上海二年级学生运用加法交换律的探索性研究

An Exploratory Study of Second Grade Students’Learning and Usingthe Commutative Property of Addition in Shanghai

运算律是小学数学运算的重要性质,对学生学习后继数学课程具有重要的意义.围绕二年级学生如何在不同的数学情境中运用加法交换律这个问题,采用纸笔测试与访谈的办法对上海市区一所小学的24名二年级学生进行调查.研究发现:被选择的二年级学生能运用加法交换律直接判断形如“a+b=b+a”的等式成立,但是从学生所举的例子来看,由于他们对加法认识的局限性妨碍了对加法交换律的理解.在对常规的两位数和3位数的连加运算中,约60%的学生能运用加法交换律进行简便计算,然而只有不到30%的学生能自觉运用交换律进行推算,这也间接地表明学生只是在行动中运用了运算律,但是还没真正达到概念化的程度.

Arithmetic operational properties are important in elementary school and play a significant role in students’further studies in mathematics.To address the problem of how students apply the commutative property of addition in different mathematical situations,this study was designed to investigate 24 second-grade students in an elementary school in Shanghai using a pencil-and-paper test and individual interviews.The research found that select students in second grade could use the commutative property of addition to directly judge whether an equation,such as“a+b=b+a,”is established.About 60%of the students could utilize the commutative property of addition as a short-cut strategy to quickly calculate addition involving two-digit and three-digit numbers,but they had some misconceptions in realistic contexts because of their limited understanding of addition.However,only 30%of the students could consciously use the commutative property of addition in computation deductively.The results suggest that many students are able to use the commutative property in direct computation,but they haven’t achieved a conceptual understanding of the commutative property.