类别表征与策略的脑科学研究及对思维教学的启示

脑科学研究表明,分类中对物体的知觉表征激活颞下叶皮层和颞中区等区域;语义表征激活前额皮层等。语义加工和知觉表征相互作用的脑机制表现为额区与视觉区域间信息的传递、提取。分类策略主要有规则策略和相似性策略两种。规则策略激活额区等广泛区域;相似性策略与视觉区域相关,包含着对个别样例的记忆过程。基于以上研究结果,本文从学习材料的表征和对材料进行表征时的策略两个方面为思维教学提出了一些建议。     

3~6岁儿童数感发展的研究

从上海两所中等水平幼儿园以年龄班分层随机抽取180名3~6岁儿童为被试,采用个别测查法考察其数感发展状况。结果表明:(1)3~6岁儿童的数感发展存在显著年龄差异,无性别差异;(2)顺数、实物比较和数符号辨认是其表现较好的三项技能,而倒数和序数却表现较差;(3)数感各组成部分发展不同步,倒数,序数和数符号在中班到大班期间发展迅速,而顺数,基数概念,加减理解却在小班到中班期间发展较快。     

视知觉学习的认知与神经机制研究

知觉学习是指由于训练或经验而引起的长期稳定的知觉变化,是一种内隐性的学习。近20年来,视知觉学习的大量研究结果提示大脑皮层的各个区域,甚至包括初级感觉皮层,在成熟之后仍然具有一定的可塑性。该文根据近年来的研究进展,对视知觉学习在大脑的什么地方,什么时候,以何种方式发生等热点问题进行了探讨。研究提示,视知觉学习涉及了包括初级视皮层在内的多个大脑皮层,并且存在一种自上而下的调控机制;视知觉学习可以在不同的时间尺度上发生,快速学习之后将伴随着慢速学习;通过视知觉学习,人们对于复杂物体的表征将从高级皮层区域移向低级皮层区域,任务执行也将趋于自动化     

McGurk效应的影响因素与神经基础

McGurk效应(麦格克效应)是典型的视听整合现象, 该效应受到刺激的物理特征、注意分配、个体视听信息依赖程度、视听整合能力、语言文化差异的影响。引发McGurk效应的关键视觉信息主要来自说话者的嘴部区域。产生McGurk效应的认知过程包含早期的视听整合(与颞上皮层有关)以及晚期的视听不一致冲突(与额下皮层有关)。未来研究应关注面孔社会信息对McGurk效应的影响, McGurk效应中单通道信息加工与视听整合的关系, 结合计算模型探讨其认知神经机制等。     

人类路径整合的心理机制与神经基础

路径整合是指巡航者对与自身运动有关的信息进行整合来完成巡航任务的过程。这些与自身运动有关的信息可以是内源性的,如前庭感觉、本体感觉、动作指令的信息;也可以是外源性的,如视觉流。路径整合在许多物种中存在。人类路径整合的行为实验表明,以自我为参照系的空间表征和以环境为参照系的空间表征都有可能支持路径整合。神经科学的研究则表明,海马、内嗅皮层等内侧颞叶区域和以楔前叶等顶叶区域都与人类路径整合密切相关。     

4～5岁儿童对书面数符号的表征和理解能力的发展

本研究对61名中班儿童的书面数符号表征和理解能力进行了跟踪调查。一年中三次个别面试的结果表明,约40％的4岁儿童已能运用1—10的书面数符号表征数量。至中班末期,大多数5岁儿童能够较熟练地运用至少1一17的书面数符号来表征数量,尽管其中有人在两位数的表征和数字的正确写法上有困难。儿童的书面数符号表征与他们的基数概念发展水平密切相关。大学附属幼儿园4—5岁儿童的书面数符号表征能力好于为工人家庭服务的幼儿园儿童的能力。     

计数单位的空间联合编码效应

采用Dehaene等人的研究范式,以计数单位中的“千”为基线,要求被试快速作大于“千”还是小于“千”的分类判断,考察计数单位在心理数字线上的空间表征方式.结果表明:(1)计数单位和数字有着相同的加工机制,小计数单位表征在心理数字线的左侧,大计数单位表征在心理数字线的右侧,存在显著的SNARC效应. (2) SNARC效应不仅仅出现在数量的空间表征上,同样能够出现在顺序信息的空间表征上.     

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。     

LPN新／旧效应与汉字颜色来源提取的关联

已有研究表明,前额皮层在诸多种类来源的提取任务中起着重要作用,但不同记忆内容的来源提取研究存在不同的结果。为探索与汉字颜色来源提取相关联的头皮时空分布特征,本研究运用与Cycowicz等人(2001,2003,2005)相似的研究范式,以汉语名词作为实验材料,研究了颜色来源提取新/旧效应的头皮时空分布特征。结果显示,汉语名词在650~950ms存在与Cycowicz等人图形研究中相似的颜色来源提取的LPN新/旧效应。该结果表明,汉字的颜色来源提取与非言语材料一样,也与LPN新/旧效应相关联。     

心算的加工机制：来自认知神经科学的研究

心算加工分编码（表征）、运算（或提取）和反应三个阶段,这三个阶段相互影响。不同输入形式的数字表征在顶叶的不同区域完成。算术知识提取主要与左脑顶内沟有关,但当心算变得更复杂时而需要具体运算时,左脑额叶下部出现明显激活。所有与心算有关的脑区涉及大脑前额皮层和颞顶枕联合皮层的综合作用,并总体表现为左脑优势,但估算、珠心算以及某些具有特殊心算能力的人的心算还依赖视空间表征,这与右脑额顶区和楔前叶的活动有关     

Are the Natural Numbers Fundamentally Ordinals?

There are two ways of thinking about the natural numbers: as ordinal numbers or as cardinal numbers. It is, moreover, well‐known that the cardinal numbers can be defined in terms of the ordinal numbers. Some philosophies of mathematics have taken this as a reason to hold the ordinal numbers as (metaphysically) fundamental. By discussing structuralism and neo‐logicism we argue that one can empirically distinguish between accounts that endorse this fundamentality claim and those that do not. In particular, we argue that if the ordinal numbers are metaphysically fundamental then it follows that one cannot acquire cardinal number concepts without appeal to ordinal notions. On the other hand, without this fundamentality thesis that would be possible. This allows for an empirical test to see which account best describes our actual mathematical practices. We then, finally, discuss some empirical data that suggests that we can acquire cardinal number concepts without using ordinal notions. However, there are some important gaps left open by this data that we point to as areas for future empirical research.     

Inducing ordinal and cardinal representations of the first five natural numbers

The prediction that the ordinal property of natural number symbols (using these symbols to represent the terms in an ordered progression) is more easily learned than the cardinal property of natural number symbols (using these symbols to represent the manyness of collections) was examined in this experiment. Preschoolers who evidenced no proficiency with either the ordinal or cardinal properties of natural number symbols were trained to acquire these properties via simple feedback. Both properties proved to be trainable. The most important findings were that the ordinal property was much easier to train than the cardinal property, ordinal training effects were more durable across a 1-week interval than cardinal training effects, and ordinal training appeared to transfer better than cardinal training.     

Numerical ordering ability mediates the relation between number-sense and arithmetic competence

What predicts human mathematical competence? While detailed models of number representation in the brain have been developed, it remains to be seen exactly how basic number representations link to higher math abilities. We propose that representation of ordinal associations between numerical symbols is one important factor that underpins this link. We show that individual variability in symbolic number-ordering ability strongly predicts performance on complex mental-arithmetic tasks even when controlling for several competing factors, including approximate number acuity. Crucially, symbolic number-ordering ability fully mediates the previously reported relation between approximate number acuity and more complex mathematical skills, suggesting that symbolic number-ordering may be a stepping stone from approximate number representation to mathematical competence. These results are important for understanding how evolution has interacted with culture to generate complex representations of abstract numerical relationships. Moreover, the finding that symbolic number-ordering ability links approximate number acuity and complex math skills carries implications for designing math-education curricula and identifying reliable markers of math performance during schooling.     

One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers

We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also measured by asking the children to assess the correctness of a cartoon character's counting in both contexts. In general, the children performed cardinal tasks significantly better than ordinal ones. Tasks requiring the production of the number for a given quantity or position were solved more accurately than those testing the ability to select a set of n objects or the object in the nth position. Different profiles were obtained for the principles; those principles shared by the two contexts were mastered earlier in the cardinal context. Regarding order (ir)relevance, older children adhered to rigid ways of counting, producing better results in the ordinal context and incorrect rejections in the cardinal trials. Altogether, our data indicate that the acquisitions of cardinal and ordinal meanings of numbers are related, and cardinality precedes the development of ordinality.     

Evaluation of dominance‐based ordinal multiple regression for variables with few categories

Dominance‐based ordinal multiple regression (DOR) is designed to answer ordinal questions about relationships among ordinal variables. Only one parameter per predictor is estimated, and the number of parameters is constant for any number of outcome levels. The majority of existing simulation evaluations of DOR use predictors that are continuous or ordinal with many categories, so the performance of the method is not well understood for ordinal variables with few categories. This research evaluates DOR in simulations using three‐category ordinal variables for the outcome and predictors, with a comparison to the cumulative logits proportional odds model (POC). Although ordinary least squares (OLS) regression is inapplicable for theoretical reasons, it was also included in the simulations because of its popularity in the social sciences. Most simulation outcomes indicated that DOR performs well for variables with few categories, and is preferable to the POC for smaller samples and when the proportional odds assumption is violated. Nevertheless, confidence interval coverage for DOR was not flawless and possibilities for improvement are suggested.     

KNOWLEDGE OF THE ORDINAL POSITION OF LIST ITEMS IN RHESUS MONKEYS

Abstract —What is learned during mastery of a serial task: associations between adjacent and remote items, associations between an item and its ordinal position, or both? A dear answer to this question is lacking in the literature on human serial memory because it is difficult to control for a "naive" subject's linguistic competence and extensive experience with serial tasks. In this article, we present evidence that rhesus monkeys encode the ordinal positions of items of an arbitrary list when there is no requirement to do so. First, monkeys learned four nonverbal lists (1–4). each containing four novel items (photographs of natural objects). The monkeys then learned four 4-item lists that were derived exclusively and exhaustively from Lists 1 through 4, one item from each list. On two derived lists, each item s original ordinal position was maintained. Those lists were acquired with virtually no errors. The two remaining derived lists, on which the original ordinal position of each item was changed, were as difficult to learn as novel lists. The immediate acquisition of lists on which ordinal position was maintained shows that knowledge of ordinal position can develop without the benefit of language, extensive list-learning experience, or explicit instruction to encode ordinal information.     

The mental representation of ordinal sequences is spatially organized

In the domain of numbers the existence of spatial components in the representation of numerical magnitude has been convincingly demonstrated by an association between number magnitude and response preference with faster left- than right-hand responses for small numbers and faster right- than left-hand responses for large numbers (Dehaene, S., Bossini, S., & Giraux, P. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396). Because numbers convey not only real or integer meaning but also ordinal meaning, the question of whether non-numerical ordinal information is spatially coded naturally follows. While previous research failed to show an association between ordinal position and spatial response preference, we present two experiments involving months (Experiment 1) and letters (Experiment 2) in which spatial coding is demonstrated. Furthermore, the response-side effect was obtained with two different stimulus-response mappings. The association occurred both when ordinal information was relevant and when it was irrelevant to the task, showing that the spatial component of the ordinal representation can be automatically activated.     

The development of ordinal numerical competence in young children

Two experiments assessed ordinal numerical knowledge in 2- and 3-year-old children and investigated the relationship between ordinal and verbal numerical knowledge. Children were trained on a 1 vs 2 comparison and then tested with novel numerosities. Stimuli consisted of two trays, each containing a different number of boxes. In Experiment 1, box size was held constant. In Experiment 2, box size was varied such that cumulative surface area was unrelated to number. Results show children as young as 2 years of age make purely numerical discriminations and represent ordinal relations between numerosities as large as 6. Children who lacked any verbal numerical knowledge could not make ordinal judgments. However, once children possessed minimal verbal numerical competence, further knowledge was entirely unrelated to ordinal competence. Number may become a salient dimension as children begin to learn to count. An analog magnitude representation of number may underlie success on the ordinal task.     

What is the relationship between synaesthesia and visuo-spatial number forms?

This study compares the tendency for numerals to elicit spontaneous perceptions of colour or taste (synaesthesia) with the tendency to visualise numbers as occupying particular visuo-spatial configurations (number forms). The prevalence of number forms was found to be significantly higher in synaesthetes experiencing colour compared both to synaesthetes experiencing taste and to control participants lacking any synaesthetic experience. This suggests that the presence of synaesthetic colour sensations enhances the tendency to explicitly represent numbers in a visuo-spatial format although the two symptoms may nevertheless be logically independent (i.e. it is possible to have number forms without colour, and coloured numbers without forms). Number forms are equally common in men and women, unlike previous reports of synaesthesia that have suggested a strong female bias. Individuals who possess a number form are also likely to possess visuo-spatial forms for other ordinal sequences (e.g. days, months, letters) which suggests that it is the ordinal nature of numbers rather than numerical quantity that gives rise to this particular mode of representation. Finally, we also describe some consequences of number forms for performance in a number comparison task.     

Fitting multilevel models with ordinal outcomes: performance of alternative specifications and methods of estimation

Previous research has compared methods of estimation for fitting multilevel models to binary data, but there are reasons to believe that the results will not always generalize to the ordinal case. This article thus evaluates (a) whether and when fitting multilevel linear models to ordinal outcome data is justified and (b) which estimator to employ when instead fitting multilevel cumulative logit models to ordinal data, maximum likelihood (ML), or penalized quasi-likelihood (PQL). ML and PQL are compared across variations in sample size, magnitude of variance components, number of outcome categories, and distribution shape. Fitting a multilevel linear model to ordinal outcomes is shown to be inferior in virtually all circumstances. PQL performance improves markedly with the number of ordinal categories, regardless of distribution shape. In contrast to binary data, PQL often performs as well as ML when used with ordinal data. Further, the performance of PQL is typically superior to ML when the data include a small to moderate number of clusters (i.e., ≤ 50 clusters).