Cognitive diagnostic analysis of mathematics key competencies based on PISA data

Area of Science:

• Educational Measurement
• Cognitive Psychology
• Mathematics Education

Background:

• Cognitive diagnosis is an advanced assessment tool integrating measurement objectives with cognitive models.
• It enables fine-grained diagnosis of student knowledge and competencies.
• The PISA 2012 dataset from Shanghai, Hong Kong, Macau, and Taiwan provides a rich source for comparative analysis.

Purpose of the Study:

• To construct a cognitive model for diagnosing students' mathematical competencies.
• To analyze the mastery of mathematical attributes among students in four East Asian regions.
• To identify and compare the learning paths of students' mathematical competencies.

Main Methods:

• Development of a cognitive model with attributes: Mathematical Abstraction, Logical Reasoning, Mathematical Modeling, Intuitive Imagination, Mathematical Operation, and Data Analysis.
• Analysis of the PISA 2012 mathematics dataset for Shanghai, Hong Kong, Macau, and Taiwan.
• Construction and comparison of student learning paths based on cognitive diagnosis.

Main Results:

• Shanghai students demonstrated significant advantages across all assessed mathematical attributes.
• Students in Hong Kong, Macau, and Taiwan exhibited a common mastery pattern, with notable lower percentages in Logical Reasoning and Intuitive Imagination.
• Learning paths varied across regions, yet distinct main learning paths were evident, with differing distributions of knowledge state abilities.

Conclusions:

• Cognitive diagnosis effectively differentiates mathematical competencies and learning paths across regions.
• Shanghai leads in mathematical attribute mastery compared to Hong Kong, Macau, and Taiwan.
• Understanding regional learning paths offers valuable insights for targeted educational interventions and curriculum development.