现代力学中的现代数学方法

本文简要介绍了力学与数学再次结合趋势的历史背景和现状。根据当代科学技术向力学提出的问题,简要综述了现代力学所涉及的现代数学领域和方法.     

Large deviation theory for a homogenized and “corrected” elliptic ODE

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a “pointwise” large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quantification are considered.     

Reinventing the formal definition of limit: The case of Amy and Mike

Relatively little is known about how students come to reason coherently about the formal definition of limit. While some have conjectured how students might think about limits formally, there is insufficient empirical evidence of students making sense of the conventional ?-δ definition. This paper provides a detailed account of a teaching experiment designed to produce such empirical data. In a ten-week teaching experiment, two students, neither of whom had previously seen the conventional ?-δ definition of limit, reinvented a formal definition of limit capturing the intended meaning of the conventional definition. This paper focuses on the evolution of the students’ definition, and serves not only as an existence proof that students can reinvent a coherent definition of limit, but also as an illustration of how students might reason as they reinvent such a definition.     

高等数学多媒体课堂教学浅议

从使用多媒体讲授高等数学的经验出发,分析高等数学教学中应用多媒体教学手段的优势,同时给出在多媒体教学条件下进一步提高教学效果的几点建议,指出教师必须用现代化的教学思想为指导,综合运用各种教学手段提高高等数学教学效果,适应现代化教学的发展.     

高等数学求极限教学的一些建议

分析极限教学中出现的一些问题,并给出相应建议．     

线性代数教材改革指导思想探析

论述线性代数教材改革的必要性及其指导思想,主张线性代数教材建设应以矩阵为主线,以教育部颁发的硕士研究生人学考试线性代数部分的大纲为纲,结合教学现代化的现状,强调几何与代数相结合,重视代数学思想方法的渗透,化抽象为具体,同时在教学中还要引入数学建模的思想．     

Developing prospective teachers’ covariational reasoning through a model development sequence

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers’ ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented with 20 participants in a mathematical modeling course offered to prospective teachers. The participants’ developing abilities of covariational reasoning were documented under three categories: (i) identifying the variables, (ii) ways of coordinating the variables, and (iii) ways of quantifying the rate of change. The results revealed significant improvement in the prospective teachers’ ways of identifying and coordinating the variables, and in quantifying the rate of change. Moreover, the results indicated that preference for a particular way of thinking in identifying and coordinating the variables determined the prospective teachers’ way of quantifying the rate of change and thereby their level of covariational reasoning.     

Three modes of STEM integration for middle school mathematics teachers

Of the four subjects in an integrated science, technology, engineering, and mathematics (STEM) approach, mathematics has not received enough focus. This could be in part because mathematics teachers may be apprehensive or unsure about how to implement integrated STEM education in their classrooms. There are benefits to integrated STEM in a mathematics classroom though, including increased motivation, interest, and achievement for students. This article discusses three methods that middle school mathematics teachers can utilize to integrate STEM subjects. By focusing on open‐ended problems through engineering design challenges, mathematical modeling, and mathematics integrated with technology middle school students are more likely to see mathematics as relevant and valuable. Important considerations are discussed as well as recent research with these approaches.     

Empirically supporting school STEM culture—The creation and validation of the STEM Culture Assessment Tool (STEM‐CAT)

School STEM Culture—an aspect of culture within a school community—is defined as the beliefs, values, practices, and resources in STEM fields as perceived by students, parents, teachers, and administrators and counselors within a school. This study validates the STEM Culture Assessment Tool (STEM‐CAT), an instrument intended to advance the use of the School STEM Culture construct within the research community. Internal consistency was determined through the use of Cronbach's alpha and factor analyses, and the instrument was found to be a reliable measure of School STEM Culture. The instrument can be used in future research to quantify School STEM Culture to determine if interventions change the culture of a school to further STEM education.     

Subitising activity relative to units construction: a case study

Subitising, a quick apprehension of the numerosity of a small set of items, has been found to change from an individual's reliance on perceptual to conceptual processes. In this study, we utilised a constructivist teaching experiment methodology to investigate how the subitising activity of one preschool student, Amy, related to her construction of prenumerical units. Subitising and counting tasks were designed to assess and perturb Amy's thinking relative to her construction of units, and to observe changes in Amy's activity associated with the different tasks. Findings indicate that as Amy's subitising activity changed from perceptual to conceptual, she constructed subitised motor units and subitised figurative units. Implications of this study suggest that the construction of subitised units may support young children's later development of arithmetic units.