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笔者在多年的教学实践中,发现有时学生的解法乍看似乎有一定的道理,甚至于他们的答案也与标准答案一致.但如果仔细推敲,就可以发现其中隐性的错误.这些错误的产生,有些是因为对知识的理解不到位;有些是因为对解题方法的掌握不完备;有些是因为学生的思维不缜密等等.下面,笔者结合具体的问题进行评析:1因片面理解概念致错题1已知命题p:存在实数m,使得m+1≤0,命题对任意,都有,若且q为假命题,求实数m的取值范围.q:x∈R2x+mx+1>0p错解且为假命题,∴与q中至少有一个为假命题.不妨设两个命题均为真命题,当真时,∵p q p p
In the years of teaching practice, the author discovered that sometimes the students’ method of solution seems to have some truth at first glance. Even their answers are consistent with the standard answers. But if they are carefully scrutinized, they can find hidden mistakes. These mistakes are produced. Some of them are because the understanding of knowledge is not in place; some are because of the incompleteness of the methods for solving problems; some of them are because the students’ thinking is not careful and so on. Hereinbelow, the author makes an analysis based on specific issues: 1 Due to a one-sided understanding of the concept Wrong problem 1 Known propositions p: There are real numbers m such that m+1 ≤ 0, propositions are arbitrary, and if q is a false proposition, the range of values for real numbers m is .q: x∈R2x+mx+1 >0p is a false solution and is a false proposition. At least one of ∴ and q is a false proposition. It may be possible to set two propositions as true propositions. When true, ∵pqpp