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初中算术教材里关于小數除法所要研究的,就是小数除以整数的除法。如果这一法则得出了,这末,当小数除以小数时,只要把被除数和除数扩大同样的倍数,使除数变成整数,就成了小数(或整数)除以整数的除法,小数除以整数的除法中,有时需要取近似商。决定不足近似商与过剩近似商,二者的取舍的法则是:“在精确到指定的同一小数位的不足近似商和过剩近似商里,为了使所取的近似商的誤差小于这个指定的小数位上的單位的1/2,如果除到这个小数位,所得的余数(引者註:把它当整数看)小于除数的1/2,就取不足近似商;如果所得的余数大于除数的1/2,就取过剩近似商。”(初中算术§111)。由于这一教材內容对于初一学生来说,是較难理解的,因此每当教师教完这一节以后,常常会發現学生对这个法則只是机械地掌握了,而对它的理論根据却不甚了然,教师对于这一法則原理的教学,在效果上便常常流于形式主义,今根据个人的点滴体会談一談就正于大家。
The study of decimal division in junior high school arithmetic textbooks is the division of decimal numbers by integers. If this rule is obtained, then when dividing a decimal by a decimal, if you divide the dividend and the divisor by the same multiple and make the divisor an integer, it becomes a division of a decimal (or integer) divided by an integer. In the division of integers, it is sometimes necessary to take approximate quotients. Determine the deficiencies approximation quotient and excess approximation quotient. The rule for the tradeoff between the two is: “In order to make the approximate quotient’s error less than the specified decimal point, the exact quotient and the excess approximation quotient are exactly the same as the specified decimal places. 1/2 of the units on the bit, if the remainder is divided by this decimal place, the resulting remainder (see the note as an integer) is less than 1/2 of the divisor, which is less than the approximate quotient; if the resulting remainder is greater than the divisor, 1/2, to take the surplus quotient.” (Junior arithmetic §111). Because the content of this teaching material is difficult for the students of the first grade, it is often found that after the teacher completes this section, the students often find that the rule is only mechanically controlled, but the theoretical basis for it is not. It is even more obvious that teachers’ teaching of this principle of principle is often in formality in terms of effectiveness. Today, according to the personal point of view, it is just for everyone.