Computer supported mathematics with Ωmega

Classical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces—often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited.The shift from search based methods to more abstract planning techniques however opened up a paradigm for mathematical reasoning on a computer and several systems of that kind now employ a mix of interactive, search based as well as proof planning techniques.The Ωmega system is at the core of several related and well-integrated research projects of the Ωmega research group, whose aim is to develop system support for a working mathematician as well as a software engineer when employing formal methods for quality assurance. In particular, Ωmega supports proof development at a human-oriented abstract level of proof granularity. It is a modular system with a central proof data structure and several supplementary subsystems including automated deduction and computer algebra systems. Ωmega has many characteristics in common with systems like NuPrL, CoQ, Hol, Pvs, and Isabelle. However, it differs from these systems with respect to its focus on proof planning and in that respect it is more similar to the proof planning systems Clam and λClam at Edinburgh.     

Human symbol manipulation within an integrated cognitive architecture

This article describes the Adaptive Control of Thought–Rational (ACT–R) cognitive architecture (Anderson et al., 2004; Anderson & Lebiere, 1998) and its detailed application to the learning of algebraic symbol manipulation. The theory is applied to modeling the data from a study by Qin, Anderson, Silk, Stenger, & Carter (2004) in which children learn to solve linear equations and perfect their skills over a 6-day period. Functional MRI data show that: (a) a motor region tracks the output of equation solutions, (b) a prefrontal region tracks the retrieval of declarative information, (c) a parietal region tracks the transformation of mental representations of the equation, (d) an anterior cingulate region tracks the setting of goal information to control the information flow, and (e) a caudate region tracks the firing of productions in the ACT–R model. The article concludes with an architectural comparison of the competence children display in this task and the competence that monkeys have shown in tasks that require manipulations of sequences of elements.     

The Good, The Bad, and The Ugly: Domestic Violence Survivors’ Experiences with Their Informal Social Networks

Informal social networks play a critical role in buffering the negative effects of stressful life events. For women experiencing the stress of a violent relationship, family and friends are among the first sources of support sought; however, reactions to the abuse by family and friends are not uniformly perceived as helpful by survivors. The current study takes a qualitative approach to examining the range of possible reactions survivors may encounter from their social networks regarding the abuse. Special attention is given to negative and mixed reactions, as they have previously been under-examined in the literature. Findings suggest that survivors (N = 45) regularly experience negative and mixed reactions. Emergent themes suggest that both positive and negative reactions to abuse could be understood in four broad arenas: safety, emotional availability, input, and aid. However, positive and negative reactions emerged as distinct constructs within each arena; mixed reactions took multiple forms including being within person and within network.     

试论批判性思维与逻辑的关系

“批判性思维”一词已成为当今教育界一个十分时髦的术语。心理学家、教育学家、哲学家都在讨论批判性思维。但是,什么是批判性思维?其逻辑基础是什么呢?我们认为,目前学界对此的认识有待进一步澄清。在逻辑学界,批判性思维已成为当前逻辑学教学改革和发展的一种重要方向。有学者认为,批判性思维与非形式逻辑有着密不可分的联系,甚至有人认为批判性思维与非形式逻辑两者可以不加区别交互使用。该文首先考察了心理学家、教育学家和哲学家们分别给出的批判性思维的定义,然后分析批判性思维与非形式逻辑、形式逻辑之间的相互联系与区别,进而认为形式逻辑和非形式逻辑共同构成了批判性思维的逻辑基础。     

小学儿童数学态度与数学成就的纵向联系：学业拖延和数学元认知的作用

为深入探讨小学儿童的数学态度、学业拖延、数学元认知与数学成就之间的纵向联系及内在作用机制,对515名三、五年级小学生进行为期半年的追踪研究。结果表明:(1)学业拖延在儿童的数学态度与数学成就之间发挥着即时和纵向中介作用;(2)不同水平数学元认知个体在纵向中介模型中“数学态度→数学成就”这一路径上存在差异。这意味着较积极的数学态度有利于减少小学儿童的学业拖延行为,进而提高其数学成就,而高数学元认知则能够监控和调节个体的数学态度,使其发挥积极作用,从而提高数学成就。该发现为有效促进儿童的数学学习提供了重要实践启示。     

Using a taped intervention to improve kindergarten students' number identification

A multiple baseline design across students was used to evaluate the effects of a taped numbers (TN) intervention on the number‐identification accuracy of 4 kindergarten students. During TN, students attempted to name the numbers 0 through 9 on randomized lists before each number was provided via a tape player 2 s later. All 4 students showed immediate increases and reached 100% in number‐identification accuracy. One student reached 100% accuracy after TN was supplemented with performance feedback, reinforcement, and overcorrection.     

Effect of Teachers' Stereotyping on Students' Stereotyping of Mathematics as a Male Domain

Abstract

This multilevel analysis used data from a representative sample from Grades 6, 7, and 8 in public schools in Switzerland. The data included information on (a) 6,602 students (3,307 girls, 3,295 boys) nested within 338 classes and (b) 321 mathematics teachers of these classes. The teachers and the students tended to stereotype mathematics as a male domain, and the teachers' stereotypes significantly affected the students' stereotypes after the author controlled for achievement, interest, and self-confidence in mathematics and for school grade and schooling track.