On the electronegativity nonlocality paradox

The electronegativity equalization principle states that, in its ground state, the electronegativity of every component in a system is the same. A paradox then arises: molecular fragments that are very far apart must still have the same electronegativity, which seems to contradict the common assumption that spatially separated molecular species can be described independently. Density-functional theory provides the tools needed to analyze this paradox at a fundamental level, and a resolution is found from the properties of the exact Hohenberg–Kohn functional. Specifically, there is no paradox because the electronegativity is not uniquely defined for separated systems. Instead, there is an “apparent electronegativity” that preserves locality. This may have implications for the treatment of charge-transfer excited states. A model for the energy as a function of the number of electrons is also presented. This model gives some insight into the utility of the grand canonical ensemble formulation (at nonzero temperature) and, unlike most previous models, this model recovers the appropriate behavior in the limits of infinitely separated and/or weakly interacting subsystems.     

利用三段式诊断法探查化学平衡概念的理解

采用三段式诊断测试的方法,以浙江省某二级重点中学的高三化学选考生为研究对象,从“化学平衡状态的判定”“平衡常数与转化率”“平衡移动的影响因素”等3个维度,探查选考生在化学平衡概念理解上的表现。结果显示,选考生化学平衡概念理解的整体水平良好,但对平衡状态的速率判据理解不够全面,相异构想严重;转化率的计算能力和自信表现稍有不足;对催化剂、压强等平衡移动的影响因素存在认知缺陷,特别是压强因素,还未真正掌握压强影响平衡移动的本质机理。     

The Gibbs' phenomenon and harmonic oscillators with periodic forcing

We present an interesting nonlinear equation originating from a geometrical problem. We show how it can be solved numerically, how algorithmic differentiation is useful, and how the problem can also be solved analytically using the computer algebra system Maple.     

中学生对“溶液”概念理解的可视化表征及启示

学生概念理解的可视化表征可以通过学生的作图来展示,分析图示可以获取学生概念理解的更加深入的信息。梳理了国内外有关中学生对“溶液”概念理解的研究,集中对学生的作图进行分析,呈现了中学生对“溶液”概念理解的可视化表征。针对作图发现的学生概念理解的结果,提出了促进中学生“溶液”概念理解的教学启示。     

Developing teacher content understanding by integrating pH and logarithms concepts

Logarithms are notorious for being a difficult concept to understand and teach. Research suggests that learners can be supported in understanding logarithms by making connections between mathematics and science concepts such as pH. This study investigated how an integrated chemistry and mathematics lesson impacted 29 teachers’ understanding of the logarithmic relationship and pH. Pre- and post-test data indicated 23 teachers improved their understanding of logarithms and 28 improved their understanding of pH, suggesting that teacher educators in both science and mathematics context can use this approach to foster better understanding with their teachers and ultimately school students. Our analysis also identified professional development components and teacher characteristics associated with gains in understanding of pH and logarithms, which mathematics and science teacher educators can use to strategically adapt and implement the lesson within other teacher education settings.     

Characterizing the growth of one student’s mathematical understanding in a multi-representational learning environment

The purpose of this study was to characterize the growth of one student’s mathematical understanding and use of different representations about a geometric transformation, dilation. We accomplished this purpose by using the Pirie-Kieren model jointly with the Semiotic Representation Theory as a lens. Elif, a 10^th- grade student, was purposefully chosen as the case for this study because of the growth of mathematical understanding about dilation she exhibited over time. Elif participated in task-based interviews before, during and after participating in a variety of transformation lessons where she used multiple representations, including physical and virtual manipulatives. The results revealed that Elif was able to progress in her mathematical understanding from informal levels to the formal levels in the Pirie-Kieren model as she performed treatments and conversions, movements involving different registers of representations. The results also showed numerous examples of Elif’s mathematical understanding based on folding back activities, complementary aspects of acting and expressing, and interventions. Using the two theories together provides a powerful and holistic approach to a deeper understanding of mathematical learning by characterizing and articulating the growth of mathematical understanding and the way of mathematical thinking.     

误差理论中几个问题的讨论

就物理实验教材中有关误差理论概念的延伸、表达,以及有效数据的理解,分别进行了剖析,以便有利于学生学习和教师教学的参考。