Contrasting two models of academic self‐efficacy – domain‐specific versus cross‐domain – in children receiving and not receiving special instruction in mathematics

In social cognitive theory, self‐efficacy is domain‐specific. An alternative model, the cross‐domain influence model, would predict that self‐efficacy beliefs in one domain might influence performance in other domains. Research has also found that children who receive special instruction are not good at estimating their performance. The aim was to test two models of how self‐efficacy beliefs influence achievement, and to contrast children receiving special instruction in mathematics with normally‐achieving children. The participants were 73 fifth‐grade children who receive special instruction and 70 children who do not receive any special instruction. In year four and five, the children's skills in mathematics and reading were assessed by national curriculum tests, and in their fifth year, self‐efficacy in mathematics and reading were measured. Structural equation modeling showed that in domains where children do not receive special instruction in mathematics, self‐efficacy is a mediating variable between earlier and later achievement in the same domain. Achievement in mathematics was not mediated by self‐efficacy in mathematics for children who receive special instruction. For normal achieving children, earlier achievement in the language domain had an influence on later self‐efficacy in the mathematics domain, and self‐efficacy beliefs in different domains were correlated. Self‐efficacy is mostly domain specific, but may play a different role in academic performance depending on whether children receive special instruction. The results of the present study provided some support of the Cross‐Domain Influence Model for normal achieving children.     

The mathematics of sharing / Las matemáticas que realizan los niños al compartir

Abstract

The purpose of sharing is to construct equivalent sets, making it an ideal context for analysing important quantitative concepts such as counting, equivalence and cardinality. Two studies analysed how four- and five-year-olds shared blocks in equal sharing and reciprocity conditions and their number inferences about one set after counting the other. The researcher asked children to share double and single blocks between two characters. They succeeded more in building equivalent shares in an equal sharing than reciprocity condition. Most children who shared correctly also made appropriate number inferences. To examine whether perceptual cues helped children share the blocks, a second study used Canadian $1 and $2 coins. A double block is twice the size of a single, whereas there is no visual cue about the value relation between coins because they are the same size. Unexpectedly, children shared equally well with blocks and coins, and most children made number inferences.     

The Willingness of Military Members to Seek Help: The Role of Social Involvement and Social Responsibility

Anchored in the social organization theory of action and change, we use data from a large sample of active‐duty Air Force members to examine the direct and indirect influence of social involvement and social responsibility on willingness to seek help in times of need via trust in formal systems and informal supports. Group comparisons are conducted between junior male, junior female, senior male, and senior female service members. The key mediational path in the model for all groups is the connection between social involvement and willingness to seek help via trust in formal systems. These results can inform both unit‐ and community‐level interventions intended to increase the likelihood that active‐duty AF members will seek help in times of need.     

5～6岁不同数学能力水平儿童的执行功能差异研究

为了考察不同数学能力水平儿童的执行功能差异,根据331名学前儿童的数学能力得分选取了潜在数学学习困难儿童组、低分组、典型发展儿童组和数学优秀组等4个实验组。首先分析了各组儿童的执行功能差异特点,之后使用判别分析进一步探索了各执行功能子结构对儿童早期数学能力差异分组的贡献。结果表明:相对于典型发展儿童组,潜在数学学习困难儿童在执行功能的更新、抑制和转换方面普遍缺损;低分组儿童则仅表现出数字更新能力不足;数学优秀组在数字更新和有时间要求的认知转换方面比典型发展组有明显优势。进一步判别分析表明,对早期数学能力差异分组贡献最大的并非独立执行功能子结构,而是更新和转换的共同因素结构。     

‘Infinity Means it Goes on Forever’: Siblings' Informal Teaching of Mathematics

Sibling‐directed teaching of mathematical topics during naturalistic home interactions was investigated in 39 middle‐class sibling dyads at two time points. At time 1 (T1), siblings were 2 and 4 years of age, and at time 2 (T2), siblings were 4 and 6 years of age. Intentional sequences of sibling‐directed mathematical teaching were coded for (i) topics (e.g., number), (ii) contexts (e.g., play with materials/toys), and (iii) type of knowledge (conceptual and procedural). Siblings engaged in teaching number, geometry, and measurement at T1 and demonstrated preliminary evidence of teaching of grouping, relations, and operations at T2. Regarding context, at T1, mathematical teaching occurred most frequently during play with materials/toys, while at T2, games with rules were prominent. Teaching of conceptual or procedural knowledge varied over time and by topic and context. Findings are discussed in light of recent work on understanding children's mathematical knowledge as it develops in the informal family context. Copyright © 2015 John Wiley & Sons, Ltd.     

A Naturalistic Look into Maddy's Naturalistic Philosophy of Mathematics

This paper discusses Penelope Maddy's (b.1950) naturalistic philosophy of mathematics,which is one of the most influential forms of post-Quinean naturalism in the philosophy of mathematics.Two defining features of Maddy's theory,namely the methodological autonomy of mathematics and the equivalence of Thin Realism and Arealism,are analyzed,and some criticisms of them are posed from within the naturalistic line of thought itself.In the course of this analysis and criticism,the paper will also consider Maddy's objections to the Quinean Indispensability Argument,which are the starting point of her own version of naturalism.     

父母教育卷入与小学儿童数学焦虑的纵向联系:数学态度的中介作用

为探讨父母教育卷入与学龄期儿童数学焦虑之间的纵向联系及内在作用机制,从山东省聊城市两所普通小学选取1734名三、四年级学生,对其进行为期一年的追踪研究。结果发现：（1）T1父母教育卷入能够显著负向预测T2儿童数学焦虑,但T1儿童数学焦虑对T2父母教育卷入的预测不显著;（2）在同一时间点上,儿童数学态度在父母教育卷入与儿童数学焦虑之间发挥显著中介作用;（3）在不同时间点上,儿童数学态度的中介作用仍然成立,表明儿童数学态度的中介作用具有跨时间的稳定性。该结果强调了父母教育卷入对学龄期儿童数学焦虑变化的重要作用,亦为从父母教育卷入和数学态度角度降低儿童的数学焦虑水平提供了初步有力证据。     

儿童执行功能与早期学业能力的关系:学习品质的中介作用

以上海市6所幼儿园245名3~6岁儿童为研究对象,分别采用头–脚–膝盖–肩膀(HTKS)任务、修订后的儿童行为评定量表(CBRS)及亚太学前儿童发展量表中的语言和前阅读分量表以及认知分量表考察执行功能、学习品质及早期语言和数学学业发展状况。结果表明:(1)执行功能对学习品质、早期语言能力和数学能力均有显著正向预测作用;(2)学习品质在执行功能和早期数学能力关系中起部分中介作用,但对执行功能和早期语言能力的关系无中介作用。     

Some Implications of a Behavioral Analysis of Verbal Behavior for Logic and Mathematics

The evident power and utility of the formal models of logic and mathematics pose a puzzle: Although such models are instances of verbal behavior, they are also essentialistic. But behavioral terms, and indeed all products of selection contingencies, are intrinsically variable and in this respect appear to be incommensurate with essentialism. A distinctive feature of verbal contingencies resolves this puzzle: The control of behavior by the nonverbal environment is often mediated by the verbal behavior of others, and behavior under control of verbal stimuli is blind to the intrinsic variability of the stimulating environment. Thus, words and sentences serve as filters of variability and thereby facilitate essentialistic model building and the formal structures of logic, mathematics, and science. Autoclitic frames, verbal chains interrupted by interchangeable variable terms, are ubiquitous in verbal behavior. Variable terms can be substituted in such frames almost without limit, a feature fundamental to formal models. Consequently, our fluency with autoclitic frames fosters generalization to formal models, which in turn permit deduction and other kinds of logical and mathematical inference.