p维向量型Dirichlet级数的收敛性

研究了p维向量型Dirichlet级数的收敛性、一致收敛性及绝对收敛性 ,以及收敛平面及收敛半平面上的收敛性、一致收敛性及绝对收敛性 ,给出了p维向量型Dirichlet级数的收敛横坐标、一致收敛横坐标、绝对收敛横坐标及Valiron(瓦里隆 )公式 .     

An Ode to Imre Lakatos: Quasi-Thought Experiments to Bridge the Ideal and Actual Mathematics Classrooms

This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom discourse that conveys the Lakatosian (thought-experimental) view of mathematics as that of continual conjecture-proof-refutation which involves rich mathematizing experiences. I present a pathway towards this pedagogical goal by presenting student insights into an unusual counting problem and by using these outcomes to construct ideal mathematical possibilities (content and process) for discourse. In particular, I re-construct the quasi-empirical approaches of six!4-year old students’ attempts to solve this unusual counting problem and present the possibilities for mathematizing during classroom discourse in the imaginative spirit of Imre Lakatos. The pedagogical implications for the teaching and learning of mathematics in the secondary classroom and in mathematics teacher education are discussed.     

有关自然数的平方剩余和因子积的几个渐近公式

本文的主要目的是研究有关因子积序列和平方剩余的渐近性质。得到有关这两个序列的渐近公式。     

关于思维和问题解决的几种研究评析

心理学中很早就开始了关于思维和问题解决的研究。归结起来主要有:实验内省法、生理解释理论、尝试和错误解释说、顿悟解释说和信息加工解释说。这些研究均曾做出了应有的贡献,但其仍然存在着一些不足。探讨这些不足有助于以后更为健康地开展此类研究。     

Keiyo Cattle Raiding, Kechui Mathematics and Science Education: What do They Have in Common?

In the context of globalization, indigenous educational systems of endangered cultures are faced with extinction. Biologists recognize that biodiversity is dependent upon sustaining and promoting knowledge and values of indigenous cultures. Education researchers have a similar responsibility — to promulgate educational diversity before several thousand years of valuable educational knowledge is extirpated. This paper presents the Keiyo of Kenya who have a rich educational system. Its focus is on an indigenous game, Kechui (using calculations to sharpen your mind), based on cattle raiding, and the Keiyos' use of the game for learning mixed strategy-based probabilistic problem solving. Kechui may also have international potential for teaching probabilistic problem solving in contemporary mathematics and science, especially genetics.     

Problem-Solving Preferences of Mathematics Teachers: Focusing on Symmetry

The aim of the study presented in this paper was to explore factors that influence teachers' problem-solving preferences in the process of (a) solving a problem, (b) explaining it to a peer, (c) liking it, and (d) teaching it. About 170 mathematics teachers took part in the different stages of the study. A special mathematical activity was designed to examine factors that influence teachers' problem-solving preferences and to develop teachers' preferences concerning whether to use symmetry when solving the problems. It was implemented and explored in an in-service program for professional development of high-school mathematics teachers. As a result, three interrelated factors that influence teachers' problem-solving preferences were identified: (i) Two patterns in teachers' problem-solving behavior, i.e., teachers' tendency to apply a stereotypical solution to a problem and teachers' tendency to act according to problem-solving beliefs, (ii) the way in which teachers characterize a problem-solving strategy, (iii) teachers' familiarity with a particular problem-solving strategy and a mathematical topic to which the problem belongs. Findings were related to teachers' developing thinking in solving problems and using them with their students. The activity examined in this paper may serve as a model for professional development of mathematic teachers and be useful for different professional development programs.     

合作讨论和元认知监控与排列组合问题的解决

排列组合问题是高中数学的一个重要内容,也是与日常生活密切相关的一个主题.合作讨论、元认知监控和成功解决排列组合问题之间的内在关系密切.合作讨论会导致较高层次的元认知监控,高层次的元认知监控会导致更大的解题成功率.     

对一道几何问题的思索及推广

初等数学中几何题型变化万千,题目数不胜数,给学生解题带来了一定的难度.因此,教师在教学中一定要因材施教,这样,对培养学生的系统性和灵活性大有好处.     

“主体性问题解决”课堂教学模式初探

本文提出了数学教学当中“主体性问题解决”教学模式的理论依据、特点、基本流程图及教学实施原则