The influence of number line estimation precision and numeracy on risky financial decision making

This study examined whether different aspects of mathematical proficiency influence one's ability to make adaptive financial decisions. “Numeracy” refers to the ability to process numerical and probabilistic information and is commonly reported as an important factor which contributes to financial decision‐making ability. The precision of mental number representation (MNR), measured with the number line estimation (NLE) task has been reported to be another critical factor. This study aimed to examine the contribution of these mathematical proficiencies while controlling for the influence of fluid intelligence, math anxiety and personality factors. In our decision‐making task, participants chose between two options offering probabilistic monetary gain or loss. Sensitivity to expected value was measured as an index for the ability to discriminate between optimal versus suboptimal options. Partial correlation and hierarchical regression analyses revealed that NLE precision better explained EV sensitivity compared to numeracy, after controlling for all covariates. These results suggest that individuals with more precise MNR are capable of making more rational financial decisions. We also propose that the measurement of “numeracy,” which is commonly used interchangeably with general mathematical proficiency, should include more diverse aspects of mathematical cognition including basic understanding of number magnitude.     

Rapid proportion comparison with spatial arrays of frequently used meaningful visual symbols

It has been shown that when two arrays of Arabic numerals were briefly presented, observers could accurately indicate which array contained the larger number of a target numeral. This study investigated whether this rapid proportion comparison can be extended to other meaningful symbols that share some of notable properties of Arabic numerals. We tested mainly several Japanese Kanji letters, each of which represents a meaning and can work as a word. Using physically identical stimulus sets that could be interpreted as different types of letters, Experiment 1 first confirmed the rapid proportion comparison with Arabic numerals for Japanese participants. Experiment 2 showed that the rapid proportion comparison can be extended to Kanji numerals. Experiment 3 successfully demonstrated that rapid proportion judgments can be found with non-quantitative Kanji letters that are used frequently. Experiment 4 further demonstrated the rapid proportion comparison with frequently used meaningful non-letter symbols (gender icons). The rapid processing cannot be attributed to fluent processing of familiar items, because it was not found with familiar phonograms (Japanese Kana letters). These findings suggest that the rapid proportion comparison can be commonly found with frequently used meaningful symbols, even though their meaning is not relevant to the task.     

First Language Attrition Induces Changes in Online Morphosyntactic Processing and Re‐Analysis: An ERP Study of Number Agreement in Complex Italian Sentences

First language (L1) attrition in adulthood offers new insight on neuroplasticity and the role of language experience in shaping neurocognitive responses to language. Attriters are multilinguals for whom advancing L2 proficiency comes at the cost of the L1, as they experience a shift in exposure and dominance (e.g., due to immigration). To date, the neurocognitive mechanisms underlying L1 attrition are largely unexplored. Using event‐related potentials (ERPs), we examined L1‐Italian grammatical processing in 24 attriters and 30 Italian native‐controls. We assessed whether (a) attriters differed from non‐attriting native speakers in their online detection and re‐analysis/repair of number agreement violations, and whether (b) differences in processing were modulated by L1‐proficiency. To test both local and non‐local agreement violations, we manipulated agreement between three inflected constituents and examined ERP responses on two of these (subject, verb , modifier ). Our findings revealed group differences in amplitude, scalp distribution, and duration of LAN/N400 + P600 effects. We discuss these differences as reflecting influence of attriters’ L2‐English, as well as shallower online sentence repair processes than in non‐attriting native speakers. ERP responses were also predicted by L1‐Italian proficiency scores, with smaller N400/P600 amplitudes in lower proficiency individuals. Proficiency only modulated P600 amplitude between 650 and 900 ms, whereas the late P600 (beyond 900 ms) depended on group membership and amount of L1 exposure within attriters. Our study is the first to show qualitative and quantitative differences in ERP responses in attriters compared to non‐attriting native speakers. Our results also emphasize that proficiency predicts language processing profiles, even in native‐speakers, and that the P600 should not be considered a monolithic component.     

Categories of Large Numbers in Line Estimation

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and response time are expected near the boundaries between categories. In contrast to previous work (Landy, Silbert, & Goldin, 2013) that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers.     

特征和结构信息对草图人脸识别的影响

在人脸认知研究的特征说、结构说和整体说的基础上,通过草图人脸与人脸相似程度主观评价的调查,发现五官位置、拓扑结构、五官比例、轮廓外形和五官外形等五个维度对人脸识别影响的权重依次减小,并且存在着多种显著的不同水平的交互作用。进而提出,五官位置和拓扑结构可组合成具体图形意义上的结构关系,这种结构关系将整体人脸分解成有序的特征集。     

On the masking and disclosure of unconscious elaborate processing. A reply to Van Opstal, Reynvoet, and Verguts (2005)

We have recently argued that unconscious numerical stimuli might activate responses by a match with prespecified action trigger codes (action trigger account) rather than by semantic prime processing (elaborate processing account). [Van Opstal, F., Reynvoet, B., and Verguts, T. (2005). How to trigger elaborate processing? A comment on Kunde, Kiesel, and Hoffmann (2003). Cognition] replicate one piece of evidence for our inference—an inefficiency of primes not presented in target format (verbal or Arabic). But this was found only with letter masks and not with hash masks. The authors conclude that letter masks block unconscious prime processing, and that elaborate processing can account for unconscious priming effects if all its (sometimes subtle) side conditions are considered. We agree that the type of mask in general is an important factor in priming studies but we note that (i) the authors' mask-blocking hypothesis is not well supported by the data, (ii) clear evidence for semantic prime processing in their study is lacking and, (iii) differences in mask efficiency (rather than mask type) might account for the conflicting results. To corroborate this inference we replicate van Opstal et al.'s results with letter masks but reduced mask efficiency. Altogether their data do not challenge the action-trigger account nor do they strongly support the elaborate processing view.     

4-6岁儿童数学认知中的多元表征研究

本研究以早期儿童数学认知中的数、数运算以及模式三个维度为切入点,对来自上海市的120名4-6岁儿童采用个别面试法考察其数学认知中的多元表征,采用描述性统计、多元方差分析、卡方检验等方法探查儿童多元表征的发展特点、相互关系及影响因素。结果表明：4-6岁儿童已具备初步的数、数运算、模式的多元表征能力,其中数的多元表征能力最好;4-6岁儿童在数、模式的多元表征中未出现明显的年龄差异与性别差异,在数运算多元表征中有明显的年龄差异,无性别差异;儿童使用的表征形式数量随年龄增长相应增加,且更倾向于使用描绘性表征中的实物情境表征与教具模型表征;4-6岁儿童数、数运算、模式的多元表征能力之间存在一定的相关;除年龄之外,已有学习经验、学习材料的呈现样式也是影响儿童多元表征的可能性因素。     

今、帛、竹书《周易》卦爻辞补释

出土简帛易学文献,为今人探索卦爻辞之本义提供了宝贵的资料.本文即以马王堆帛书《周易》、上海博物馆藏战国楚竹书《周易》与今本《周易》相对比,选取坤、蒙、比、履等十五卦中的诸本差异较大的辞句予以训释疏证,辨析其异同,间亦涉及帛本流传等学术问题.     

Sensitivity to number: Reply to Gebuis and Gevers

Past research showing a bias towards the larger non-symbolic number by adults and children in line bisection tasks (de Hevia & Spelke, 2009) has been challenged by Gebuis and Gevers, suggesting that area subtended by the stimulus and not number is responsible for the biases. I review evidence supporting the idea that although sensitivity to number might be relatively affected by visual cues, number is a major, salient property of our environment. The influence of non-numerical cues might be seen as the concurrent processing of dimensions that entail information of magnitude, without implying that number is constructed out of those dimensions.     

Hierarchy and scope of planning in subject–verb agreement production

Two subject–verb agreement error elicitation studies tested the hierarchical feature-passing account of agreement computation in production and three timing-based alternatives: linear distance to the head noun, semantic integration, and a combined effect of both (a scope of planning account). In Experiment 1, participants completed subject noun phrase (NP) stimuli consisting of a head NP followed by two prepositional phrase (PP) modifiers, where the first PP modified the first NP, and the second PP modified one of the two preceding NPs. Semantic integration between the head noun and the local noun within each PP was held constant across structures. The mismatch error pattern showed an effect of linear distance to the head noun and no influence of hierarchical distance. In Experiment 2, participants completed NP PP PP stimuli in which both PPs modified the head noun, and both the order of the two PPs and the local nouns’ degree of semantic integration with the head noun were varied. The pattern of mismatch errors reflected a combination of semantic integration and linear distance to the head noun. These studies indicate that agreement processes are strongly constrained by grammatical-level scope of planning, with local nouns planned closer to the head having a greater chance of interfering with agreement computation.