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以平方差公式为例,人教版初中课本中的乘法公式是这样引入的:我们来计算:(a+b)(a-b)(a+b)(a-b)=a2-ab+ab-b2=a2-b1,即(a+b)(a-b)=a2-b2①然后把①式当作公式,并列举了大量形式多变的例子来套用此公式。课本的这种编排方式简明扼要,逻辑性强,可以充分体现用字母代替数字的优越性以及字母可以代替更为复杂的代数式这一优越的数学符号思维。展现了数学的简洁美。但是,相对于初一学生的认知水平来说,这一教学过程却存在着三个难以克服的弊病:(一)在初一学生眼中,(a+b)(a-b)只不过
Take the squared difference formula as an example. The multiplication formula in the junior high school textbook for PEP is introduced as follows: Let us calculate: (a+b)(ab)(a+b)(ab)=a2-ab+ab-b2= A2-b1, ie, (a+b)(ab)=a2-b21 Then treat Formula 1 as a formula, and list a large number of examples of variants to apply this formula. This arrangement of textbooks is concise and logical. It can fully embody the superiority of using letters instead of numbers and letters can replace the more complex algebraic type of mathematical thinking. Shows the simplicity of mathematics. However, there are three insurmountable shortcomings in the teaching process compared to the level of cognitive performance of the first grade students: (a) In the eyes of junior students, (a+b) (a-b) is only