Hierarchical linear model analysis of PISA2003 based on levels of student and nation

The purpose of this study was to investigate the PISA2003 database by Hierarchical Linear Model (HLM). The plan of PISA2003 aimed at the evaluation of mathematics cognition and problem-solving ability. The sample included 41 nations,and the task-takers participating in PISA2003were high school students whose age was about 15-year-olds.There will be estimation errors if all the task-takers were put inthe same level when it went to analyze thecasual relation between the variables of nation and student. Therefore, HLM of two levels was used to analyze the PISA2003 database. The unit in level-1 was students. The variables belonging to the level-1 were scores of mathematics cognition, mathematics viewpoint and mathematics thinking. As to the level-2, the unit was nations and the variable was NRI (Networked Readiness Index). Four sub-models were processed so that the hierarchical information between students and nationswill be clearly understood. The results showed that mean of mathematics cognition among nations differed and the NRI can explain the variance of mathematics cognition. The mathematicsviewpoint and mathematics thinking of studentswill influence their own mathematics cognition and this influence varied among nations. Moreover, the NRI can explain the different influences of mathematics viewpoint on mathematics cognition among nations. Finally, based on the findings of this study, some suggestionsfor future research were provided.