Dynamics Versus Development in Numerosity Estimation: A Computational Model Accurately Predicts a Developmental Reversal

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model—a situation in which children's estimates of numerosity would be better than those of adults. Consistent with the model simulations, task contexts led to a clear developmental reversal: children made more adult-like, linear estimates when to-be-estimated numbers were descending over trials (i.e., backward condition), whereas adults became more like children with logarithmic estimates when numbers were ascending (i.e., forward condition). In addition, adults’ estimates were subject to inter-trial differences regardless of stimulus order. In contrast, children were not able to use the trial-to-trial dynamics unless stimuli varied systematically, indicating the limited cognitive capacity for dynamic updates. Together, the model adequately predicts both developmental and trial-to-trial changes in number-line tasks.     

Preference structures and threshold models

Preferences are often represented in terms of a function, in the deterministic case as well as in the probabilistic case. In the present paper we develop a new numerical representation of preference structures for which the strict preference relation (P) is without circuit but not necessarily transitive. Moreover, we investigate the consequences of the representation for the usual preference structures. In particular, we propose new formulations for the numerical representation of the interval order structure.     

The acquisition of complex predicates in japanese specifically language-impaired and normally developing children

Japanese exhibits two different types of morphological processes. Some morphologically complex predicates are generated within the domain of the lexicon, whereas others are generated outside the domain of the lexicon. An elicited production task involving both types of complex predicates was administered to six Japanese children with specific language impairment (JSLI) and six children with normal language development (JNLD). The JSLI children experienced significant difficulty forming the lexicon-external complex predicates but much less difficulty with the lexicon-internal complex predicates while the performance of the JNLD children exhibited no such asymmetry. These preliminary results suggest that the deficit of SLI affects the ability to construct implicit procedural rules for morphology that are generated outside the lexicon while their lexical operations for morphology that are generated within the domain of the lexicon remain relatively unimpaired.     

The early acquisition of verb meaning in German by normally developing and language impaired children

The research reported here focuses on the early acquisition of event structure in German. Based on longitudinal studies from 5 normally developing (ND) and 6 language-impaired (LI) children, a model of "event structural bootstrapping" is presented that spells out how ND children log into the verb lexicon. They project a target-consistent event tree, depicting the head-of-event of transitions. Young LI children, failing to employ this bootstrapping strategy, resort to radically underspecified event representations. The results from a truth-value judgment experiment with 16 ND and 16 LI children showed that ND children perform correctly on transitional verbs, while LI children perform at chance level on the same tasks. These findings are accounted for by the model of event structural bootstrapping to the extent that LI children lack an explicit representation of the head-of-event.     

Are historic years understood as numbers or events? An fMRI study of numbers with semantic associations

While numbers generally cue processing of quantity or order, they can also contain semantic information, as in the case of historic years (e.g., “1492” calls forth associations of Columbus sailing the ocean blue). Whether these dates are processed as quantities or events may depend on the context in which they occur. We examined such “ambiguous number” processing in two different contexts using a paired-comparison task, recording both behavioral responses and brain activity. Participants were either asked to think of all items as numbers and to choose the larger number, or were told to treat the comparators as events and to choose the later event. Behaviorally, all events showed a normal distance effect, establishing that they may be understood and compared in an ordinal sequence. Functional magnetic resonance imaging (fMRI) demonstrated significant differences between years when treated as numbers versus as events. Dates in both contexts shared activity in parietal lobe regions previously implicated in number processing. Dates as numbers showed no extra-numeric activity, while dates thought of as events evoked activity in temporal semantic processing and frontal semantic retrieval areas. These differences suggest that extra-numeric information may be easily accessed and incorporated during processing when supported by even a weak context. This work supports previous studies showing a dissociation between quantity and meaning, and illustrates the brain areas involved in these different aspects.     

The essential moral self

It has often been suggested that the mind is central to personal identity. But do all parts of the mind contribute equally? Across five experiments, we demonstrate that moral traits—more than any other mental faculty—are considered the most essential part of identity, the self, and the soul. Memory, especially emotional and autobiographical memory, is also fairly important. Lower-level cognition and perception have the most tenuous connection to identity, rivaling that of purely physical traits. These findings suggest that folk notions of personal identity are largely informed by the mental faculties affecting social relationships, with a particularly keen focus on moral traits.     

从数量表征到数表征：具身认知视角下的人类数能力获得

数能力是数学认知的基本成分。与动物所具有的基本数能力不同,人类不仅具备数量表征能力,更重要的是还拥有对数概念进行表征的数表征能力。虽然具身认知与离身认知都对数概念的表征问题进行了解释,但二者却存在明显理论分歧。具身认知观点主要从具身数量表征和数能力发展的具身认知机制两方面为人类独特数能力的获得提供了理论支撑及实证证据。这启示人们需要重视具身学习在数能力形成实践中的关键作用,重视具身数量表征在数学教学中的作用,仍需进一步揭示其内在的心理和神经基础。     

Frequency of finger looking during finger counting is related to children's working memory capacities

Finger counting can be useful in solving arithmetic problems, noticeably because it reduces the working memory demand of mental calculations. However, proprioceptive information might not be sufficient to keep track of the number of fingers raised during problem solving, and visual input may play an important role in this process. The present study was designed to address this question and shows that 8-year-old children look at their fingers in 60% of the trials during finger counting when solving additive problems. Moreover, our results reveal that the frequency of finger looking is negatively correlated with working memory capacities and is higher for more difficult problems. These findings suggest that finger looking is recruited in managing the cognitive demand of the arithmetic task, probably by providing additional external cues to monitor the number of steps that have to be incremented during finger counting.     

Shifts of spatial attention cued by irrelevant numbers: Electrophysiological evidence from a target discrimination task

Fischer et al. demonstrated that a centrally presented number can shift attention to the left/right when its magnitude is small/large. Two electrophysiological studies described these attentional effects as event-related potentials (ERPs) at centro-parietal sites. Since both studies used target detection tasks, it remains currently unknown whether similar results would be obtained with a discrimination task. We used ERPs to test whether digit cues also induce attention shifts when participants perform a feature-discrimination task on targets. ERPs were recorded whereas subjects discriminated the colour of lateral targets that were preceded by a central non-predictive digit. Analysis of cue-locked controlateral vs. ipsilateral ERP activity showed the emergence of early preparatory attention-directing components in parietal and frontal regions. Moreover, target-locked P1 components at occipito-parietal sites were significantly modulated by digit magnitude-target side congruency. These results demonstrate that irrelevant digit cues also bias sensory processing when embedded in a feature-discrimination task.