Bayesian reasoning in avalanche terrain: a theoretical investigation

In this article, I explore a Bayesian approach to avalanche decision-making. I motivate this perspective by highlighting a version of the base-rate fallacy and show that a similar pattern applies to decision-making in avalanche-terrain. I then draw out three theoretical lessons from adopting a Bayesian approach and discuss these lessons critically. Lastly, I highlight a number of challenges for avalanche educators when incorporating the Bayesian perspective in their curriculum.     

Diagnosing Teachers’ Understandings of Rational Numbers: Building a Multidimensional Test Within the Diagnostic Classification Framework

We report a multidimensional test that examines middle grades teachers’ understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers’ and students’ reasoning in this content area. We administered the test to a national sample of 990 in‐service middle grades teachers and analyzed the item responses using the log‐linear cognitive diagnosis model. We report the diagnostic quality of the test at the item level, mastery classifications for teachers, and attribute relationships. Our results demonstrate that, when a test is grounded in research on cognition and is designed to be multidimensional from the onset, it is possible to use diagnostic classification models to detect distinct patterns of attribute mastery.     

基于BAN逻辑分析Otway-Rees协议

Otway-Rees协议主要功能是完成身份的双向认证,本文探讨了形式化分析在设计密码认证协议中的作用C基于Otway-Rees协议,用BAN逻辑对它进行形式分析,指出形式分析可以辅助发现协议的设计缺陷。     

新安理学盛衰始终的内因探微

新安理学的盛衰始终,除了不断变化着的社会历史条件等外部原因外,还有着深刻的内在原因,主要表现为新安理学初始即具有的对朱子学尤其是朱熹本人的尊崇以致于迷信。这一内在原因,深刻地引导、规定和制约着新安理学的存在和发展。同样身为新安学者的戴震,以“志存闻道”为治学旨归,并通过考据学方法,揭示了程朱理学援引老庄、释氏诠释儒学经典的实质,以及因此对儒家思想所造成的巨大危害,从而在根本上颠覆了程朱理学接续孔孟道统的传统观念,消解了新安理学得以成立的思想理论依据,新安理学因此而告终结。     

Promoting teachers’ algebraic reasoning and self-regulation with metacognitive guidance

This study investigates algebraic reasoning and self-regulation skills among elementary school teachers who participated in a professional development program either with IMPROVE metacognitive questioning (PD + Meta) or with no metacognitive guidance (PD). Sixty-four Israeli teachers participated in a 3-year program designed to enhance mathematical knowledge. Results indicated that the PD + Meta teachers outperformed the PD teachers on various algebraic procedural and real-life tasks regarding conceptual mathematical explanations. In addition, the PD + Meta group outperformed the PD group in using self-monitoring and evaluation strategies in algebraic problem solving. We discuss educational and practical implications.     

数学教学中的类比推理

针对数学教学中只注重演绎论证的现状,用实例说明了类比推理是进行发现性数学思维的有效方法;列举数学分析、复变函数、矢量分析等教学中大量可作类比的材料和“用类比推导定理”“用类比寻找习题解法”两教学实例,阐述了类比推理能培养学生举一反三、触类旁通地独立分析问题和解决问题．是数学中进行再创造的主要方法;通过对微分中值定理六种证法思维共性和异性的分析对比,指出了类比教学应因材施教,教师应能广泛而有效地运用类比推理于教学之中,以培养学生创造性思维能力。     

软计算方法和广义模糊认知哲学

"软计算"以语言表达代替数的表达,通过不确定性计算解决常规计算(硬计算)难以处理的问题。数学上的不确定性包括随机性、模糊性、粗糙性等,它们分别由概率统计、模糊数学、粗糙集理论等非经典数学加以处理。鉴于这些性质间的内在联系,对各种软计算方法的整合研究也将是软计算发展的一大趋势。     

大学生思想政治教育创新的发展理路

改革开放以来,大学生思想政治教育所处的时代、可利用的条件、面对的对象都发生了深刻变化,要实现长远发展,有必要明晰发展理路。一是准确把握社会历史方位谋求大学生思想政治教育的科学发展;二是针对当代大学生的思想特点着力于思想政治教育的服务性价值和发展性价值;三是依据时代的变化拓展大学生思想政治教育的内容体系;四是顺应现代科技的迅猛发展开发大学生思想政治教育新载体;五是适应高等教育大众化推进大学生思想政治教育特色化发展。