The Cognitive Diagnosis Study Of Primary Students' Mathematics Estimation Ability

In 2001,the "Mathematics Curriculum Standards for Compulsory Education(Trial Edition)" brought the "estimation" into the teaching content of mathematics in primary schools,arousing extensive concerns from many expert researches and front-line teachers.Generally,the related documents divided the estimation into three classes: computational estimation,measurement estimation and numerical estimation,By means of the oral report,the present study found that the numerical estimate is the basic of computational estimation and measurement estimation.DINA model is a widely recognized cognitive model with characteristics of simple structure and good understandability.In order to compare structural differences between the first stage and the second stage in primary school students in terms of computational estimation,measurement estimation and numerical estimation,this study developed two test questions with the combination of "Mathematics Curriculum Standards for Compulsory Education(2011 Edition)" and Compulsory education mathematics textbooks which published by The People's Education Press.Using the cognitive diagnosis theory.,a total of473 students in grade three and 426 students in grade six were randomly selected from two primary schools.Data were analyzed by R language software using two parameter estimation models: maximum likelihood estimation(MLE)and maximum a posterior estimation(MAP).Not only the estimated parameters of the two models all exceed 60%,but also with good fitting accuracy.Guess parameter and error parameter of the DINA model were below 0.4,showing a good reliability.This study found that students in first stage have advantages in numerical estimation and measurement estimation,while students in second stage have advantages in computational estimation;students in first stage have mastered numerical estimation.