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如何使学生在深刻透彻理解所学知識的基础上达到牢固地掌握,从而在实践中能熟练、正确的运用,是提高数学教学貭量的中心环节。下面,就这个問題,談几点体会。一、闡明問題的关鍵,搞清問題的本貭要想掌握一个定义、定理、公式或者法則,必須善于抓住其中最根本的东西。例如,在算术中讲成正比例的量的定义时,学生往往认为“甲量增大,乙量也随之增大,則称乙量与甲量成正比例”。其实,这是不对的,他們忽略了定义中最根本的东西——“增大同样倍数”。为了闡明这个关鍵,可以举出下面的例子: “掘一井,第1米用10分钟,第2米用12分钟,以下每深一米,多用2分钟。这样,掘井的米数与所花时間成正比例嗎?为什么?”听取囘答以后,着重指出:量虽然都增大了,但不是增大同样倍数,因而不成正比例。又如在代数中讲因式分解时,学生往往演算到
How to enable students to acquire a firm grasp on the basis of a profound and thorough understanding of what they have learned, so that they can skillfully and correctly use it in practice is a central link in improving mathematics teaching. Below, on this issue, talk about a few experiences. I. The key to clarifying the issue and clarifying the issue is to master a definition, a theorem, a formula, or a rule. It must be good at grasping the most fundamental thing. For example, when speaking about the definition of a proportionate quantity in arithmetic, students often think that “A quantity will increase and B quantity will increase. Then, B quantity is proportional to A quantity.” In fact, this is wrong, they overlooked the most fundamental thing in the definition - “enlarge the same multiple”. In order to clarify this key point, the following example can be cited: “Dig I-well, 10 minutes for the first metre, 12 minutes for the second metre, followed by one metre per second, and 2 minutes more. In this way, the number of wells dug Is the time spent in a positive proportion and why?” After listening to the answer, I emphasized that although the amount has increased, it does not increase the same multiple and is therefore not proportional. Again, when factoring in algebra, students often run into