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Deaf children usually achieve lower scores on numerical tasks than normally hearing peers. Explanations for mathematical disabilities in hearing children are based on quantity representation deficits (Geary, 1994) or on deficits in accessing these representations (Rousselle & Noël, 2008). The present study aimed to verify, by means of symbolic (Arabic digits) and nonsymbolic (dot constellations and hands) magnitude comparison tasks, whether deaf children show deficits in representations or in accessing numerical representations. The study participants were 10 prelocutive deaf children and 10 normally hearing children. Numerical distance and magnitude were manipulated. Response time (RT) analysis showed similar magnitude and distance effects in both groups on the 3 tasks. However, slower RTs were observed among the deaf participants on the symbolic task alone. These results suggest that although both groups' quantity representations were similar, the deaf group experienced a delay in accessing representations from symbolic codes.

Numerical quantity seems to affect the response in any task that involves numbers, even in tasks that do not demand access to quantity (e.g., perceptual tasks). That is, readers seem to activate quantity representations upon the mere presentation of integers. One important piece of evidence in favor of this view comes from the finding of a distance effect in perceptual tasks: When one compares two numbers, response times (RTs) are a function of the numerical distance between them. However, recent studies have suggested that the physical similarity between Arabic numbers is strongly correlated with their numerical distance, and that the former could be a better predictor of RT data in perceptual tasks in which magnitude processing is not required (Cohen, 2009a). The present study explored the Persian and Arabic versions of Indian numbers (Exps. 1 and 2, respectively). Naïve participants (speakers of Spanish) and users of these notations (Pakistanis and Jordanians) participated in a physical same-different matching task. The RTs of users of the Indian notations were regressed on perceptual similarity (estimated from the Spanish participants' RTs) and numerical distance. The results showed that, regardless of the degree of correlation between the perceptual similarity function and the numerical distance function, the critical predictor for RTs was perceptual similarity. Thus, participants do not automatically activate Indian integers' quantity representations, at least not when these numbers are presented in simple perceptual tasks.

It is a common assumption for multiplication-solving models that single-digit multiplications are automatically retrieved. However, the experimental evidence for this is based on paradigms under suspicion. In this research, we employed a new procedure with the aim of assessing the automatic retrieval of multiplication more directly. In two experiments, multiplication automatism was studied using briefly presented primes (stimulus onset asynchrony = 48 msec) in a number-naming task. In Experiment 1, in the congruent conditions, the target and the prime were the same numbers (e.g., prime, 6; target, 6) or the target was the solution to the multiplication prime (e.g., prime, 2 x 3 = ; target, 6). In the incongruent conditions, no relationship existed between the primes and the targets (e.g., prime, 32; target, 6; or prime, 4 x 8 = ; target, 6). Experiment 2 explored the relevance of the equal sign for the multiplication-priming effect. Data showed that naming was faster when the solution of the multiplication prime matched the target, as compared with the incongruent condition (multiplication-priming effect), and that these effects were found irrespective of the presence of the equal sign. The fact that this priming effect was found even though the participants were unaware of the presentation of the primes supports the automatic character of single-digit multiplication. We conclude by arguing that this procedure is highly valuable for exploring the mechanisms involved in simple arithmetic solving.

This study is about JS, a patient who suffered from anomia, phonological dyslexia and severe writing problems following a left hemispheric stroke. He showed good arabic numeral comprehension as evidenced in number-comparison tasks, but impairment in transcoding arabic numerals into verbal numbers and verbal numbers into arabic numerals. Although JS had several operand reading errors, the four arithmetic operations were not affected. In calculations with arabic numerals, he produced the correct results both in oral and written responses. For instance, when presented with the multiplication "7 x 3", JS read the operation as "four times five", but provided the correct response orally "twenty one" and written "21". This behavior goes against those hypotheses which posit that multiplication facts are verbally-based, and those which establish the same route for verbal number production in calculation and arabic numeral reading.

The present study explores the effect of two instructional methods for children with different levels of mathematical skills. One of these methods uses a conventional approach to learning multiplication and emphasizes the memorization of all arithmetic facts, whereas the other method is based on psychological principles and combines: a) the memorization of a small subset of problems aided by color cues and a portable time-table, with b) the use of single-step rules. One hundred and sixty second-grade children (aged 7-8) received instruction in one of these approaches – either the conventional method or the memory and rules method (M&R) – over the course of 6 months as part of their normal school education. Moderation analysis revealed that children with poor mathematical skills in the conventional group scored significantly better than their counterparts in the M&R group, whereas a significant advantage was observed in the M&R group for those children with strong mathematical skills. [ABSTRACT FROM AUTHOR]