Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities

Previous research has found a relationship between individual differences in children’s precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2 years. In addition, at the final time point, we tested children’s informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children’s numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction.     

Temperature-dependent crack surface tension

The fracture surface energy is calculated for a one-dimensional, exactly solvable model of a crack. The temperature dependence of the crack surface tension is determined on the basis of a self-consistent Einstein approach. It is found that lattice vibrations result in a strong reduction in the crack surface tension.     

幼儿在集合比较中运用数数的实验研究

本研究中运用了两个实验探讨数数干预和测查条件对儿童在集合比较中运用数数的影响。干预对3岁儿童(M=3：9)没有影响。在平均年龄为4岁4个月时．干预组儿童比控制组儿童更倾向于用数数比较集合．自然组儿童也比传统组更倾向于用数数。许多4岁儿童在无干预时不用数数可能是因为,1)不知数数比视觉性比较更有效,或2)他们在集合比较中的数数极易受测查情景因素的影响。儿童在集合比较中的数数运用与他们的数数水平密切关联。     

Belief Reasoning and Emotion Understanding in Balanced Bilingual and Language-Dominant Mexican American Young Children

Belief reasoning and emotion understanding were measured among 102 Mexican American bilingual children ranging from 4 to 7 years old. All children were tested in English and Spanish after ensuring minimum comprehension in each language. Belief reasoning was assessed using 2 false and 1 true belief tasks. Emotion understanding was measured using subtests from the Test for Emotion Comprehension. The influence of family background variables of yearly income, parental education level, and number of siblings on combined Spanish and English vocabulary, belief reasoning, and emotion understanding was assessed by regression analyses. Age and emotion understanding predicted belief reasoning. Vocabulary and belief reasoning predicted emotion understanding. When the sample was divided into language-dominant and balanced bilingual groups on the basis of language proficiency difference scores, there were no significant differences on belief reasoning or emotion understanding. Language groups were demographically similar with regard to child age, parental educational level, and family income. Results suggest Mexican American language-dominant and balanced bilinguals develop belief reasoning and emotion understanding similarly.     

符号数量和非符号数量的空间表征:5岁儿童的SNARC效应和距离效应

对物理刺激的数量信息表征是符号数字表征的前提和基础,据此假设在儿童的SNARC效应发生的时序问题上,非符号数量(如面积)的空间表征早于符号数量(如阿拉伯数字)的空间表征。本研究邀请5岁幼儿完成数字比较和面积比较两类任务,结果发现在数字比较任务中没有出现SNARC效应,但却存在距离效应;在面积比较任务中出现了SNARC效应和距离效应。可以推断,在阿拉伯数字的空间表征出现之前,儿童已经能够对非符号数量信息进行空间表征。     

Studies on spontaneous attention to number (SAN) are based on spontaneous focusing on numerosity (SFON)

Li and Baroody presented a study in which they investigate children’ spontaneous attention to exact quantity without acknowledging how previous studies of spontaneous focusing on numerosity (SFON) are related to their concept and methods. The authors’ reaction to our pointing this out makes it is clear that SFON research has had foundational role in the development of Baroody and his colleagues spontaneous attention to number (SAN) idea. Thus the authors must acknowledge the SFON literature as the substantial part of their theoretical and methodological construct. The latest definition of SAN states this undeniably. “SAN is the attentional process that underlies exact number recognition initiated by the mathematical thinking triggered by SFON (e.g., attention to “threeness” directed by conceptual knowledge of “three” activated by SFON).” Furthermore, in their response, Dr Baroody and Dr Li admit that “An awareness of the SFON literature did help us explicitly recognize that, given the ambiguous instructions that do not explicitly direct a child’s attention to number, both the nonverbal production and matching tasks were useful in assessing unguided or spontaneous attention to a number.” It is surprising that in their response to the European Journal of Educational Psychology, the authors maintain their claim that they have cited the SFON literature adequately in their study about SAN.     

不同注意提示线索条件下汉字数字加工的SNARC效应

采用Ponser的实验范式.以判断"壹"到"玖"的汉字数字奇偶为任务,探讨不同提示线索时在注意条件与非注意条件下的空间数字反应编码联合效应(SNARC效应).实验结果发现: (1)当有效提示线索为80%时,注意条件下汉字数字出现了SNARC效应,而非注意条件下对汉字数字的加工没有出现SNARC效应; (2)当有效提示线索为50%时,在注意和非注意条件下汉字数字都出现了明显的SNARC效应.结果表明注意水平对SNARC效应产生了影响.     

Quantified Propositional Logic and the Number of Lines of Tree-Like Proofs

There is an exponential speed-up in the number of lines of the quantified propositional sequent calculus over Substitution Frege Systems, if one considers proofs as trees. Whether this is true also for the number of symbols, is still an open problem. This revised version was published online in June 2006 with corrections to the Cover Date.