三~六年级学生分数概念的错误理解及其发展

Misconceptions and Development of Grades 3 to 6 Students on the Concepts of Fractions

基于分数的7个子概念,采用4套包含式问卷,选取306名三~六年级学生,考察其分数概念的错误理解类型及发展趋势.结果发现,三~六年级学生出现的主要错误是:错误理解“等分”概念,错误理解“单位量”概念(包含3个子类型),不会用数线表示分数与错误理解“等值分数”概念(包含3个子类型)等8类错误;其中6类错误的错误率峰值出现在四年级,两类出现在五年级.重要的顽固型错误是:四年级学生错误理解“等分”概念;五年级学生错误理解“单位量”“分数在数线上的表示”概念.建议:在四年级适当加入分数内容;提高三年级“等分”“单位量”概念、五年级“分数在数线上的表示”概念的教学比重;教师应当对8类主要错误有针对性地进行教学.

Based on the seven subconcepts of fractions,using four sets of inclusive questionnaires,306 students in Grades 3 to 6 were selected to investigate types of misconceptions and development trends.It was found that the main mistakes were as follows:misunderstanding the concept of“equipartitioning,”misunderstanding the concept of“one whole”(including 3 subtypes),not using the number line to represent the fraction,and misunderstanding the concept of“equivalent fraction”(including 3 subtypes).The peak rate of 6 types of mistakes appeared in Grade 4,and the others appeared in Grade 5.Students made persistent mistakes in the seven subconcepts of fractions:Grade 4 students had the most mistakes on the concept of equipartitioning and Grade 5 students had the most mistakes on the one whole concept and the representation of fractions on the number line.We propose the following suggestions:Offer appropriate fraction content to fourth grade;provide more opportunities for students to learn the concepts of equipartitioning and one whole in the third grade and the expression of fractions on the number line in the fifth grade;and teachers should pay more attention to major mistakes.