中学生社会支持对数学学习坚持性的影响:数学自我效能感的中介作用

以北京市通州区一所普通中学的228名初一和初二学生为被试,采用领悟社会支持量表、数学自我效能感和数学学习坚持性问卷,考察在中学生数学学习中不同来源的社会支持对数学学习坚持性的影响,并检验数学自我效能感在其中的中介作用。结果发现:(1)社会支持中的教师支持和同伴支持能够显著正向预测数学学习坚持性水平,而父母支持的预测作用不显著;(2)数学自我效能感在同伴支持和数学学习坚持性之间起完全中介作用,在教师支持和数学学习坚持性之间起部分中介作用。     

Proof theory and mathematical meaning of paraconsistent C-systems

A proof-theoretic analysis and new arithmetical semantics are proposed for some paraconsistent C-systems, which are a relevant sub-class of Logics of Formal Inconsistency (LFIs) introduced by W.A. Carnielli et al. (2002, 2005) [8] and [9]. The sequent versions BC, CI, CIL of the systems bC, Ci, Cil presented in Carnielli et al. (2002, 2005) [8] and [9] are introduced and examined. BC, CI, CIL admit the cut-elimination property and, in general, a weakened sub-formula property. Moreover, a formal notion of constructive paraconsistent system is given, and the constructivity of CI is proven. Further possible developments of proof theory and provability logic of CI-based arithmetical systems are sketched, and a possible weakened Hilbert?s program is discussed. As to the semantical aspects, arithmetical semantics interprets C-system formulas into Provability Logic sentences of classical Arithmetic PA (Artemov and Beklemishev (2004) [2], Japaridze and de Jongh (1998) [19], Gentilini (1999) [15], Smorynski (1991) [22]): thus, it links the notion of truth to the notion of provability inside a classical environment. It makes true infinitely many contradictions B∧¬B and falsifies many arbitrarily complex instances of non-contradiction principle ¬(A∧¬A). Moreover, arithmetical models falsify both classical logic LK and intuitionistic logic LJ, so that a kind of metalogical completeness property of LFI-paraconsistent logic w.r.t. arithmetical semantics is proven. As a work in progress, the possibility to interpret CI-based paraconsistent Arithmetic PACI into Provability Logic of classical Arithmetic PA is discussed, showing the role that PACIarithmetical models could have in establishing new meta-mathematical properties, e.g. in breaking classical equivalences between consistency statements and reflection principles.     

Structuralism as a philosophy of mathematical practice

This paper compares the statement ‘Mathematics is the study of structure’ with the actual practice of mathematics. We present two examples from contemporary mathematical practice where the notion of structure plays different roles. In the first case a structure is defined over a certain set. It is argued firstly that this set may not be regarded as a structure and secondly that what is important to mathematical practice is the relation that exists between the structure and the set. In the second case, from algebraic topology, one point is that an object can be a place in different structures. Which structure one chooses to place the object in depends on what one wishes to do with it. Overall the paper argues that mathematics certainly deals with structures, but that structures may not be all there is to mathematics. I wish to thank Colin McLarty as well as the anonymous referees for helpful comments on earlier versions of this paper.     

中国苏州与美国15岁学生数学学习特征比较

本研究首次采用"学生能力国际评估计划"(PISA)的学生问卷,对苏州市504名15岁学生的数学学习心理及特征进行了调查研究,并与美国学生数据作比较.调查表明:中国苏州大多数学生在数学学习上具有较强的竞争意识与合作意识,他们会运用多种学习策略;那些对数学有更大兴趣和更高动机的学生,有更积极的自我概念和更少的焦虑体验.中美两国学生的数学学习特征性别差异显著.     

The ontological commitments of inconsistent theories

In this paper I present an argument for belief in inconsistent objects. The argument relies on a particular, plausible version of scientific realism, and the fact that often our best scientific theories are inconsistent. It is not clear what to make of this argument. Is it a reductio of the version of scientific realism under consideration? If it is, what are the alternatives? Should we just accept the conclusion? I will argue (rather tentatively and suitably qualified) for a positive answer to the last question: there are times when it is legitimate to believe in inconsistent objects.     

Is ZF a hack?: Comparing the complexity of some (formalist interpretations of) foundational systems for mathematics

This paper presents Automath encodings (which are also valid in LF/λP) of various kinds of foundations of mathematics. Then it compares these encodings according to their size, to find out which foundation is the simplest.

The systems analyzed in this way are two kinds of set theory (ZFC and NF), two systems based on Church's higher order logic (Isabelle/Pure and HOL), three kinds of type theory (the calculus of constructions, Luo's extended calculus of constructions, and Martin-Löf's predicative type theory) and one foundation based on category theory.

The conclusions of this paper are that the simplest system is type theory (the calculus of constructions), but that type theories that know about serious mathematics are not simple at all. In that case the set theories are the simplest. If one looks at the number of concepts needed to explain such a system, then higher order logic is the simplest, with twenty-five concepts. On the other side of the scale, category theory is relatively complex, as is Martin-Löf's type theory.

(The full Automath sources of the contexts described in this paper are one the web at http://www.cs.ru.nl/~freek/zfc-etc/.)     

Development of the Japanese Version of the Achievement Emotions Questionnaire – Elementary School (AEQ-ES-J)1,2

The purpose of this study was to develop and validate a Japanese version of the Achievement Emotions Questionnaire – Elementary School (AEQ-ES), which assesses enjoyment, anxiety, and boredom experienced by elementary school students within the settings of attending class, doing homework, and taking tests. Japanese elementary school students (n = 863 for the first survey; n = 332 for the second survey) participated in the questionnaire survey. The results showed that the psychometric properties of the Japanese AEQ-ES were comparable to those of the original version. Moreover, the results showed that students' achievement emotions were associated with their control and value appraisals, as well as their academic motivation, learning strategies, academic performance, and support from teachers. These results indicated that the Japanese version of the AEQ-ES was a good measure of elementary school students' emotions and supported the propositions of the control–value theory of achievement emotions.     

Learning Abilities and Disabilities: Generalist Genes, Specialist Environments

ABSTRACT— Twin studies comparing identical and fraternal twins consistently show substantial genetic influence on individual differences in learning abilities such as reading and mathematics, as well as in other cognitive abilities such as spatial ability and memory. Multivariate genetic research has shown that the same set of genes is largely responsible for genetic influence on these diverse cognitive areas. We call these "generalist genes." What differentiates these abilities is largely the environment, especially nonshared environments that make children growing up in the same family different from one another. These multivariate genetic findings of generalist genes and specialist environments have far-reaching implications for diagnosis and treatment of learning disabilities and for understanding the brain mechanisms that mediate these effects.     

两类数学学习困难小学儿童抑制控制水平的实验研究

为考察单纯型数学困难与混合型数学困难小学儿童的抑制控制水平及特点,使用Stroop色词命名测验和颜色匹配反转作业,对各30名的单纯型困难、混合型困难和对照组小学儿童的优势反应抑制能力进行测试、分析。结果发现:单纯型数学困难儿童抑制优势反应的能力显著低于对照组,但其对事物初次学习的能力与对照组相当;混合型数学困难儿童在对事物初次学习能力及对优势反应的抑制能力方面均显著低于对照组儿童,其中对事物的初次学习能力也显著低于单纯型数学困难儿童。