Use of number by crows: investigation by matching and oddity learning

Hooded crows were trained in two-alternative simultaneous matching and oddity tasks with stimulus sets of three different categories: color (black and white), shape (Arabic Numerals 1 and 2, which were used as visual shapes only), and number of elements (arrays of one and two items). These three sets were used for training successively and repeatedly; the stimulus set was changed to the next one after the criterion (80% correct or better over 30 consecutive trials) was reached with the previous one. Training was continued until the criterion could be reached within the first 30 to 50 trials for each of the three training sets. During partial transfer tests, familiar stimuli (numerals and arrays in the range from 1 to 2) were paired with novel ones (numerals and arrays in the range from 3 to 4). At the final stage of testing only novel stimuli were presented (numerals and arrays in the range from 5 to 8). Four of 6 birds were able to transfer in these tests, and their performance was significantly above chance. Moreover, performance of the birds on the array stimuli did not differ from their performance on the color or shape stimuli. They were capable of recognizing the number of elements in arrays and comparing the stimuli by this attribute. It was concluded that crows were able to apply the matching (or oddity) concept to stimuli of numerical category.     

Ambiguous probabilities: when does p=0.3 reflect a possibility,and when does it express a doubt?

Verbal phrases denoting uncertainty are usually held to be more vague than numerical probability statements. They are, however, directionally more precise, in the sense that they are either positive, suggesting the occurrence of a target outcome, or negative, drawing attention to its non‐occurrence. A numerical probability will, in contrast, sometimes be perceived as positive and sometimes as negative. When asked to complete sentences such as ‘The operation has a 30% chance of success, because’ some people will give reasons for success (‘the doctors are expert surgeons’), whereas others will give reasons for failure (‘it is a difficult operation’). It is shown in two experiments that positive reasons are given more often than negative ones, even for p values below 0.5, especially when the probability is higher than expected, and the target outcome is non‐normal, undesirable, and phrased as a negation. We conclude that the directionality of numerical probabilities (as opposed to verbal phrases) is context‐dependent, but biased towards a positive interpretation. Copyright © 2000 John Wiley & Sons, Ltd.     

人类数能力的演化基础——数能力比较研究的启示

人类的数能力可以发展到很高的抽象水平,但大量研究表明,人类婴儿和非人灵长类也具有基本的数表征和数推理能力。文章从表征内容和表征形式两个方面系统地比较了人类婴儿和非人灵长类的数能力,并对比了成人和非人灵长类数表征的生理基础。人类和非人灵长类在这三方面存在的相似性揭示了他们可能享有相同的数表征系统。在今后的研究中,进一步探讨这两者相似的数表征核心系统,可以加深我们对人类数能力起源和本质的理解     

儿童数字估计中的心理长度

从儿童对数字属性的认识角度探讨一年级儿童在不同数字范围中采用不同表征形式的根本原因。两个实验均采用数字线估计任务,实验一测量一年级儿童在15cm数字线长度下0～100与0～1000两种范围上的数字估计;实验二测量一年级儿童对0～1000范围10cm和20cm数字线长度的估计。结果显示,无论在不同的数字范围还是在不同的数字线长度下,儿童对低端数字的估计均存在心理长度,即儿童倾向于将低端数字与固定的线段长度对应起来,且这种对应关系不随数字范围与数字线长度的变化而变化。心理长度的存在是儿童在不同数字范围和不同数字线长度中采用不同数字表征形式的根本原因,也是儿童对数概念的认识发展到等距水平时出现的一种独特特点。     

前运动皮质与数字加工:脑功能成像研究的元分析研究

许多应用PET与fMRI技术的脑功能成像研究发现,数字加工任务会显著引起前运动皮质的激活。习惯上认为,这一结果可能与任务执行过程中的动作反应,如手指按键、默读或眼动等有关。近年来的研究则表明,这一区域不仅具有动作功能,同时也具有其它非动作的认知功能。在本研究中,对17篇关于数字加工的脑功能成像研究进行了元分析,以考察前运动皮质在数字加工中的作用。研究结果发现,运动前区的背外侧(PMd)与腹外侧(PMv)在大多数数字加工任务中有显著激活,而运动辅助区(SMA)的激活则相对较少。数字比较、加法与减法任务在PMd区域有更多的激活,而乘法任务则在PMv区域有更多激活。数字自身特征对PMd、PMv与SMA喙部区域的激活有显著的调节作用。这一结果表明,前运动皮质在数字加工过程中可能扮演着比动作反应更为重要的角色。     

数字加工的脑功能成像研究进展及其皮层定位

数字加工是人类最重要的认知功能之一。当前的脑功能成像研究有助于对数字加工与皮层之间的联系进行更精确的定位。基于对上世纪80年代来有关数字加工脑功能成像研究的主要成果的回顾,尤其是一些重要区域,如双侧顶叶与前额叶等在数字加工中的地位与作用,以及不同脑区之间的关系进行了探讨,并对一个广泛运用的数字加工神经机制模型进行了简要评述。在此基础上,对数字加工的皮层定位问题进行了简要的总结。     

数学困难儿童的数学估计能力

对数学困难儿童(简称数困)的数学估计进行探讨有助于理解数困的成因和寻找适当的干预措施。本文在简要回顾数困和估计的概念基础上, 重点对近年来国内外关于数困儿童数学估计(主要是估算和估数)的表现及影响因素、神经基础和相关的干预研究进行了回顾和梳理, 并强调未来对数困儿童的数学估计研究应注重从选取被试、扩展研究范围和加强干预方案设计等方面开展探讨。     

手指的感知、运动以及数量表征对数字认知的促进作用

手指是儿童在习得数字符号之前最常使用的表征数量的工具,大量研究都表明手指在数字认知中具有促进作用。但是,目前仍不清楚手指在数字认知中的作用机制。综述从手指感知、手指运动以及手指数量表征三个方面总结了手指在数字认知中所起的作用。手指感知可能通过影响儿童的数量表征能力间接地影响其它数学能力;与表征量有关的手指运动可能促进了数量大小的加工。关于手指数量表征在数字认知中的作用存在两种有争议的观点：一种认为手指数量表征促进了儿童由非符号数量表征向符号数量表征的转化;另一种认为手指数量表征可能是一种数量语义表征方式。未来应该在发展、作用机制、性别差异等方向继续开展研究,进一步探讨手指在数字认知中所起的作用。     

On representational content and format in core numerical cognition

Carey has argued that there is a system of core numerical cognition – the analog magnitude (AM) system – in which (approximate) cardinal numbers are explicitly represented in iconic format. While the existence of this system is beyond doubt, this paper aims to show that its representations cannot have the combination of features attributed to them by Carey. According to the argument from abstractness, the representation of the (approximate) cardinal number of a collection of individuals as such requires the representation of individuals as such, and this in turn requires non-iconic format, from which it is concluded that the explicit representation of the (approximate) cardinal number of some individuals requires non-iconic representational format. In support of the first premise, an account is given of what approximate cardinal numbers might be (namely, quantifiers), and in support of the second, a direct argument is articulated and defended. Finally, in response to an objection, a second argument (from parts) for the central thesis is provided. While the discussion is couched in the terms of Carey’s work, the considerations it adduces are perfectly general, and the conclusion should therefore be taken into consideration by all those aiming to characterize the AM system.