An Examination of Implicitly Activated,Explicitly Activated,and Nullified Stereotypes on Mathematical Performance: It's Not Just a Woman's Issue

This study was designed to examine the different ways that stereotypes might become activated in testing situations and the effects this activation has on task performance. In Experiment 1, women undergraduates exposed to an explicitly activated stereotype (i.e., told men outperform women in mathematics) performed worse than women exposed to a nullified stereotype (i.e., told men and women perform at the same level in mathematics). The stereotype threat also was activated implicitly under normal conditions (i.e., just given the test with nothing else stated) such that performance in this condition was at the same (low) level as the explicitly activated threat. In Experiment 2, the results were replicated with White male undergraduates using the stereotype that Asians are better than Whites in mathematics. In addition, in a small field survey we found that this belief about ethnicity did occur spontaneously for White men in college calculus courses. Taken together, the results of these studies suggest that even under normal circumstances, math test situations may lead to nonoptimal performance for both stigmatized (women) and traditionally nonstigmatized (White men) group members. Implications for threat nullification techniques are discussed.     

The Role of Mathematics in Deleuze’s Critical Engagement with Hegel

Abstract

The role of mathematics in the development of Gilles Deleuze’s (1925–95) philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic is demonstrated in this paper by differentiating Deleuze’s interpretation of the problem of the infinitesimal in Difference and Repetition from that which G. W. F Hegel (1770–1831) presents in the Science of Logic. Each deploys the operation of integration as conceived at different stages in the development of the infinitesimal calculus in his treatment of the problem of the infinitesimal. Against the role that Hegel assigns to integration as the inverse transformation of differentiation in the development of his dialectical logic, Deleuze strategically redeploys Leibniz’s account of integration as a method of summation in the form of a series in the development of his philosophy of difference. By demonstrating the relation between the differential point of view of the Leibnizian infinitesimal calculus and the differential calculus of contemporary mathematics, I argue that Deleuze effectively bypasses the methods of the differential calculus which Hegel uses to support the development of the dialectical logic, and by doing so, sets up the critical perspective from which to construct an alternative logic of relations characteristic of a philosophy of difference. The mode of operation of this logic is then demonstrated by drawing upon the mathematical philosophy of Albert Lautman (1908–44), which plays a significant role in Deleuze’s project of constructing a philosophy of difference. Indeed, the logic of relations that Deleuze constructs is dialectical in the Lautmanian sense.     

Intrinsic Explanation and Field’s Dispensabilist Strategy

Abstract

Hartry Field defended the importance of his nominalist reformulation of Newtonian Gravitational Theory, as a response to the indispensability argument, on the basis of a general principle of intrinsic explanation. In this paper, I argue that this principle is not sufficiently defensible, and can not do the work for which Field uses it. I argue first that the model for Field’s reformulation, Hilbert’s axiomatization of Euclidean geometry, can be understood without appealing to the principle. Second, I argue that our desires to unify our theories and explanations undermines Field’s principle. Third, the claim that extrinsic theories seem like magic is, in this case, really just a demand for an account of the applications of mathematics in science. Finally, even if we were to accept the principle, it would not favor the fictionalism that motivates Field’s argument, since the indispensabilist’s mathematical objects are actually intrinsic to scientific theory.     

儿童早期工作记忆与数学学习的关系

以往研究认为工作记忆对数学学习很重要,但是以往工作记忆和早期数学学习的关系研究结果并不一致。本研究运用元分析的方法回顾了33篇独立研究,含307项相关系数作为效应值,总被试量为42423名平均年龄3~8岁的儿童,旨在探讨工作记忆的3个主成分PL(语音回路)、VSSP(视觉空间画板)、CE(中央执行)与数学学习不同方面之间的关系,以及样本年龄对工作记忆和数学学习相关程度的调节作用。结果显示:工作记忆与数学学习确实存在强相关,工作记忆子成分中,CE与数学学习平均相关的程度最强。并且,CE与数学学习不同方面之间的相关程度不存在显著差异,PL、VSSP与数运算的相关程度比数概念更强,存在显著差异。样本年龄对CE、PL与数学学习之间相关关系存在显著调节作用,对VSSP与数学学习之间的相关关系不存在显著调节作用。文献梳理还发现,以往研究对数学学习的考察,大都聚焦数概念、数运算的内容,未来研究需要关注几何与空间、测量等方面内容。     

TPS: A hybrid automatic-interactive system for developing proofs

The theorem proving system Tps provides support for constructing proofs using a mix of automation and user interaction, and for manipulating and inspecting proofs. Its library facilities allow the user to store and organize work. Mathematical theorems can be expressed very naturally in Tps using higher-order logic. A number of proof representations are available in Tps, so proofs can be inspected from various perspectives.     

初中生感知到的同伴支持与数学学习投入—基于变量为中心和个体为中心的分析

为考察同伴支持对初中生数学学习投入的影响机制,采用问卷法对1177名七、八年级学生感知到的同伴支持、数学认同、数学焦虑和数学学习投入进行测查。结果发现：同伴支持不仅能直接预测初中生的数学学习投入,还通过数学认同经数学焦虑的链式中介作用来预测数学学习投入;对数学认同和数学焦虑的得分进行潜剖面分析,可将学生分为高认同-低焦虑、中认同-中焦虑和低认同-高焦虑三组,同伴支持可预测学生的不同亚组,三组学生的数学学习投入得分存在显著差异。上述发现为促进基础教育阶段学生数学学习投入的教育实践提供了理论依据。     

What Is an Inconsistent Truth Table?

Do truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than any one logic being privileged, then, on this count partisans across the logical spectrum are in relatively similar dialectical positions.     

Memory abilities in generally gifted and excelling-in-mathematics adolescents

This paper presents part of a multidimensional examination of mathematical giftedness. The present study examined the memory mechanisms associated with general giftedness (G) and excellence in mathematics (E) in four groups of 10th–12th grade students (16–18 years old) varying in levels of G and E. The participants first underwent the Raven test for general ability evaluation and SAT-M — the mathematical excellence tests in order to design the study groups. Afterwards, the students were tested on a battery of three memory tests including tests for short-term (STM) and working memory (WM). The results reveal that the G factor is related to high STM for both phonological loop and phonological central executive mechanisms. It was also found that the E factor is associated with high visual–spatial memory (VSM), in particular with the visual central executive mechanism. An interaction effect was found between G and E factors regarding WM. The central executive mechanism appeared to be related to both G and E factors. In addition, gender differences were shown within the groups. Male participants performed better than their female counterparts on a phonological storage task and a phonological central executive mechanism task. The results can contribute to the theoretical knowledge regarding similarities and differences in memory mechanisms in G and E groups.     

《周易》对中国古代数学的影响

分析中国古代数学史上重要的数学著作可以看出,《周易》往往被古代数学家们视作数学发展最早的源头,而且在一些重要的数学著作中,数学家们运用《周易》中的有关概念表述数学问题,对《周易》中的数学问题及其相关问题进行深入的研究,取得了重要的数学成就。这一切足以表明《周易》对于古代数学发展具有非常重要的影响。