医学留学生化学实验全英文教学资源建设与实践*

针对目前化学实验全英文在线教学资源匹配度较低、相对匮乏等问题,以医学留学生为中心,建设了有声课件、模块化实景实验操作视频以及测试题库3种不同类型的化学实验全英文教学资源,通过资源的线下使用和基于雨课堂的在线预习,实现从“集中、定时、定点”的传统教学模式向“模块化、碎片化、信息化”的混合教学模式转变,可以丰富教学资源和教学手段,改进教学秩序,提高医学留学生化学知识和技能学习的积极性和主动性,使“教”“学”良性循环,可切实提高化学实验国际化教学质量。     

高二学生“变化观念与平衡思想”素养表现的追踪评价——以化学反应原理模块为例

基于《普通高中化学课程标准(2017年版2020年修订)》和已有研究,明确了化学反应原理模块“变化观念与平衡思想”素养表现水平,基于水平构建了人教版化学反应原理模块各章的评价指标,通过Rasch模型优化形成了质量良好的评价工具。运用评价工具对470名高二学生开展5次追踪评价,获得了2 149个有效样本,分析高二学生在化学反应原理模块“变化观念与平衡思想”素养表现的变化情况和整体现状。     

不同版本高中化学教科书中学生必做实验的分析与启示——基于“科学探究与创新意识”素养

以人教版、苏教版、鲁科版(2019年版)和沪科版(2020年版)高中化学教科书中的学生必做实验文本为研究对象,基于“科学探究与创新意识”素养构建高中化学教科书中学生必做实验文本的分析框架,分析和比较4个版本教科书中学生必做实验文本“科学探究与创新意识”素养的体现及其异同,为学生必做实验教学提供启示和建议。     

On hyperbolicity cones associated with elementary symmetric polynomials

Elementary symmetric polynomials can be thought of as derivative polynomials of . Their associated hyperbolicity cones give a natural sequence of relaxations for . We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence of this recursion, we give an alternative characterization of these cones, and give an algebraic characterization for one particular dual cone associated with together with its self-concordant barrier functional.     

High school students’ understanding of the function concept

This paper is a study of part of the Algebra Project's program for underrepresented high school students from the lowest quartile of academic achievement, social and economic status. The study focuses on students’ learning the concept of function. The curriculum and pedagogy are part of an innovative, experimental approach designed and implemented by the Algebra Project. The instructional treatment took place over 7 weeks during the Junior Year of 15 students from our target population. Immediately after instruction, a written instrument was administered followed, several weeks later, by in-depth interviews. The results are that many of our participants achieved a level of knowledge and understanding of functions on a par with beginning college students, including preservice teachers, as reported in the literature. Many conceptual difficulties that have been reported in the research literature were not as prevalent for our participants and some of them were capable of solving difficult problems involving composition of functions. We conclude that, with appropriate pedagogy, it is possible for students in the Algebra Project's target population to learn substantial and non-trivial mathematics at the high school level, and that the Algebra Project approach is one example of such a pedagogy.     

Representation for the Lagrangian numerical differentiation formula involving elementary symmetric functions

By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29-52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes.     

Essential numerical range of elementary operators

Let and denote two -tuples of operators with and Let denote the elementary operators defined on the Hilbert-Schmidt class by We show that

Here is the essential numerical range, is the joint numerical range and is the joint essential numerical range.

     

A task that elicits reasoning: A dual analysis

This paper reports on the forms of reasoning elicited as fourth grade students in a suburban district and sixth grade students in an urban district worked on similar tasks involving reasoning with the use of Cuisenaire rods. Analysis of the two data sets shows similarities in the reasoning used by both groups of students on specific tasks, and the tendency of a particular task to elicit numerous forms of reasoning in both groups of students. Attributes of that task and ways that those attributes can be replicated in other domains may have implications in the teaching of early reasoning.     

Elementary symmetric polynomials in Shamir's scheme

The concept of k-admissible tracks in Shamir's secret sharing scheme over a finite field was introduced by Schinzel et al. (2009) [10]. Using some estimates for the elementary symmetric polynomials, we show that the track (1,…,n) over Fp is practically always k-admissible; i.e., the scheme allows to place the secret as an arbitrary coefficient of its generic polynomial even for relatively small p. Here k is the threshold and n the number of shareholders.     

Incompressibility of strange matter

Strange stars (ReSS) calculated from a realistic equation of state (EOS), that incorporate chiral symmetry restoration as well as deconfinement at high density [Phys. Lett. B 438 (1998) 123; Phys. Lett. B 447 (1999) 352, Addendum; Phys. Lett. B 467 (1999) 303, Erratum; Indian J. Phys. B 73 (1999) 377] show compact objects in the mass radius curve. We compare our calculations of incompressibility for this EOS with that of nuclear matter. One of the nuclear matter EOS has a continuous transition to ud-matter at about five times normal density. Another nuclear matter EOS incorporates density dependent coupling constants. From a look at the consequent velocity of sound, it is found that the transition to ud-matter seems necessary.