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(一) 在数学教学中应当指导学生扎扎实实地练好基本功。数学教学中的基本功,就是“正确地理解数学概念,巩固地掌握定理、公式,计算正确、熟练,能够进行综合运算。”由于数学本身具有高度的抽象性、概括性,再加上中学生的认识水平有限,中学生在学习数学的时候,对于概念、定理、公式、法则的认识,在最初的阶段,总是或多或少地带有表面性和片面性,有时还会产生一些混淆或者错误。例如,在数学教学中,通过圆的面积与半径,匀速运动的路程与时间、单价一定的货物的总价与数量这些具体事实抽象出函数概念时,学生就可能产生“一个量的变化引起另一个量的变化,这就是函数关系”的假象。导出了函数的定义以后,教师提出问题:“田地的收获量与施肥量之间是否存在着函数关系?”许多学生都认为:“存在着函数关系。这是因为施肥量的变化将引起收获量的变化。”教师进一步提出:“已知在一亩麦地里施了五担粪肥,可以收获多少呢?”学生就会发现:虽然收获量与施肥量有关,然而仅由施肥量的数
(1) In mathematics teaching, students should be instructed to practice basic skills in a down-to-earth manner. The basic work in mathematics teaching is to “accurately understand the concept of mathematics, consolidate the theorem and formula, and calculate correctly and skillfully, and be able to perform comprehensive calculations.” Because mathematics itself has a high degree of abstraction and generality, coupled with the understanding of middle school students The level is limited. When middle school students study mathematics, their understanding of concepts, theorems, formulas, and rules is always more or less superficial and one-sided, and sometimes it causes some confusion or mistakes. For example, in mathematics teaching, when the concept of function is abstracted from the specific facts of the area and radius of the circle, the distance and time of uniform motion, the total price and the quantity of the unit price of a certain goods, the student may produce “a change of quantity to cause another A quantitative change, this is the illusion of a functional relationship. After deriving the definition of the function, the teacher asks the question: “Is there a functional relationship between the amount of harvested land and the amount of fertilizer applied?” Many students believe that: “There is a functional relationship. This is because changes in the amount of fertilizer will cause harvests. The teacher further pointed out: ”How much can we harvest by knowing how to harvest five manure in an acre of wheat?" Students will find that although the amount of fertilizer is related to the amount of fertilizer, only the amount of fertilizer is used.