Mathematical cognitive structures in Grade 12 students: a mixed-methods concept map study of gender differences and...

This study employs a mixed-methods research design, primarily relying on quantitative analysis while incorporating qualitative analysis as a complementary approach. A total of 368 concept maps constructed by Grade 12 students were evaluated using the total proposition scoring method, the Novak's structural scoring method, and the new structural scoring method. The study aims to explore the characteristics of Grade 12 students' mathematical cognitive structures and to examine differences across gender and varying levels of mathematical computational ability. This study selected 189 Grade 12 students from four schools in Beijing and Shandong Province, China, focusing on the topics of sequences and trigonometric functions for the concept map drawing test, and after excluding invalid samples, a total of 184 students were included. The study found that Grade 12 students' mathematical cognitive structures are mainly concentrated between two and five levels. Most students did not form cross-links, and very few exhibited linear structures. Based on the statistical analysis of the frequencies of different concepts and methods appearing in students' concept maps, significant differences were found in students' understanding of key concepts and methods in the topics of sequences and trigonometric functions. There were gender differences in students' mathematical cognitive structure scores (p < 0.001), with females scoring slightly higher than males (sequences: Cohen's d = 0.38; trigonometric functions: Cohen's d = 0.19). Students with different levels of mathematical computational ability showed significant differences in their cognitive structure test scores (p < 0.001), with the high-ability group > the medium-ability group > the low-ability group.