International Comparative Study of Statistics Learning Trajectories Based on PISA Data on Cognitive Diagnostic Models

The cognitive diagnosis model is an emerging evaluation theory. The mastery of fine-grained knowledge points of students can be obtained via the cognitive diagnostic model (CDM), which can subsequently describe the learning trajectory. The latter is a description of the learning progress of students in a specific area, through which teaching and learning can be linked. This research is based on nine statistical items in the Program for International Student Assessment (PISA) 2012 and an analysis of the response data of 30,092 students from 14 countries from four attributes based on CDM. Then, it obtains the learning trajectory of students in statistical knowledge. The study found that Bulgaria, Costa Rica, Peru, Mexico, and Serbia have the same learning trajectories. The learning trajectories of almost 14 countries are as follows: (1) uncertainty, (2) data handling, (3) statistical chart, and (4) average.