Squeezing, striking, and vocalizing: Is number representation fundamentally spatial?

Numbers are fundamental entities in mathematics, but their cognitive bases are unclear. Abundant research points to linear space as a natural grounding for number representation. But, is number representation fundamentally spatial? We disentangle number representation from standard number-to-line reporting methods, and compare numerical estimations in educated participants using line-reporting with three nonspatial reporting conditions (squeezing, bell-striking, and vocalizing). All three cases of nonspatial-reporting consistently reproduced well-established results obtained with number-line methods. Furthermore, unlike line-reporting—and congruent with the psychophysical Weber–Fechner law—nonspatial reporting systematically produced logarithmic mappings for all nonsymbolic stimuli. Strikingly, linear mappings were obtained exclusively in conditions with culturally mediated elements (e.g., words). These results suggest that number representation is not fundamentally spatial, but builds on a deeper magnitude sense that manifests spatially and nonspatially mediated by magnitude, stimulus modality, and reporting condition. Number-to-space mappings—although ubiquitous in the modern world—do not seem to be rooted directly in brain evolution but have been culturally privileged and enhanced.     

儿童数字线表征的发展——心理长度的影响

探讨儿童在数字线估计任务中心理长度的发展及其对数量表征模式的影响.选取7~9岁儿童共109名进行数字线估计任务测试,设置了10cm和20cm两种长度条件,要求儿童完成根据位置判断数字任务(position to number,PN任务).结果表明儿童在数字线PN任务中存在心理长度,且7岁儿童心理长度的范围超过10,随着儿童年龄的增长,他们的心理长度范围不断缩小;心理长度范围影响儿童的表征模式,随着心理长度范围的缩小,儿童的数字线表征出现从指数模式到线性模式的变化趋势;与表征模式的发展趋势一致,儿童估计的精确性随年龄增长逐渐提高.     

Number words in young children's conceptual and procedural knowledge of addition, subtraction and inversion

Three studies addressed children's arithmetic. First, 50 3- to 5-year-olds judged physical demonstrations of addition, subtraction and inversion, with and without number words. Second, 20 3- to 4-year-olds made equivalence judgments of additions and subtractions. Third, 60 4- to 6-year-olds solved addition, subtraction and inversion problems that varied according to the inclusion of concrete referents and number words. The results indicate that number words play a different role in conceptual and procedural development. Children have strong addition and subtraction concepts before they can translate the physical effects of these operations into number words. However, using number words does not detract from their calculation procedures. Moreover, consistent with iterative relations between conceptual and procedural development, the results suggest that inversion acquisition depends on children's calculation procedures and that inversion understanding influences these procedures.     

Asymmetrical retention functions for sequences of light flashes or tone bursts in the rat

In Experiment 1, rats were trained in a symbolic delayed matching-to-sample task to discriminate sample stimuli that consisted of sequences of magazine light flashes. The intertrial interval was illuminated by the houselight for Group Light, and it was dark for Group Dark. Retention functions exhibited a choose-many response bias when the delay interval was illuminated by the houselight in both groups, and no consistent response bias when the delay interval was dark. In Experiment 2, rats were trained to discriminate sample stimuli that consisted of sequences of tone bursts. During delay testing, a different tone (i.e., different frequency and location than the sample tone) was present or absent during the delay interval. The retention functions exhibited a significant choose-many bias when tone was present during the delay and a choose-few bias when tone was absent. Asymmetrical retention functions for tone burst and light flash sequences are due to the similarity between the stimulus conditions of the delay interval and the modality of the sequential event being discriminated. These results are consistent with an instructional ambiguity explanation of response biases in memory for number.     

Boys will be boys: a pre‐line‐up gameplay has beneficial effects on boys' but not girls' identification performance

Fifty children, aged between 4 and 7 years, underwent a sequential photo line‐up procedure in order to identify a man they had met the previous day. Half of the participants engaged in a pre‐procedure gameplay with the female interviewer. It was hypothesised that the game would stimulate rapport building and would ultimately result in an increased performance during the line‐up procedure. The beneficial effect was indeed observed, but only for the male participants. This finding suggests that gameplay may be a fruitful strategy to decrease child witness discomfort and to increase participation. Copyright © 2006 John Wiley & Sons, Ltd.     

4岁幼儿线条偏好实验研究

本研究采用对偶比较法,对4岁幼儿进行6类常见线条的偏好调查研究,得出以下结果:4岁幼儿线条偏好的顺序依次是:漩涡线、曲线、弧形线、波浪线、折线、直线;男生和女生对线条的偏好没有明显差异;4岁幼儿对不同方向的漩涡线的偏好有明显差异,对不同方向的直线、波浪线、折线、曲线和弧形线的偏好没有明显差异。     

Exaggerated leftward bias in the mental number line of patients with schizophrenia

Several visuo-motor tasks can be used to demonstrate biases towards left hemispace in schizophrenic patients, suggesting a minor right hemineglect. Recent studies in neglect patients used a new number bisection task to highlight a lateralized defect in their visuo-spatial representation of numbers. To test a possible lateralized representational deficit in schizophrenia, we used the number bisection task in 11 schizophrenic patients compared to 11 healthy controls. Participants were required to orally indicate the central number of an interval orally presented. Whereas healthy subjects showed no significant bias, schizophrenic patients presented a significant leftward bias. Therefore, these results suggest an impairment in higher order representations of the number space in patients with schizophrenia, an impairment that is qualitatively similar to the deficit described in neglect patients.     

From grammatical number to exact numbers: early meanings of 'one', 'two', and 'three' in English, Russian, and Japanese

This study examined whether singular/plural marking in a language helps children learn the meanings of the words 'one,' 'two,' and 'three.' First, CHILDES data in English, Russian (which marks singular/plural), and Japanese (which does not) were compared for frequency, variability, and contexts of number-word use. Then young children in the USA, Russia, and Japan were tested on Counting and Give-N tasks. More English and Russian learners knew the meaning of each number word than Japanese learners, regardless of whether singular/plural cues appeared in the task itself (e.g., "Give two apples" vs. "Give two"). These results suggest that the learning of "one," "two" and "three" is supported by the conceptual framework of grammatical number, rather than that of integers.     

Numerical and non-numerical ordinality processing in children with and without developmental dyscalculia: Evidence from fMRI

Ordinality is – beyond numerical magnitude (i.e., quantity) – an important characteristic of the number system. There is converging empirical evidence that (intra)parietal brain regions mediate number magnitude processing. Furthermore, recent findings suggest that the human intraparietal sulcus (IPS) supports magnitude and ordinality in a domain-general way. However, the latter findings are derived from adult studies and with respect to children (i.e., developing brain systems) both the neural correlates of ordinality processing and the precise role of the IPS (domain-general vs. domain-specific) in ordinality processing are thus far unknown. The present study aims at filling this gap by employing functional magnetic resonance imaging (fMRI) to investigate numerical and non-numerical ordinality knowledge in children with and without developmental dyscalculia. In children (without DD) processing of numerical and non-numerical ordinality alike is supported by (intra)parietal cortex, thus extending the notion of a domain-general (intra)parietal cortex to developing brain systems. Moreover, activation extents in response to numerical ordinality processing differ significantly between children with and without dyscalculia in inferior parietal regions (supramarginal gyrus and IPS).     

Children's mappings of large number words to numerosities

Previous studies have suggested that children's learning of the relation between number words and approximate numerosities depends on their verbal counting ability, and that children exhibit no knowledge of mappings between number words and approximate numerical magnitudes for number words outside their productive verbal counting range. In the present study we used a numerical estimation task to explore children's knowledge of these mappings. We classified children as Level 1 counters (those unable to produce a verbal count list up to 35), Level 2 counters (those who were able to count to 35 but not 60) and Level 3 counters (those who counted to 60 or above) and asked children to estimate the number of items on a card. Although the accuracy of children's estimates depended on counting ability, children at all counting skill levels produced estimates that increased linearly in proportion to the target number, for numerosities both within and beyond their counting range. This result was obtained at the group level (Experiment 1) and at the level of individual children (Experiment 2). These findings provide evidence that even the least skilled counters do exhibit some knowledge of the form of the mapping between large number words and approximate numerosities.