浅谈中学数学教学中的反例

在新的<数学课程标准>中,要证明一个命题正确,必须经过严密的推论,而要否定一个命题,却只需要能举出一个与结论相矛盾的例子就行,这个与命题相矛盾的例子便称为反例.反例是简明有力的否定方法;反例是加深理解的重要手段;反例是纠正错误解答的常用办法;反例可以发现问题;构造反例是活跃思维的一种途径.     

我该怎样选择？——《一次函数图像》互动课程

互动课程是在“支架式学习”理论和学生认知的“临近发展区”理论指导下，以问题为导向，利用由计算机和互联网构建的具有良好交互性的学习软件，开展学习和自主探究的新型课程。互动课程通过互动的多媒体活动程序，为学生提供了学习活动的支架，使学生能够进行比较复杂的学习活动，并投入到高级的思考和问题解决活动中去。在互动课程的实施中，教师运用认知的支架来促进复杂的思考，     

全球化背景下文化冲突的深层根源

经济全球化本身是一个涉及每个民族国家的政治和文化的复杂过程.其中,经济全球化与世界范围内文化的多元化、多样化会不会发生矛盾,会发生怎样的矛盾,就是一个经常引起人们深入思考的问题.     

蚕食鲸吞

不同的进食方式一个细嚼慢咽,一个大口吞食,这是蚕和鲸不同的吃饭方式。想一想,造成这种差异的原因是什么?没错,主要原因就是它们的身体构造不同。     

添加梯形辅助线方法探索

辅助线对处理复杂的图形问题非常重要．通过构造辅助线，复杂的图形可以分解成简单的图形．现以求解梯形问题为例与同学们共同研究．     

构造全等三角形解四边形问题

全等三角形和四边形知识联系非常紧密，四边形的许多性质、定理都是用全等三角形知识导出的．因此，运用几何转换，适当构造全等三角形，有助于四边形问题的解决。     

Fuzzy Comprehensive Assessment Method to Determine Tectonic Stress Patterns

The tectonic stress patterns were determined by a fuzzy comprehensive assessment method. Data of in-situ survey and fault information were utilized in the method. First, by making pressure and tension in the directions of along-river, cross-river, shear clockwise, and shear counterclockwise , 26 types of tectonic stress patterns were presented. And the stress vector of each pattern was obtained with FE software by taking unit displacement as boundary load. Then, by taking the 26 types of tectonic stress patterns as index set and 3 main stresses as factor set and choosing various operators, comparison of directions of computational stress vector and survey stress vector was made and the most possible tectonic stress pattern was obtained. Taking the 26 types of tectonic stress patterns as index set and strike angle as factor set, comparison of relationships between formation of fault and tectonic stress was made,and the tectonic stress patterns were assessed with known fault information. By summarizing the above assessment results, the most impossible tectonic stress pattern was obtained . Finally an engineering case was quoted to validate that the method is more feasible and reliable than traditional empirical method.     

构造三元齐次线性方程组解题

本文介绍构造三元齐次线性方程组,应用其有非零解的充要条件是它的系数行列式为零的定理,对部分代数、几何、三角问题和著名的牛顿“牛吃草”问题进行巧思妙解。     

运用构造法求最值

一、构造一元二次方程法例1 已知x为实数,求函数y=3x2+x+2/x2+2x+1的最小值. 解:将原函数解析式变为关于x的二次方程: (y一3)x2+(2y-1)x+(y-2)=0. 因为x是实数,所以△≥0. 即(2y-1)2-4(y-3)(y-2)≥0. 解得y≥23/16.