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.     

Approximate quantification in young,healthy older adults’, and Alzheimer patients

Forty young adults, 40 healthy older adults, and 39 probable AD patients were asked to estimate small (e.g., 25) and large (e.g., 60) collections of dots in a choice condition and in two no-choice conditions. Participants could choose between benchmark and anchoring strategies on each collection of dots in the choice condition and were required to use either benchmark or anchoring on all configurations in the no-choice conditions (one per strategy). The benchmark strategy involves visual estimation processes whereas the anchoring strategy involves both enumeration and estimation processes. Results showed that strategy use was influenced by collection, participant, and strategy characteristics. Age-related and dementia-related differences were found in both strategy use and strategy execution. The findings have implications for our understanding of aging effects in approximate quantification, strategic variations in Alzheimer’s patients, and sources of cognitive decline during early stages of Alzheimer’s disease.     

Automatic quantity processing in 5-year olds and adults

In this study adults performed numerical and physical size judgments on a symbolic (Arabic numerals) and non-symbolic (groups of dots) size congruity task. The outcomes would reveal whether a size congruity effect (SCE) can be obtained irrespective of notation. Subsequently, 5-year-old children performed a physical size judgment on both tasks. The outcomes will give a better insight in the ability of 5-year-olds to automatically process symbolic and non-symbolic numerosities. Adult performance on the symbolic and non-symbolic size congruity tasks revealed a SCE for numerical and physical size judgments, indicating that the non-symbolic size congruity task is a valid indicator for automatic processing of non-symbolic numerosities. Physical size judgments on both tasks by children revealed a SCE only for non-symbolic notation, indicating that the lack of a symbolic SCE is not related to the mathematical or cognitive abilities required for the task but instead to an immature association between the number symbol and its meaning.     

汉语并列式合成词的词汇通达

汉语并列式合成词具有三种类型,这三种类型内部不同的词素组合在心理词典中则需要不同的词汇通达时间。实验结果表明,在对汉语并列式合成词的词汇通达过程中,第一成分并不总是起决定作用;同样,并列式合成词中的两个成分在词汇通达过程中并不总是同等重要。实验证明,语义透明度对并列式合成词的词汇通达起重要作用。实验还发现,在心理词典中对并列式合成词的词汇通达需要一个证实原则。     

Intra‐sentential context effects on the interpretation of logical metonymy⋆

Verbs such as enjoy in the student enjoyed the book exhibit logical metonymy: enjoy is interpreted as enjoy reading. Theoreticalwork [Computational Linguistics 17 (4) (1991) 409; The Generative Lexicon, MIT Press, Cambridge, MA, 1995] predicts that this interpretation can be influenced by intra‐sentential context, e.g., by the subject of enjoy. In this article, we test this prediction using a completion experiment and find that the interpretation of a metonymic verb is influenced by the semantic role of its subject. We present a Bayesian model that accounts for the interpretation of logical metonymy and achieves a good fit on our experimental data. We show that the parameters of the model can be estimated from completion data or from corpus data.     

形声字心理词典中义符和音符线索的作用

本实验采用启动条件下的词汇判断法,用形声字的义符或音符作为启动刺激,对形声字心理词典中义符和音符线索的作用进行探讨。结果发现：义符线索比音符线索的作用更大;义符、音符对低频字的影响比对高频字的影响更大;当义符、音符与字义、字音一致和不一致时,又符线索和音符线索的作用不一样。     

Working memory and number line representations in single-digit addition: Approximate versus exact,nonsymbolic versus symbolic

How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills.     

Proficiency in a second language influences the processing of number words

We evaluated whether proficiency in a second language (L2) influenced the processing of numerical information. In Experiment 1, two groups of German/English bilinguals, one less proficient in English (L2) and the other more proficient in L2, performed two-digit number comparison tasks while the unit–decade compatibility was evaluated. All participants presented compatibility effect with Arabic digits regardless of their L2 proficiency. However, when bilinguals with less proficiency in L2 performed verbal number comparison tasks they showed regular compatibility effect in German and reverse compatibility effect in English, whereas more proficient bilinguals did not show compatibility effects in either German or English. In Experiment 2, the same pattern of results was obtained with highly proficient bilinguals after controlling their working memory span. These results indicate that L2 proficiency influences the processing of two-digit number words.     

Weber's Law influences numerical representations in rhesus macaques (Macaca mulatta)

We present the results of two experiments that probe the ability of rhesus macaques to match visual arrays based on number. Three monkeys were first trained on a delayed match-to-sample paradigm (DMTS) to match stimuli on the basis of number and ignore continuous dimensions such as element size, cumulative surface area, and density. Monkeys were then tested in a numerical bisection experiment that required them to indicate whether a sample numerosity was closer to a small or large anchor value. Results indicated that, for two sets of anchor values with the same ratio, the probability of choosing the larger anchor value systematically increased with the sample number and the psychometric functions superimposed. A second experiment employed a numerical DMTS task in which the choice values contained an exact numerical match to the sample and a distracter that varied in number. Both accuracy and reaction time were modulated by the ratio between the correct numerical match and the distracter, as predicted by Weber's Law.