What the eyes already ‘know’: using eye movement measurement to tap into children's implicit numerical magnitude representations

To date, a number of studies have demonstrated the existence of mismatches between children's implicit and explicit knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty‐six children from grades one to three (i.e. 6–9 years) were presented with two parallel versions of a number line estimation task of which one was restricted to behavioural measures, whereas the other included the recording of eye movement data. The results of the eye movement experiment indicate a quantitative increase as well as a qualitative change in children's implicit knowledge about numerical magnitudes in this age group that precedes the overt, that is, behavioural, demonstration of explicit numerical knowledge. The finding that children's eye movements reveal substantially more about the presence of implicit precursors of later explicit knowledge in the numerical domain than classical approaches suggests further exploration of eye movement measurement as a potential early assessment tool of individual achievement levels in numerical processing. Copyright © 2009 John Wiley & Sons, Ltd.     

Uniforms affect the accuracy of children's eyewitness identification decisions

A substantial proportion of line‐up identifications involving child eyewitnesses in the UK are conducted by police officers wearing uniform. This study examined the possibility that wearing a uniform constitutes an authority cue that adversely affects a child's ability to make accurate eyewitness identifications. Sixty participants aged 9–10 years old witnessed a staged crime and were later asked to identify a ‘burglar’ from a simultaneous line‐up using a 2 (uniform: present vs. absent) × 2 (target: present vs. absent) design. Children in the uniform present conditions made significantly more choices than children in the uniform absent conditions. More importantly, in the presence of a uniform, children made significantly more false identifications in target‐absent line‐ups. Analysis of supplementary, identification‐related variables (identification time and confidence, state anxiety) suggested that (1) the children experienced uncertainty if the target was absent from the line‐up, but (2) this uncertainty was not expressed when the line‐up administrator wore a uniform, leading to an increase in false identifications. Implications for line‐up administration procedures for children are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

正负数混合呈现对负数SNARC效应的影响

采用数字大小判断任务,探讨正负数混合呈现对负数SNARC效应的影响。结果发现,负数单独呈现条件下,负数出现反转的SNARC效应;负数和无加号正数混合呈现,且只对负数作反应条件下,负数有反转SNARC效应;负数和有加号正数混合呈现,且只对负数作反应条件下,负数出现反转SNARC效应;负数和无加号正数混合呈现,并对正负数分别作反应的条件下,负数有反转SNARC效应出现,而正数出现SNARC效应。说明负数空间表征受其绝对值大小的影响,绝对值较小的负数(-1、-2)表征在心理数字线的左侧,绝对值较大的负数(-8、-9)表征在数字线的右侧,且不能延伸至心理数字线左侧。     

How to learn the natural numbers: inductive inference and the acquisition of number concepts

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51-B60.] argue that such an inductive inference is consistent with a representational system that clearly does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles.     

Synesthesia and number cognition in children

Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific color (photisms), has been shown to be consistent, involuntary, and linked with number concept in adults, yet there have been no comparable investigations with children. We present a systematic study of grapheme-color synesthesia in children aged between 7 and 15 years. Here we show that such children (but not children with phoneme-color synesthesia) experience involuntary difficulties in numerical tasks when digits are presented in colors incongruent with their photisms. Synesthesia in children may thus have important consequences for certain aspects of numerical cognition.     

Parallel non-verbal enumeration is constrained by a set-based limit

Adults can represent approximate numbers of items independently of language. This approximate number system can discriminate and compare entities as varied as dots, sounds, or actions. But can multiple different types of entities be enumerated in parallel and stored as independent numerosities? Subjects who were prevented from verbally counting watched an experimenter hide sequences of objects in two locations. The number of object types, which contrasted in category membership, color, shape, and texture, varied from 1 to 5, and object types were completely temporally intermixed. Subjects were then asked how many objects of each type were in each location. In three experiments, subjects successfully enumerated the objects of each type in each location when 1-3 types were presented, but failed with 4 or 5 types, regardless of the total number of objects seen. Thus, adults can perform simultaneous enumeration of multiple sets that unfold in temporally intermixed fashion, but are limited to 3 such sets at a time. Furthermore, they perform these parallel enumerations in the absence of training or instruction, and can do so for sets of objects that are hidden in distinct locations. The convergence of this 3-set capacity limit with the 3-item capacity limit widely observed in studies of working memory suggests that each enumeration requires a single slot in memory, and that storage in memory is required before enumeration can occur.     

Number Created by the Interaction Between Consciousness and Memory: A Mathematical Basis for Preafference

I would like to deal with a process that numbers are generated by the interaction between consciousness and memory, associated with time with a finite width. It is pointed out that this process can be related with the emergence of preafference. It is concluded that only humans can create numbers, whereas animals simply produce ‘random’ sequences of symbols because they lack intentionality to search for an appropriate internal observation window that makes intention and memory compatible.

Do fish count? Spontaneous discrimination of quantity in female mosquitofish

The spontaneous tendency to join the largest social group was used to investigate quantity discrimination in fish. Fish discriminated between shoals that differed by one element when the paired numbers were 1vs2, 2vs3 and 3vs4, but not when 4vs5 or larger. Using large numerosities (>4), the ability to discriminate between two numbers improved as the numerical distance between them increased and a significant discrimination was found only with ratios of 1:2 or smaller (4vs8, 8vs16 and 4vs10). Experiments to control for non-numerical variables evidenced the role played by the total area of stimuli with both large and small numerosities; the total quantity of movement of the fish within a shoal appeared also important but only when large numerosities were involved. Even though the pattern of discrimination exhibited by female mosquitofish is not fully consistent with any of the existing models of quantity representation, our results seem to suggest two distinct mechanisms in fish, one used to compare small numbers of objects and one used when larger numerosities are involved.     

Food and token quantity discrimination in capuchin monkeys (<Emphasis Type="Italic">Cebus apella</Emphasis>)

Quantity discrimination is adaptive in a variety of ecological contexts and different taxa discriminate stimuli differing in numerousness, both in the wild and in laboratory settings. Quantity discrimination between object arrays has been suggested to be more demanding than between food arrays but, to our knowledge, the same paradigm has never been used to directly compare them. We investigated to what extent capuchin monkeys’ relative numerousness judgments (RNJs) with food and token are alike. Tokens are inherently non-valuable objects that acquire an associative value upon exchange with the experimenter. Our aims were (1) to assess capuchins’ RNJs with food (Experiment 1) and with tokens (Experiment 2) by presenting all the possible pair-wise choices between one to five items, and (2) to evaluate on which of the two proposed non-verbal mechanisms underlying quantity discrimination (analogue magnitude and object file system) capuchins relied upon. In both conditions capuchins reliably selected the larger amount of items, although their performance was higher with food than with tokens. The influence of the ratio between arrays on performance indicates that capuchins relied on the same system for numerical representation, namely analogue magnitude, regardless of the type of stimuli (food or tokens) and across both the small and large number ranges.     

情境对序数的空间表征之影响

通过设置垂直维度上不同的情境,本研究采用“奇偶判断任务”探讨了情境对序数空间表征的影响。结果发现,只有序数的情况下,被试对小数的上键反应或下键反应、对大数的上键反应或下键反应都没有显著差异;在楼层情境下,被试对小数的下键反应更快,对大数的上键反应更快;在家谱情境下,被试对小数的上键反应更快,对大数的下键反应更快。以上结果表明,垂直维度上序数的空间表征受到情境的影响,这说明在垂直维度上数字的空间表征具有动态性,且受到具体和情境的调节。