A common representational system governed by Weber's law: nonverbal numerical similarity judgments in 6-year-olds and rhesus macaques

This study compared nonverbal numerical processing in 6-year-olds with that in nonhuman animals using a numerical bisection task. In the study, 16 children were trained on a delayed match-to-sample paradigm to match exemplars of two anchor numerosities. Children were then required to indicate whether a sample intermediate to the anchor values was closer to the small anchor value or the large anchor value. For two sets of anchor values with the same ratio, the probability of choosing the larger anchor value increased systematically with sample number, and the psychometric functions superimposed when plotted on a logarithmic scale. The psychometric functions produced by the children also superimposed with the psychometric functions produced by rhesus monkeys in an analogous previous experiment. These examples of superimposition demonstrate that nonverbal number representations, even in children who have acquired the verbal counting system, are modulated by Weber's law.     

How do we convert a number into a finger trajectory?

How do we understand two-digit numbers such as 42? Models of multi-digit number comprehension differ widely. Some postulate that the decades and units digits are processed separately and possibly serially. Others hypothesize a holistic process which maps the entire 2-digit string onto a magnitude, represented as a position on a number line. In educated adults, the number line is thought to be linear, but the “number sense” hypothesis proposes that a logarithmic scale underlies our intuitions of number size, and that this compressive representation may still be dormant in the adult brain. We investigated these issues by asking adults to point to the location of two-digit numbers on a number line while their finger location was continuously monitored. Finger trajectories revealed a linear scale, yet with a transient logarithmic effect suggesting the activation of a compressive and holistic quantity representation. Units and decades digits were processed in parallel, without any difference in left-to-right vs. right-to-left readers. The late part of the trajectory was influenced by spatial reference points placed at the left end, middle, and right end of the line. Altogether, finger trajectory analysis provides a precise cognitive decomposition of the sequence of stages used in converting a number to a quantity and then a position.     

The relationship between emotional-state language and emotion understanding: A study with school-age children

We carried out an investigation with primary-school children on the relationship between both use and comprehension of emotional-state language and emotion understanding. Participants were 100 students between 7 and 10 years old (mean age=8 years and 10 months; SD=15.3 months), equally divided by gender. They completed four tests evaluating their language ability, use of emotional-state language, comprehension of emotional-state language and emotion understanding (EU) respectively. Significant correlations were found between both use and comprehension of emotional-state talk and children's EU. In addition, regression analyses showed that comprehension of emotional-state language, rather than its use, plays a significant role in explaining children's emotion understanding.     

Participant recruitment methods and statistical reasoning performance

Optimal Bayesian reasoning performance has reportedly been elusive, and a variety of explanations have been suggested for this situation. In a series of experiments, it is demonstrated that these difficulties with replication can be accounted for by differences in participant-sampling methodologies. Specifically, the best performances are obtained with students from top-tier, national universities who were paid for their participation. Performance drops significantly as these conditions are altered regarding inducements (e.g., using unpaid participants) or participant source (e.g., using participants from a second-tier, regional university). Honours-programme undergraduates do better than regular undergraduates within the same university, paid participation creates superior performance, and top-tier university students do better than students from lower ranked universities. Pictorial representations (supplementing problem text) usually have a slight facilitative effect across these participant manipulations. These results indicate that studies should take account of these methodological details and focus more on relative levels of performance rather than absolute performance.     

The role of numerosity in processing nonsymbolic proportions

The difficulty in processing fractions seems to be related to the interference between the whole-number value of the numerator and the denominator and the real value of the fraction. Here we assess whether the reported problems with symbolic fractions extend to the nonsymbolic domain, by presenting fractions as arrays of black and white dots representing the two operands. Participants were asked to compare a target array with a reference array in two separate tasks using the same stimuli: a numerosity task comparing just the number of white dots in the two arrays; and a proportion task comparing the proportion of black and white dots. The proportion task yielded lower accuracy and slower response, confirming that even with nonsymbolic stimuli accessing proportional information is relatively difficult. However, using a congruity manipulation in which the greater numerosity of white dots could co-occur with a lower proportion of them, and vice versa, it was found that both task-irrelevant dimensions would interfere with the task-relevant dimension suggesting that both numerosity and proportion information was automatically accessed. The results indicate that the magnitude of fractions can be automatically and holistically processed in the nonsymbolic domain.     

The spatial representation of numerical and non-numerical ordered sequences: Insights from a random generation task

It is widely believed that numbers are spatially represented from left to right on the mental number line. Whether this spatial format of representation is specific to numbers or is shared by non-numerical ordered sequences remains controversial. When healthy participants are asked to randomly generate digits they show a systematic small-number bias that has been interpreted in terms of “pseudoneglect in number space”. Here we used a random generation task to compare numerical and non-numerical order. Participants performed the task at three different pacing rates and with three types of stimuli (numbers, letters, and months). In addition to a small-number bias for numbers, we observed a bias towards “early” items for letters and no bias for months. The spatial biases for numbers and letters were rate independent and similar in size, but they did not correlate across participants. Moreover, letter generation was qualified by a systematic forward direction along the sequence, suggesting that the ordinal dimension was more salient for letters than for numbers in a task that did not require its explicit processing. The dissociation between numerical and non-numerical orders is consistent with electrophysiological and neuroimaging studies and suggests that they rely on at least partially different mechanisms.     

Processing negative numbers by transforming negatives to positive range and by sign shortcut

Numerals are processed by a phylogenetically old analogue magnitude system. Can culturally new negative numerals be processed using this same representation? To find out whether magnitude representation could be used, we contrasted three possible processing mechanisms: an extended magnitude system for both positive and negative numbers, a mirroring mechanism that could transform negative values to the positive range to be processed on the positive magnitude system, and a sign shortcut strategy that can process the signs of numbers independently of the absolute values of numerals. To test these three hypotheses, a comparison task was used and the reaction time pattern, numerical distance, and Spatial-Numerical Association of Response Codes (SNARC) effect was analysed. The results revealed a mirroring process along with a sign shortcut mechanism. The SNARC effect was observed only when positive numbers were compared.     

Limiting attentional resources influences performance and output monitoring of an event-based prospective memory task

One of the most frequently used markers in research on numerical cognition is the distance effect. Recently, we have suggested that a distance effect can have different origins depending on the experimental task. By dissociating the comparison distance effect from the priming distance effect we revealed the need to study the origin of this effect before drawing any conclusions from it (van Opstal, Gevers, de Moor, &; Verguts, 2008). Because a distance effect in a same–different task is also commonly used to study number representations (e.g., Dehaene &; Akhavein, 1995), the present study aimed at uncovering the origin of the effect in this task. Computational and empirical results indicate clearly that the distance effect in the same–different task originates from number representations rather than a decision process.     

Constituent-morpheme priming: Implications from the morphology of two-kanji compound words

Abstract: The diversity in the morphological structure of two‐kanji compound words is a matter of special concern for models of the Japanese mental lexicon. This study discusses two proposals for models of the Japanese mental lexicon – Hirose’s (1992, 1994, 1996 ) hypotheses and a Japanese lemma‐unit version of the multilevel interactive‐activation framework – in terms of their ability to cope with this diversity. As the proposals make different predictions concerning constituent‐morpheme priming, patterns of facilitation were examined in two experiments with five word‐formation principles as experimental conditions. Experiment 1, using the long stimulus onset asynchrony (SOA) of 3000 ms employed by Hirose (1992 ), only found significant differences between the first‐ and second‐element conditions in one of the word‐formation conditions. Experiment 2, using a short SOA of 250 ms, confirmed the pattern of priming obtained in Experiment 1. These results are more consistent with the prediction from the Japanese lemma‐unit model.