谈高等代数理论的三条主线

提出贯穿高等代数理论的三条主线。它们是:从具体的数学对象向抽象的代数系统的转变;从各类数学对象的传统表示向统一的矩阵表示的转变;从数学对象间的具体关系向集合元素间的抽象关系的转变。     

高频词与低频词的界分及词频估算法

Mr. J.C. Donohue, in 1973, believe that there was a critical value in the demarcation of high-and low-frequency terms used in articles, and at the same time he proposed formulas of calculation. On the basis of adopting maximum value to determine grades of terms, this article brings forth and introduces a new formula of demarcating the high-and low-frequency terms which is not only simple and direct in the process of calculation but also more practical as compared with that of Mr. Donohue. Having made a study of ways of calculating for various kinds of terms with similar frequency,the article also gives a formula of calculation and reveals the inheret law governing the number of frequency of terms ans terms with similar frequency.The author holds that the frequency of terms appeared in the article and the number of terms with similar frequency have something to do with the number of different terms but have nothing to do with the length of the articles.10 formulas.5 tables.4 references.     

空间向量与立体几何

现行过渡教材(B)尝试用空间向量来处理立体几何，但作为过渡教材，还是保留大部分定理，是一种“向量代数法”与“综合演绎法”相结合的折衷做法。在新一轮的高中课程改革中，这一步我们能走多远?能否完全用向量计算来取代综合演绎?这当然是需要综合《数学教育学》的各方面因素进行平衡、取舍，才能得出最后的结果，本只是从部分角度对此问题进行一些研究，供读参考。     

应当纠正数学概念的"一名多义"现象

文章例举了代数学中三个“一名多义”的概念,剖析了由于这三个概念的“一名多义”现象导致的相关理论的混乱,呼吁应当纠正数学概念的“一名多义”现象。     

初中代数入门教学值得注意的问题

要使新生尽快适应初中阶段的学习,必须从数的概念和具体显现形式的多样性、初中与小学数学内容之间的联系等方面,注重入门阶段的学习,同时,还要运用直观教学,创设情景,趣引新知识,灵活运用多种教法,尽快促使学生实现学习方式的和观念的转变.