Biomedical subjects

Hilary Barth

Publications and source records attributed to Hilary Barth.

4 recordsLinked to original sources

PubMed2007

rTMS over the intraparietal sulcus disrupts numerosity processing.

It has been widely argued that the intraparietal sulcus (IPS) is involved in tasks that evoke representations of numerical magnitude, among other cognitive functions. However, the causal role of this parietal region in processing symbolic and non-symbolic numerosity has not been established. The current study used repetitive Transcranial Magnetic Stimulation (rTMS) to the left and right IPS to investigate the effects of temporary deactivations of these regions on the capacity to represent symbolic (Arabic numbers) and non-symbolic (arrays of dots) numerosities. We found that comparisons of both symbolic and non-symbolic numerosities were impaired after rTMS to the left IPS but enhanced by rTMS to the right IPS. A signature effect of numerical distance was also found: greater impairment (or lesser facilitation) when comparing numerosities of similar magnitude. The reverse pattern of impairment and enhancement was found in a control task that required judging an analogue stimulus property (ellipse orientation) but no numerosity judgements. No rTMS effects for the numerosity tasks were found when stimulating an area adjacent but distinct from the IPS, the left and right angular gyrus. These data suggest that left IPS is critical for processing symbolic and non-symbolic numerosity; this processing may thus depend on common neural mechanisms, which are distinct from mechanisms supporting the processing of analogue stimulus properties.

Adult↗

PubMed2005

Abstract number and arithmetic in preschool children.

Educated humans use language to express abstract number, applying the same number words to seven apples, whistles, or sins. Is language or education the source of numerical abstraction? Claims to the contrary must present evidence for numerical knowledge that applies to disparate entities, in people who have received no formal mathematics instruction and cannot express such knowledge in words. Here we show that preschool children can compare and add large sets of elements without counting, both within a single visual-spatial modality (arrays of dots) and across two modalities and formats (dot arrays and tone sequences). In two experiments, children viewed animations and either compared one visible array of dots to a second array or added two successive dot arrays and compared the sum to a third array. In further experiments, a dot array was replaced by a sequence of sounds, so that participants had to integrate quantity information presented aurally and visually. Children performed all tasks successfully, without resorting to guessing strategies or responding to continuous variables. Their accuracy varied with the ratio of the two quantities: a signature of large, approximate number representations in adult humans and animals. Addition was as accurate as comparison, even though children showed no relevant knowledge when presented with symbolic versions of the addition tasks. Abstract knowledge of number and addition therefore precedes, and may guide, language-based instruction in mathematics.

Child, Preschool↗

PubMed2005

Non-symbolic arithmetic in adults and young children.

Five experiments investigated whether adults and preschool children can perform simple arithmetic calculations on non-symbolic numerosities. Previous research has demonstrated that human adults, human infants, and non-human animals can process numerical quantities through approximate representations of their magnitudes. Here we consider whether these non-symbolic numerical representations might serve as a building block of uniquely human, learned mathematics. Both adults and children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Success at these tasks did not depend on non-numerical continuous quantities, modality-specific quantity information, the adoption of alternative non-arithmetic strategies, or learned symbolic arithmetic knowledge. Abstract numerical quantity representations therefore are computationally functional and may provide a foundation for formal mathematics.

Adult↗

PubMed2003

The construction of large number representations in adults.

What is the nature of our mental representation of quantity? We find that human adults show no performance cost of comparing numerosities across vs. within visual and auditory stimulus sets, or across vs. within simultaneous and sequential sets. In addition, reaction time and performance in such tasks are determined by the ratio of the numerosities to be compared; absolute set size has no effect. These findings suggest that modality-specific stimulus properties undergo a non-iterative transformation into representations of quantity that are independent of the modality or format of the stimulus.

Adolescent↗