Which notion of implication is the right one? From logical considerations to a didactic perspective

Implication is at the very heart of mathematical reasoning. As many authors have shown, pupils and students experience serious difficulties in using it in a suitable manner. In this paper, we support the thesis that these difficulties are closely related with the complexity of this notion. In order to study this complexity,we refer to Tarski's semantic truth theory,which contributes to clarifying the different aspects of implication: propositional connective, logically valid conditional, generalized conditional,inference rules. We will show that for this purpose, it is necessary to extend the classical definition of implication as a relation between propositions to a relation between open sentences with at least one free variable. This permits to become aware of the fact that, in some cases, the truth-value of a given mathematical statement is not constrained by the situation, contrary to the common standpoint that, in mathematics, a statement is either true or false. In the present paper, the didactic relevance of this theoretical stance will be illustrated by an analysis of two problematic situations and the presentation of some experimental results from our research on first-year university students' understanding of implication. This revised version was published online in August 2006 with corrections to the Cover Date.     

创造、创新和逻辑

创造和创新必须遵守逻辑规律。通常,人们思考问题都是从真前提进而得到真结论,在创造和创新活动中,一般都要经过由假前提寻求真结论的思维过程。     

Backwards writing: An unexpected ability in writing

Summary The case of a left-handed female patient is described who presented serious problems in learning how to write during childhood, particularly in relation to directionality and letter sequence. The patient then learned to write correctly with her left hand, but practiced and maintained her ability to write backwards (from the last letter to the first). Implications of the case are discussed.Send Correspondence to Dr. Alfredo Ardila, Miami Institute of Psychology of the Caribbean Center for Advanced Studies, 8180 NW 36 Street, Second floor, Miami, Florida 33166-6612.     

对2004年FIBA篮球规则修改部分的分析与研究

为了使篮球比赛更加流畅,国际篮联又一次修改了比赛规则,新修改的篮球竞赛规则已于2004年9月1日起执行。本文就修改后的篮球竞赛规则有哪些新的特点和变化进行分析与研究,将有利于运动员、教练员、裁判员理解规则和执行规则,有助于篮球运动在中国的推广和发展。     

美国知识产权保护规则的新一轮变迁——以《双边投资协定》为拓展的保护手段

为应对经济发展需求,美国不断在全球推行高标准、宽范围、强制约的知识产权保护制度,引发了现代知识产权国际保护规则的新一轮变迁。BIT作为知识产权国际保护的一种重要形式,在投资争端解决机制、技术化本地措施、政府竞争中立等方面都对知识产权予以强保护。通过对2012年BIT范本中知识产权保护新议题的研究,探讨知识产权保护规则的未来趋势,为我国在调整争议解决机制、待遇适用标准和政府管制范围等方面提供建议,以应对美国知识产权保护新规则带来的挑战。     

一矩阵方程组的反射解

We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф is the set of all reflexive （or antireflexive） solutions of the system mentioned above, and ｜｜·｜｜ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.     

全美教育协会教育专业伦理规范的制定及启示

我国历来有重视师德建设的传统,但通过制定规范推进师德建设的做法却一直效果不佳。全美教育协会教育专业伦理规范于1975年定稿以来,已沿用三十五年有余,并为许多国家、地区制定规范时所效仿。本文从制定主体、形成过程、执行制度及规范内容等方面,对比该规范与其他师德规范,展现其所体现出的教育专业自主、专业人员本位、专业自律、专业自由等特点,以期为我国师德规范建设提供一定参考。     

简析篮球规则中的抗议程序

通过对1998-2010年篮球规则对球队抗议程序的修改进行对比研究,总结出篮球规则对球队抗议程序的要求在逐年加强,但还存在不完善的地方,为完善规则提供参考。     

现代装饰画的艺术特征

现代装饰画与传统装饰画的区别,主要体现在他不再是时间意义上的现代,而是意义上的创新,出现了与美相悖的装饰画作品内容,其名称的界定变得模糊了,并且形式和内容倾向于理论化,造型倾向于抽象化。     

应用型本科学生从事公益活动的意义研究

从应用型本科学生群体自身的特殊性、培养目标的定位来看,从事公益活动有助于学生规则意识的培养、综合能力的提升和良好思想道德、心理素质的培养,有助于应用型本科院校人才培养目标的实现。