on numerosity tasks and mathematics achievement. Our findings confirmed that the visual stimulus manipulations affect numerosity judgments; more important, we found that these influences changed with increasing age and differed between the comparison and the same-different tasks. Consequently, direct comparisons between numerosity studies using different tasks and age groups are difficult. No meaningful relationship between the performance on the comparison and same-different tasks and mathematics achievement was found in typically developing children, nor did we find consistent differences between children with and without mathematical learning disability (MLD).

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