对两道数学题的解法探究

我教数学"期望"时给学生布置了这样一道题: 例1 一射手对靶射击,直到第一次命中为止,每次命中率为0.6,现有4颗子弹,命中后剩余子弹数目ξ的期望为( )     

How Quality of Writing Instruction Impacts High-risk Fourth Graders’ Writing

From a larger longitudinal study of 610 fourth graders in 17 inner city schools, 40 students were randomly selected from 10 classrooms rated high (i.e., top quartile) or low (i.e., bottom quartile) in quality of writing instruction in grades 3 and 4. The written compositions of these students were scored in three ways: (1) according to a rating scale within a reliable scoring rubric, (2) according to countable surface features such as words correctly sequenced, and (3) according to the frequency of specific phonological, morphosyntactic, and orthographic errors in the children’s writing. A multivariate analysis of variance was conducted to examine whether quality of writing instruction in grades 3 and 4 predicted students’ writing performance at the end of grade 4. Students who received high quality instruction in fourth grade wrote longer compositions with more correctly spelled words than those who had poor quality writing instruction. There was a tendency for two years of quality instruction to be better than one, and, among students who had poor quality instruction in grade 3, compositions were longer in grade 4 when they received quality instruction in fourth grade. Foundational problems of language formulation, production and representation, however, were ubiquitous across the sample. Although these students were within the average range on standardized reading tests, spelling and writing were not developing at average levels. The study confirms the urgent need for more and better writing instruction for high risk, minority children.     

化归思想在数学分析解题中的应用

化归思想是数学中解决问题的一种重要思想方法。本文就极限、微分学以及积分学三个方面的问题讨论 ,论述了化归思想在数学分析解题中的广泛应用     

财务问题的初等数学方法巧解

通过举例的方法,论证说明了许多财务问题可以用初等数学方法进行巧解,旨在帮助财务管理人员便捷地进行财务预测决策分析,并为数学方法在求解财务问题中的运用与推广提供理论指导.     

Instructional Procedures for Increasing Skill‐Deficient Fourth Graders’ Comprehension of Syntactic Structures

Comprehension of pronoun‐referent structures has been shown to cause difficulty for children throughout the middle grades. This study investigated the effectiveness of a pronoun‐specific approach using principles of systematic instruction in teaching students to identify pronoun antecedents and to answer factual questions based on this knowledge. This approach was contrasted to both a retell method (where the students practised paraphrasing the text) and a no intervention condition. Forty‐five fourth grade students (identified by a screening test as skill deficient) were randomly assigned to one of these three treatment groups. Students in both the pronoun‐specific and the retell group received 20 minutes of individual instruction per day for three consecutive days. On the day following treatment, all three groups were given two tests, one assessing the identification of pronoun‐referent structures and one requiring the child to answer factual questions based on the comprehension of these structures. Maintenance tests were given two weeks later. All passages in the teaching sessions and the test materials were selected from social studies or science texts currently approved for school district use. Results of an analysis of variance with planned comparisons indicated a significant difference favouring the pronoun‐specific group on the identification of pronoun antecedents. These results were also replicated on the maintenance test. No significant differences were found on measures of factual comprehension.     

数学工具主义者对归纳问题的认识论分析

在数学证明的过程中,人们经常使用的方法是数学归纳法。数学归纳法体现的是从有限上升到无穷的过程。根据希尔伯特的术语,有限体现的是实在数学,无穷体现的是理想数学。希尔伯特工具主义者坚持用理想数学替代实在数学,这就是元数学替换策略。但这种策略在归纳上有两个亟待解决的问题。首先是归纳的地位问题。这是数学哲学中的认识论问题,人们需要在有限思维中确定归纳的位置。其次是元数学替换策略是一种非直谓主义,这就招致了庞加莱的反对。庞加莱持一种直谓主义的观点,他认为希尔伯特的元数学使用了循环论证。希尔伯特工具主义者通过对证明模式的分析,解决了第一个问题。通过区分两种不同归纳,解决了第二个问题。通过对庞加莱问题的解决,希尔伯特工具主义者引出了他们的改良实在论,也就是在抽象元素中加入具体事物,而在有限思维中加入抽象对象。这就为我们提供了一种解决贝纳塞拉夫问题的方案。     

数学复杂度对物理综合问题解决的影响

将物理综合问题分为顺时性物理综合问题和同时性物理综合问题,探讨这2类物理综合问题的数学复杂度对学生解决物理问题的影响。研究发现,数学复杂度不影响学生解决顺时性物理综合问题,但影响学生解决同时性物理综合问题。这一结果对高考物理命题的设计有一定的启示,可以将物理综合性试题进行分类,针对不同学生水平设计有难度梯次的试题,从而提高高考物理试题的区分度。     

用三角代换解竞赛题

数学竞赛中的某些代数问题用代数方法求解较为复杂，若能根据题目条件与结论的结构及内在特征，恰当地进行三角代换，往往能化繁为简，化难为易．     

数理逻辑主要解题方法及疑点剖析

数理逻辑是离散数学的重要组成部分,是学好离散数学的基础。由于概念抽象、推理独特、方法灵活等原因,学生学习困难,对问题不易入手解决。本文通过解析疑点,归纳主要解题方法,使学生掌握解题方法的要领,提高分析问题和解决问题的能力。     

特征分析思想在解数学竞赛题中的应用

本文结合例题介绍特征分析思想的应用.1关系式特征数学竞赛题中,常会给出一些关系式,有的时候可恰当地转化关系式的形式,使之与我们学过的某些知识建立起联系,从而找到解题的切入点.例1已知a、b、c为△ABC的三边长,且满足a2=b2 bc.求证:∠A=2∠B.分析:考虑到已知条件给出的关系式的特征a2=b2 bc=b(b c),a.a=b.b b.c.比较这两种特征,我们可以联想到相似三角形中的比例关系,同时可以构造图形来解此题.图1证明:如图1,延长CA到D,使得AD=AB=c,则CB2=CA.CD.所以,CB为△ABD的外接圆过点B的切线.注意到∠ABC=∠ADB=∠ABD,故即∠A=2∠B…     

数学分析教学中常见问题的解读

针对数学分析教学的经典概念作较本质的剖析,对典型问题从几何或物理的角度进行较形象的处理,并用哲学的思想对重要概念或定理作较深入的思考,借以提高学生的学习兴趣、理解能力与创新能力.     

大学生数学思维的难点分析

大学生数学思维困难已经成为一个较为普遍的校园现象，本文从数学学科的本质特点、历史渊源、教育模式三方面分析了其产生的原因，剖析了两种主要的表现形式——“印象画”欣赏现象和“抖口袋”现象，认为：在大学数学教学中，突出所授知识的本质特征，提高学生模式再认的能力，以及注重生活中的合情思维在科学中的迁移，诱导启发学生在科学中的合情思维是提高大学生数学思维能力的重要方法。     

新时期文坛"鸡肋"现象透析

新时期文坛表面上的繁荣热闹掩盖不了作家创作底气的不足。克服文坛存在的低速、庸俗与浮躁的种种弊端，需要信仰和崇高的精神本质。     

数学奥林匹克问题

本期问题 初105 △ABC的重心G关于BC的对称点是G′。问:△ABC的三条边应满足怎样的充要条件,才能使A、B、G′、C四点共圆?证明你的结论。 (黄全福 安徽省怀宁县江镇中学,246142) 初106 求证:方程     

面向21世纪师专数学与应用数学专业数学分析课程改革的几个问题

简要论述了当前师专教学与应用数学（师范类）专业“数学分析”课程教学改革的几个问题,提供了可供参考的具体实施方案。     

解题小品——架桥结网

例1 10名选手参加乒乓球赛,每两名选手对赛一局．如果选手i胜选手j,选手j胜选手k,选手k胜选手i,则称为有一个“三角形”．设Wi和Li分别表示第i名选手胜和败的局数,     

用问题驱动的大学数学教学实践

一种新的教学模式：从一道常微分方程的解法不断衍生一些相关的问题,这些问题驱动作我们对这种微分方程——非齐次线性方程的解法进行不断探索,从而对比较系数法有了更深的理解。     

复变函数解题错误分析举例

对复数的运算、复变函数积分及级数等方面的习题求解过程中学生常出现的错误及出现错误的原因进行了分析,并将学生的错误解答与正确解法进行比较,从而得出解题的整体思路和一般规律,培养了学生的数学思维能力.     

大学新生心理健康状况分析及对策

大学新生处在从青少年向成年的转型期和从中学到大学的跨越期。因学习任务、生活环境发生了很大的变化,部分新生抑郁苦闷,情绪低落,自我评价失调,一时不能适应新的环境,人际交往困难。大学新生的心理健康教育应引起有关部门的重视,因为它不仅关系到大学新生未来的健康成长,而且与学校人才培养的质量息息相关。