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不少数学问题,需要充分考虑题设及解答的内涵,对它们作全面深入地分析,否则,发生了错误还察觉不到。因此,在数学教学中,注意培养学生的严谨作风,是很重要的。本文从教材和教学,题设和结论几方面,通过例题作一些初步探讨。初中学生解一元二次方程ax~2+bx+c==0时,往往死套公式,一步得解。他们认为:若有实根,就隐含了判别式△≥0,不必先讨论△的值,明确根的实虚后,再进行运算。而这样做,有时就会导致错误。如下例: x~2-(k-2)x+(k~2+3k+5)=0(k∈R)的根为x_1,x_2,那么,M=x_1~2+x_2~2
Many mathematics problems need to fully consider the connotations of the questions and answers, and make a thorough and in-depth analysis of them. Otherwise, mistakes will not be noticed. Therefore, in mathematics teaching, it is important to pay attention to cultivating students’ rigorous style. This article from the textbooks and teaching, title design and conclusions, through some examples to make a preliminary discussion. When a junior high school student solves a quadratic equation ax~2+bx+c==0, he or she usually deadlocks the formula and gets a solution in one step. They believe that if there are real roots, the discriminant △ ≥ 0 is implied, and it is not necessary to discuss the value of △ first, and after the root’s real imaginaryity is clear, the operation is performed. And doing so sometimes leads to errors. In the following example: The root of x~2-(k-2)x+(k~2+3k+5)=0(k∈R) is x_1,x_2, then, M=x_1~2+x_2~2