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较复杂的分数除法应用题历来是教学的重点,难就难在学生会将诸如“男生比女生多1/3”理解为“女生比男生少1/3”。对此,我曾在教学中对学生进行单项训练,让学生用关键句写关系式(男生比女生多1/3,数量关系式是:女生人数乘以(1+1/3)=男生人数),以求避免出现上述错误。然而错误还是难以避免,一旦给出完整的应用题,仍有相当部分学生会那样思考。造成错误的主要原因是旧知识对新知识的干扰,表现在:(1)“差比”对“倍比”的干扰。例如,“男生比女生多5人,就是女生比男生少5
The more complicated problem of fractional division is always the focus of teaching. It is difficult for students to interpret ”1/3 more boys than girls“ as ”less than 1/3 less girls than boys.“ In this regard, I used to teach students a single training, allowing students to use the key sentence to write the relationship (boys and girls more than 1/3, the quantitative relationship is: multiplied by the number of girls (1 + 1/3) = number of boys ), In order to avoid the above error. However, the mistake is still hard to avoid. Once the complete application is given, quite a few students still think that way. The main reason for the error is the interference of old knowledge on new knowledge, manifested in: (1) the interference of ”worse than“ to ”multiplier“. For example, ”5 more boys than girls, 5 less girls than boys