Object knowledge and the emergence of language

Infants' spontaneous play with objects was examined for evidence of developments in object knowledge in relation to the emergence of words and the single-word period in language development. Subjects were 7 girls and 7 boys, from different ethnic and economic backgrounds, who were studied longitudinally from 9 months to 26 months of age. Two types of displacements of objects in relation to one another were identified in the children's play: separations and constructions. The development of constructions was associated with the emergence of words, and constructions increased with age while separations decreased. The development of specific constructions, which account for knowledge of the particular properties of objects, was more strongly associated with a vocabulary spurt at the end of the single-word period than with chronological age. Despite the wide variation in the infants' ages when developments in language and play were reached, relations between achievements in the two domains were consistent among them, as confirmed with the Friedman test, p<.001. The results are discussed in terms of the cognitive developments required for play with objects and saying words.     

小学生近似数量系统敏锐度的发展趋势及其与数学能力的关系：抑制控制的中介作用

采用测量法和问卷法考察了172名小学生近似数量系统敏锐度的发展,以及抑制控制在近似数量系统敏锐度与数学能力关系中的中介效应。结果表明：(1)随着年龄增长,小学生的近似数量系统敏锐度逐渐提高;(2)近似数量系统敏锐度(负相关序列中的韦伯系数)和抑制控制均能显著正向预测小学生的数学能力;(3)抑制控制在小学生近似数量系统敏锐度(负相关序列中的韦伯系数)与数学能力的关系中起部分中介作用。     

学校氛围对学生数学成绩影响的跨文化比较:基于多水平分析的结果

学校氛围是学校中被成员所体验并对其行为产生影响的、相对持久而稳定的学校环境特征。它以成员的共同行为感知为基础,对学校和学生的发展具有重要作用。以PISA2003测试的数据为基础,采用多水平线性模型,考察了中国香港、日本、美国和土耳其的15岁学生及其所在学校的校长知觉的学校氛围对学生数学成绩的影响。结果显示:(1)学生知觉的师生关系、数学课堂秩序,校长知觉的学生士气、学校消极行为对数学成绩的显著预测作用具有较高的跨文化一致性;(2)数学课堂上的教师支持、教师负面状态、数学教师间的共识能显著预测部分国家/地区的学生数学成绩;(3)学生知觉的对学校的看法、校长知觉的教师士气对四个国家/地区的学生数学成绩均无显著预测作用。     

The associated nontargets effect: Evidence of nontarget processing at and beyond the level of letter recognition

In four visual search tasks participants were asked to make a target response if either of two targets was present and to make a nontarget response if neither target was present. Some target-absent displays included only nontarget stimuli or features that never occurred in the same displays as targets, whereas other target-absent displays included nontarget stimuli or features that did sometimes occur with targets. Nontarget responses were reliably faster in the former case than in the latter. This “associated nontargets effect” indicates that nontargets are not simply classified as nontargets but in addition are discriminated from one another. Current visual search models may underestimate the degree to which nontargets are processed during search.     

A functional analytic approach to computer-interactive mathematics

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on particular formula-to-formula and formula-to-graph relations as these formulas pertain to reflections and vertical and horizontal shifts. In training A-B, standard formulas served as samples and factored formulas served as comparisons. In training B-C, factored formulas served as samples and graphs served as comparisons. Subsequently, the program assessed for mutually entailed B-A and C-B relations as well as combinatorially entailed C-A and A-C relations. After all participants demonstrated mutual entailment and combinatorial entailment, we employed a test of novel relations to assess 40 different and complex variations of the original training formulas and their respective graphs. Six of 10 participants who completed training demonstrated perfect or near-perfect performance in identifying novel formula-to-graph relations. Three of the 4 participants who made more than three incorrect responses during the assessment of novel relations showed some commonality among their error patterns. Derived transfer of stimulus control using mathematical relations is discussed.     

数学证明:数学真理的来源?

对于一个数学实在论者来说,一个特别急迫的任务是回答数学证明是如何建立起关于数学对象的真理性问题。本文批判性考察由Resnik所提出的认知解答,指出了其中不成立的前提。并且在此基础上提出我们自己的解答,它是基于由Oliver．G所提倡的方面(aspects)概念而来的社会——论辩方案。     

How pigeons discriminate the relative frequency of events.

This study examined how pigeons discriminate the relative frequencies of events when the events occur serially. In a discrete-trials procedure, 6 pigeons were shown one light nf times and then another nl times. Next, they received food for choosing the light that had occurred the least number of times during the sample. At issue were (a) how the discrimination was related to two variables, the difference between the frequencies of the two lights, D = nf - nl, and the total number of lights in the sample, T = nf + nl; and (b) whether a simple mathematical model of the discrimination process could account for the data. In contrast with models that assume that pigeons count the stimulus lights, engage in mental arithmetic on numerons, or remember the number of stimuli, the present model assumed only that the influence of a sample stimulus on choice increases linearly when the stimulus is presented, but decays exponentially when the stimulus is absent. The results showed that, overall, the pigeons discriminated the relative frequencies well. Their accuracy always increased with the absolute value of the difference D and, for D > 0, it decreased with T. Performance also showed clear recency, primacy, and contextual effects. The model accounted well for the major trends in the data.     

Towards a topological philosophy

This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance.     

道德概念垂直空间隐喻理解中的映射:双向性及不平衡性

通过4个实验考察道德概念垂直空间隐喻理解中的映射机制和特征。实验1采用空间Stroop范式,发现被试判断完道德词后,对判断随后呈现在屏幕上方或下方字母的反应时的差异不显著,没有发现词汇类型对空间位置的影响。实验2采用有意识迫选法,要求被试出声读出屏幕中央的道德词后,对屏幕上方或下方的希腊语非词进行二择一迫选,发现被试读出道德词后倾向于选择屏幕上方的非词,读出不道德词后倾向于选择屏幕下方的非词。实验3仍采用Stroop范式,发现被试做出空间"上"的判断后,对随后道德词的词义判断反应时显著快于不道德词,做出空间"下"的判断后,对不道德词的反应时显著快于道德词。实验4探讨空间位置是否会对判断人物的道德性产生影响,结果发现被试倾向于认为屏幕上方的人物是道德的,而屏幕下方的人物是不道德的。4个实验的结果表明,在道德概念垂直空间隐喻的理解中,映射的方式是灵活的、双向的,既可以由始源域向目标域映射,也可以由目标域向始源域映射,但两个方向上的映射力量是不平衡的。