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解不等式可谓是内容纷多,形式异样,学生对这部分内容的掌握历来较为薄弱。下面是我们在解不等式(不包括证明)教学中培养能力的几个片断。在一元高次不等式的教学中,为了培养探索能力,我们的做法是: (一)设计问题、诱发探索例1 解不等式(x+3)(x-1)(x-2)>0。怎样解?这一问学生思维展开,产生两种解法: ①考虑x+3,x-1,x-2的符号,或三个同正,或一个为正,两个为负。相应地列出四个不等式组来解。
The inequality can be described as having many contents and inconsistent forms. Students’ grasp of this part of content is always weak. The following are several segments of our ability to develop in teaching in inequality (excluding proof). In the teaching of one-dimensional high-order inequality, in order to cultivate the ability to explore, our approach is: (a) design problems, induced exploration examples 1 solution inequality (x+3) (x-1) (x-2)>0. How to solve this question? This student asks to develop two solutions: 1 Consider the symbol of x+3, x-1, x-2, or three of the same positive, or one of positive, and two of negative. List the four inequalities accordingly for solution.