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

Area of Science:

• Educational Psychology
• Cognitive Science
• Mathematics Education

Background:

• Understanding students' cognitive structures is crucial for effective mathematics instruction.
• Previous research has explored cognitive structures, but less is known about Grade 12 students' mathematical cognitive structures in specific topics like sequences and trigonometric functions.
• Assessing cognitive structures can reveal learning patterns and inform pedagogical strategies.

Purpose of the Study:

• To investigate the characteristics of Grade 12 students' mathematical cognitive structures in sequences and trigonometric functions.
• To examine gender-based differences in these cognitive structures.
• To explore the relationship between mathematical computational ability and cognitive structure development.

Main Methods:

• A mixed-methods approach was used, with a primary focus on quantitative analysis.
• 184 Grade 12 students from China constructed concept maps on sequences and trigonometric functions.
• Concept maps were evaluated using total proposition, Novak's structural, and a new structural scoring methods.

Main Results:

• Grade 12 students' mathematical cognitive structures typically ranged from two to five levels, with limited cross-linking or linear structures.
• Significant differences were observed in students' understanding of key concepts and methods in sequences and trigonometric functions.
• Females scored slightly higher than males in cognitive structure scores (p < 0.001).
• Mathematical computational ability significantly correlated with cognitive structure scores, with high-ability students outperforming medium- and low-ability groups (p < 0.001).

Conclusions:

• Grade 12 students' mathematical cognitive structures in sequences and trigonometric functions are relatively basic, lacking complex interconnections.
• Gender and mathematical computational ability are significant factors influencing the development of these cognitive structures.
• Findings suggest a need for instructional interventions to foster deeper conceptual understanding and more complex cognitive structures in mathematics.