分数图式进阶模型有效性检验与学生表现分析

Verification of Fractional Schema Progression Model andAnalysis of Chinese Primary School Students’Performance

以分数图式进阶理论为理论基础,编制了分数图式进阶测评工具,对402名使用北师大版和人教版数学教材的六年级小学生的分数图式发展情况进行了分析.测验结果显示,该测验工具的质量较高,符合RASCH模型的单维性假设;中国小学生的分数推理的发展顺序与分数图式理论模型基本一致,在迭代分数图式以及分配均分图式两个阶段的发展与理论稍有差异;使用人教版的小学生在一部分分数图式阶段上的表现优于使用北师大版的学生.建议设计能够促进小学生分数图式发展的操作性游戏活动,并鼓励用合适的表征方式表达分数的度量意义以及运算过程,让学生真正理解分数的度量意义.

Fraction has always been a difficult point in primary school students’mathematics learning.Based on the advanced theory of fractional schema,a testing tool of students’learning progression on fractional schema is developed.The results of RASCH modeling shows that this tool has good reliability and validity,and the investigation of 402 primary school students of Year 6,who are using the mathematics textbooks of Beijing Normal University and the People’s Education Edition,reveals that Chinese students’actual development of fraction is basically the same as the learning progression model of fractional schema,but there are some differences between actual and expected development on two stages:iterative fractional schema and distributing fractional schema.And students using PEP mathematics textbooks perform better than those using BNUP textbooks in some fractional schema stages.According to the above conclusions,two suggestions are proposed to help students to deeply understand the measurement meaning of fraction.The first is to design the operational game activities to promote students’development of fractional schema.The second is to use suitable representations to express the measurement meaning of fraction and computational process.