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在考查学生的知識貭量时常常发現,有許多数学概念,学生并沒有掌握它的本貭,而只是从表面形式上去了解它,以至产生各种各样的錯誤。例如,由具体数值引入文字符号时,总认为a是正数,-a是負数,甚至在高三学习复数时还出現:当a<0时(-a)~(1/2)==a~(1/2)i。比較a与2a的大小时,就肯定2a>>a,不从a的值分別研究。对于无理数的概念认識不清,以为开平方就得无理数。解方程lgx~(lgx)=1时,得x1=1,x2=10,等等。有的同学机械模仿,乱套公式,不考虑条件把某些性貭和結論随便推广。例如
When examining a student’s knowledge, he often discovers that there are many mathematical concepts. Students do not grasp its essence, but only understand it from the surface form and make all kinds of mistakes. For example, when a literal symbol is introduced by a specific numerical value, it is always considered that a is a positive number, -a is a negative number, and even when the third grade learns the complex number: when a <0 (-a) ~ (1/2) == a ~ 1/2) i. When comparing the sizes of a and 2a, it is certain that 2a >> a, not from the value of a separately. The concept of irrational number is not clear, that is, to open the square have irrational number. Solve equation lgx ~ (lgx) = 1, we have x1 = 1, x2 = 10, and so on. Some students mechanical imitation, arbitrary formula, regardless of the conditions of some of the sexes and conclusions casually promotion. E.g