K2 of a Ring via the G-Construction

We interpret the Steinberg symbols x_i,j(a) as homotopies contracting the elementary matrices e_i,j(a), the latters being represented by certain arcs in a simplicial model of the K-theory. We further prove the Steinberg relations for these homotopies. This provides an explicit map from K₂ of a ring, defined classically as ker(St(R) → GL(R)), to π₂ of the G-construction assigned to R. Though the two groups are known to be isomorphic, a certain work is to be done to prove that this explicit map is an isomorphism. Mathematics Subject Classification 1991: Primary 19B99, 19D99; secondary 18E10, 18F25.     

初等Abel群的加法定理

本文中用Kneser's定理得到下列结论一个新的简单证法.设G为初等Abel p-群(运算用加法),S={a1,a2,…,an)为G的一个n项不含有零然的元素列(元素可允许重复),∣s∣=n=pm-1 p-2,,其中p为素数,若对G的任意子群H,S最多含有∣H∣-1项,则:(1)当m=2时,∑0(S)=G;(2)当m 3时,∑(S)=G.特别有(1)Olson'猜想r(ZpZp)=2p-2;(2)r(mZp)=c(mZp)=pm-1 p-2,m 3.     

Where do Fractions Encounter their Equivalents? – Can this Encounter Take Place in Elementary-School?

The concept of equivalence class plays a significant role in the structure of Rational Numbers. Piaget taught that in order to help elementary school children develop mathematical concepts, concrete objects and concrete reflection-enhancing-activities are needed. The “Shemesh” software was specially designed for learning equivalence-classes of fractions. The software offers concrete representations of such classes, as well as activities which cannot be constructed without a computer. In a discrete Cartesian system students construct points on the grid and learn to identify each such point as a fraction-numeral (a denominator-numerator pair). The children then learn to construct sets of such points, all of which are located on a line through the origin point. They learn to identify the line with the set of its constituent equivalent fractions. Subsequently, they investigate other phenomena and constructions in such systems, developing these constructions into additional fraction concepts. These concrete constructions can be used in solving traditional fraction problems as well as in broadening the scope of fraction meaning. Fifth-graders who used “Shemesh” in their learning activities were clinically interviewed several months after the learning sessions ended. These interviews revealed evidence indicating initial actual development of the desired mathematical concepts. This revised version was published online in July 2006 with corrections to the Cover Date.     

Method of solution to fuzzy relation equations in a complete Brouwerian lattice

Up to now, how to solve a fuzzy relation equation in a complete Brouwerian lattice is still an open problem as Di Nola et al. point out. To this problem, the key problem is whether there exists a minimal element in the solution set when a fuzzy relation equation is solvable. In this paper, we first show that there is a minimal element in the solution set of a fuzzy relation equation AX=b (where A=(a₁,a₂,…,a_n) and b are known, and X=(x₁,x₂,…,x_n)^T is unknown) when its solution set is nonempty, and b has an irredundant finite join-decomposition. Further, we give the method to solve AX=b in a complete Brouwerian lattice under the same conditions. Finally, a method to solve a more general fuzzy relation equation in a complete Brouwerian lattice when its solution set is nonempty is also given under similar conditions.     

高中生对化学课堂环境感知的调查研究

采用“中学化学课堂环境问卷”作为研究工具,对深圳市、长春市、佳木斯市等3个地区的4所高中861名学生的化学课堂环境进行调查,并进行差异分析。研究结果表明,高中生对化学课堂环境的总体感知较好,7个维度中“学生凝聚力”“平等”“任务取向”“合作”等4个维度的平均分大于3.4,“教师支持”和“参与”维度的平均分在3.0~3.4,只有“探究”维度的平均分小于3.0。城市高中生对课堂环境的感知明显好于乡镇高中生,学生心目中所期待的化学课堂比实际的化学课堂更积极。     

我国高中化学教科书中习题的变迁

通过对清末至今我国出版的高中化学教科书中习题的整体梳理和样本研究,发现其变化存在一些特点：它是逐步变为教科书的必要组成的,且数量增长呈折线形;其位置从集中在书后,逐步变为分散在知识内容当中;题目类型越来越丰富;习题的内容不断注重实验过程和情境应用,并逐渐注重价值导向。这些变化反映了教育理念的变迁,为今后教科书习题的编写与使用提供了思路。     

校本选修课程系统化开发的整合路径

通过整合学科资源、教师资源和地方资源,开发并实施与国家课程相协调的系统化、层次化、多样化的校本选修课程,真正发挥校本选修课程的作用。     

PCK视域下高中化学教师“学生知识”的调查研究与分析

化学教师的"学生知识"是教师学科教学知识(pedagogical content knowledg,简称PCK)中的重要组成要素,是实现化学有效课堂教学的必要条件。以新课标教材《化学1》"氧化还原反应"概念学习内容为载体,对PCK视域下湖北、重庆、四川、安徽4个省市的部分高中化学教师进行"氧化还原反应"概念学习内容"学生知识"的现状进行了调查;并对调查结果采用独立样本t检验法、单因素方差法以及一元线性回归分析法进行分析,分析结果表明教师性别、教龄、学历3因素对"学生知识"有显著影响;学习基础、学习过程、学习结果各维度对"学生知识"有不同程度的影响;最后针对教师"学生知识"存在的问题进行分析并提出了相关的改善建议。     

合成氨的微型实验

以气体实验微型装置中的双球管为主,设计了合成氨的微型实验,完成了合成氨原料气的制备、净化,氨的合成与分离及剩余尾气的收集等操作,实验前不用单独制备氢气和氮气,简单易做,可以适用于学生独立实验操作,方便了实验教学。     

我国现行“鲁科版”高中化学教材研究现状分析

山东科学技术出版社出版的《普通高中课程标准实验教科书·化学》,即“鲁科版”高中化学教材已经在我国4个省实验区,就中学化学教师和研究者对该套教材的内容评价和使用情况进行了综述和分析,其中包括教材编排体系、教材难度广度评价、实验内容、教材“栏目”和插图设计以及习题的呈现等几个主题。结果表明大多数教师和研究者认可该套教材的编排体系和内容设计,不过实施中也出现了一些问题,例如教材内容涉及知识范围较宽,实验设计安全性还需加强,插图缺乏吸引力,习题难度较大等。