中学生分式加减与乘除运算错误研究

摘要

Negative transfer is one of the reasons that causes computing errors in the secondary students' computing of fractional addition and subtraction as well as fractional multiplication and division. Among low cognitive level group of students, Fractional addition and subtraction shows significant forward transfer to fractional multiplication and division (negative migration). Fractional multiplication and division operations shows significant forward transfer to fractional addition and subtraction (negative migration). But, Fractional addition and subtraction shows little reverse migration to computing of fractional multiplication and division. Computing of fractional multiplication and division shows little forward transfer to fractional multiplication and division operations. While among high cognitive level group of students, fractional addition and subtraction shows little backward transfer or forward transfer to fractional multiplication and division, the higher cognitive level students have, the less degree transfer happens, Otherwise the higher.%中学生分式加减法和乘除法运算学习中的负迁移是导致运算错误的原因之一．在低认知水平组学生中，分式加减法运算对乘除法运算有显著的顺向迁移（负迁移）．分式乘除法运算对加减法运算有显著的逆向迁移（负迁移）．但是，分式加减法运算对乘除法运算的逆向迁移和分式的乘除法运算对加减法的顺向迁移都不显著．在高认知水平组学生中，分式加减法运算和乘除法运算之间的顺向和逆向迁移都不显著．学生认知水平愈高则发生上述迁移的程度就愈小，反之则愈大．