广义Fibonacci数列的性质定理

在文[1]中,我们已推广著名的Fibonacci数列成为第一型与第二型广义Fibonacci数列,建立了它们的通项公式、前n项和公式与其增长率数列的收敛定理,现在我们继续研究广义Fibonacci数列的性质,并建立广义Fibonacci数列的性质定理与数学模型.     

Fractions as the Coordination of Multiplicatively Related Quantities: A Cross-Sectional Study of Children's Thinking

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared) in their solutions to equal sharing problems and to see to what extent this coordination was multiplicative. A secondary goal was to document children's solutions for equal sharing problems in which the quantities had a common factor (other than 1). Data consisted of problem-solving interviews with students in 1st, 3rd, 4th, and 5th grades (n=112). We found two major categories of strategies: (a) Parts Quantities strategies and (b) Ratio Quantities strategies. Parts quantities involved children's partitions of continuous units expressed in terms of the number of pieces that would be created. Ratio quantities involved children's creation of associated sets of discrete quantities. Within these strategies, children drew upon a range of relationships among fractions, ratio, multiplication, and division to mentally or physically manipulate quantities of sharers and things to produce exhaustive and equal partitions of the items. Additionally, we observed that problems that included number combinations with common factors elicited a wider range of whole-number knowledge and operations in children's strategies and therefore appeared to support richer interconnections than problems with relatively prime or more basic number combinations.     

电磁学解题点窍

在电磁学教学中,用具体实例将知识点窍、逻辑推理、解题过程贯穿于整个解题过程中,帮助学生克服解题困惑,提高解题能力.     

"问题解决"与创新素质培养

“问题解决”国际数学教育界较为流行的一种教学模式。数学学科重视“问题解决”教学 ,有利于培养学生的创新意识 ,训练学生的创新思维 ,发展学生的创新个性 ,锻造学生的创新品质     

连锁与交换规律计算问题的研究

针对连锁与交换规律的计算问题,提出了一组完整、严密、科学的计算公式。1 当无双交换或更高数目的偶数交换时,则:重组率=交换值=图距%=重组合表型的百分率。2 当有双交换或更高数目的偶数交换时,则:单交换Ⅰ(或单交换Ⅱ)的重组率=单交换Ⅰ(或单交换Ⅱ)的交换值=图距%;单交换Ⅰ(或单交换Ⅱ)表型(或配子)的百分率=单交换Ⅰ(或单交换Ⅱ)的重组率-双交换表型的百分率-更高数目的偶数交换表型的百分率;两端基因的交换值=单交换Ⅰ的重组率(或交换值)+单交换Ⅱ的重组率(或交换值)=单交换Ⅰ表型(或配子)百分率+单交换Ⅱ表型(或配子)的百分率+2×双交换表型的百分率或更高数目的偶数交换表型的百分率=图距%。     

关于数学归纳法教学的改进

就当前数学归纳法教学中存在的问题,从发现法的角度探讨了教法的改进.结合实例阐明了问题解决的观点和方法     

转化法在数学解题中的应用

本文通过例题说明转化法在数学解题中的应用     

Teaching Critical Thinking and Problem Defining Skills

Critical thinking and skills in defining problems have been among the goals of a computers and society course that had its credits reduced and student number increased. In an attempt to prevent worsening the students' learning, four measures were taken. The results actually improved from a failure rate of 21.5% to 0.7%. This was mainly due to tighter project structure and additional student work. Reduced course material and improved teacher preparation did not seem to have any effect, while more focused project teaching may have contributed to the decreased failure rate. Further improvements may be gained through time estimation in the problem definition process.     

解数学题的基本方法只有两种吗?

本文从揭示解数学题这一过程的实质入手,科学地指出解数学题的基本方法恰有三种,而不是通常所认为的只有综合法和分析法两种,并指出了RMI法也只是第三种基本方法中的一种。     

动态生成观下高等数学解题预设分析

基于动态生成教学理念,以数学解题教学设计为入手点,利用解题预设的典型案例,对如何进行教学预设,如何更有效地改进数学解题教学,如何更有效地促进动态资源的生成进行初步研究,生动地诠释了“动态生成观”在数学解题教学中的应用。