4～8年级学生分数数量表征的准确性及形式

The Accuracy and Form of Fraction Magnitude Representation for 4 to 8 Graders

在分数学习中,分数数量表征是非常重要的方面。本研究利用数字线估计任务对四到八年级学生分数数量表征的情况进行探索。研究结果表明:随着年级升高,被试分数数量表征的准确性也随之提高;被试对单位分数和非单位分数表征的准确性存在显著差异,表现为对单位分数表征的准确性显著高于对非单位分数的表征,这种差异在低年级显著,随着年级的增长,差异逐渐消失;四到八年级学生在0~3数字线上,对分数数量的表征表现为线性形式而非对数形式,且这种线性表征形式是在六年级开始出现并随着年龄增长逐渐发展起来的。中西方儿童在分数数量表征的准确性和形式上有相似的发展路径,但是在表征准确性上中国儿童更高、线性形式出现年级上中国儿童可能更早。

Fraction is a useful tool for exploring the relationship between the two quantities in real life,and fraction magnitude representation plays an important role in fraction study. This study adopted number line task to investigate the patterns of fraction magnitude representation for fourth to eighth graders. The results demonstrated that：（ 1） The accuracy of fraction magnitude representation raised along with grade increasing;（ 2） The accuracy of unit fraction representation and non-unit fraction representation was different,the representation of unit fraction was significantly more accurate than non-unit fraction representation,furthermore,this difference was larger in junior grades（ fourth to sixth graders） and could be ignorable in senior grades（ seventh to eighth graders）;（ 3） Students showed linear rather than logarithmic form in fraction magnitude representation on the 0 ~ 3 number line,the linear representation emerged in sixth graders and developed gradually with age increasing. Children in China and the West have similar development path for the accuracy and form of fraction magnitude representation,while Chinese children showed higher accuracy,and the linear representation emerged earlier.