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在数学教学中,分析评讲学生的作业情况无疑是一个环节。对部分学生作业中的一些证(解)题的好方法,应介绍给全班同学,充实数学教学;对某些学生作业中出现的一些典型错误,应进行剖析,以便使全班学生引以为戒。本文拟初中数学教学中发现的学生作业中的典型错误以剖析。不妥之处,望指正。一、概念理解不清例1. 在实数范围内分解x~2-3y~2的因式误解:x~2-3y~2=(x~(1/2)+3~(1/2)y)(x-3~(1/2)y)=(x+3~(1/2)y)(x~(1/2)+(3~(1/2)y)~(1/2)(x~(1/2)-(3~(1/2)y)~(1/2)=……。最后还莫明其妙地写上实数范围内可无限分解下去。剖析:错误的原因是对因式分解的定义理解不清,因式分解是把一个多项式化为若干个整式的积的形式,而x~(1/2)+3~(1/2)y不是有理式,因而也
In mathematics teaching, analysis and evaluation of student’s homework is undoubtedly a link. Some good methods for some of the student’s assignments (solutions) should be introduced to the classmates to enrich mathematics teaching; some typical mistakes in the homework of students should be analyzed so that the students in the class can For the ring. This article proposes to analyze the typical mistakes in student work found in mathematics teaching in junior high schools. Inappropriate, hope correcting. First, the concept of unclear understanding of the case 1. In the real number range decomposition factor x~2-3y~2 misunderstanding: x~2-3y~2=(x~(1/2)+3~(1/2) y)(x-3~(1/2)y)=(x+3~(1/2)y)(x~(1/2)+(3~(1/2)y)~(1/ 2) (x ~ (1/2) - (3 ~ (1/2) y) ~ (1/2) = .... Finally, inexplicably written in the range of real numbers can be infinitely decomposed. The reason for the error is that the definition of the factorization is unclear. The factorization is a form of a polynomial that is a product of several polynomials, and x~(1/2)+3~(1/2)y is not rational Style, and therefore also