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.     

Concordance of teacher-rated and performance-based measures of executive functioning in preschoolers

The most common method used to evaluate child behavior and functioning is rating scales completed by parents and/or teachers. Given that executive functioning (EF) plays a fundamental role in the developing child’s cognitive, behavioral, and social-emotional development, it would be ideal if ratings of EF and performance-based EF measures assess the same construct. However, most studies report a small to negligible association between performance-based measures and ratings of EF. There are few studies investigating this association for preschoolers, and most only include parent ratings. Teachers may be more reliable reporters of EF behaviors due to the higher demand for EF skills in the preschool setting than at home and because teachers may have a better sense of what behaviors are normative. In this study, we reviewed the associations between three EF rating scales completed by teachers on 243 preschool children. Results showed small to moderate correlations with EF measures of inhibition and cognitive flexibility/switching for all three scales, with the strongest associations observed between Child Behavior Rating Scale (CBRS) Behavioral Regulation subscale and child EF measures. Exploratory multivariate path analyses showed that, after controlling for age, sex, and socioeconomic status (SES), Behavioral Regulation significantly predicted performance-based measures of EF and accounted for incrementally more variance in the models. We conclude that in ideal situations, it is best to measure EF using both rating scales and performance-based measures of EF. The CBRS seems to be a sensitive measure of EF in preschoolers and may be a helpful brief screening tool for use with teachers.     

Test–retest reliability of the Brunel Lifestyle Physical Activity Questionnaire

ObjectivesTo establish the test–retest reliability of planned physical activity (PPA) and unplanned physical activity (UPA) components of the Brunel Lifestyle Physical Activity Questionnaire (BLPAQ). To provide evidence of the BLPAQ's stability using the proportion of agreement (PoA) method over a 5-week period.DesignTest–retest over a 5-week period using three diverse samples of adults.MethodsThe 277 participants were subdivided into three adult samples: gymnasium users (n = 80), undergraduate students (n = 111), and university staff members (n = 86). They were asked to complete the test–retest measure in their places of exercise, study, or work respectively.ResultsCorrelation coefficients between test–retest administrations were calculated for each participant group and intraclass correlations were calculated for each item. Pearson's product-moment correlations ranged from r = 0.95 to r = 0.96 for the PPA subscale and r = 0.93 to r = 0.98 for the UPA subscale. Intraclass correlations ranged from R = 0.52 to R = 0.99 for PPA and R = 0.87 to R = 0.99 for UPA. Fisher's z tests indicated that the test–retest correlation coefficients for the BLPAQ subscales were, on the whole, significantly stronger than those of older, comparable subscales from lifestyle physical activity questionnaires. The PoA analysis for each item revealed that the test–retest administrations were in high agreement (>95%).ConclusionsOverall, the PPA and UPA factors of the BLPAQ demonstrated high reliability and stability. The present study also illustrates the utility of PoA analysis in establishing the stability of physical activity measures.     

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.     

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.     

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。     

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.     

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.