基于关系-表征复杂性模型的数学应用题表征能力测验

Measuring Students' Representation Level on Arithmetic Word Problems:Based on the Relational-Representational Complexity Model

基于关系-表征复杂性模型,从每道应用题涉及集合关系的嵌套程度角度事前分析其关系复杂性,编制了难度序列变化的应用题测验,以考察问题表征能力。采用该测验测查了四至七年级共165名学生,考察事前分析的合理性及表征水平随年龄的变化。结果表明:(1)事前分析对两个事后难度指标(错误率和Rasch模型分析的任务难度)的解释率分别为73.7%、78.7%;该测验得分与测查思维水平层次变化的SOLO分类测验上的得分有较高相关(r=0.65)。(2)四年级的应用题表征水平显著低于五、六、七年级,其他三个年级差异不显著;而且随着问题关系复杂性的增加,年级差异增大。这说明基于关系-表征复杂性模型的事前分析是合理的,据此编制的测验能够测查表征水平随年龄的变化。

Students often have difficulty in solving arithmetic word problems.According to the relational-representational complexity model developed by Xin Ziqiang（2003-2008）,the difficulty of an arithmetic word problem is determined partly by the relational complexity of variables in the problem.Based on the model,in the present study,a test consisting of 24 arithmetic word problems with different levels of relational complexity was designed for measuring children.The test was administrated to 165 students from grade 4,5,6 and 7.Results showed that：（1） prior analyzed problems＇ relational complexity（involving analysis of relational complexity of variables in every item） could predict most variance of task difficulty（73.7% of error percentage,78.7% of a difficulty index of Rasch model）,and the criterion validity with the SOLO taxonomy test was 0.65;（2） students＇ representation levels on the test improved with grades.Such results indicted that the test is an effective and reliable instrument for measuring children＇s representation levels changing with grades.