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April 12, 2026Thinking Skills and Creativity0 citationsOpen Access

Exploring the relationship between mathematical convergent and divergent thinking

PHPer Øystein HaavoldUiT The Arctic University of Norway BSBharath SriramanUniversity of Montana Western

Key Points

This research aims to explore the relationship between convergent and divergent thinking specifically within mathematical contexts.
Cross-sectional design with data collected at two time points, eight months apart.
Involvement of 374 students from grades 5–13 in northern Norway at T1; 359 at T2.
Convergent thinking assessed through pattern generalization and claim evaluation tasks.
Divergent thinking measured using problem-posing, redefinition, and problem-solving tasks.
Moderate positive correlation found between convergent and divergent thinking in mathematics.
Argumentation quality was more significant than correctness in the CT–achievement link.
Flexibility, a divergent thinking component, was notably associated with achievement, while originality was less relevant.
Both thinking types independently explained variance in mathematical achievement.

Abstract

• Domain-specific CT and DT tasks show stable, replicable performance patterns • CT and DT are moderately positively correlated in mathematical contexts • Argumentation quality, not correctness, accounts for the CT–achievement association • Flexibility, not originality, is the DT component linked to achievement • Both CT and DT independently account for variance in mathematical achievement The relationship between convergent and divergent thinking in mathematics remains largely unknown, yet understanding this relationship is critical for educational practice and theory. This cross-sectional study examined performance patterns and relationships between convergent and divergent thinking using domain-specific mathematical tasks, with data collected at two time points approximately eight months apart to assess replication across task operationalizations and stability of individual differences. At T1, 374 students from grades 5–13 (ages 10–19) in northern Norway participated; T2 data were collected from 359 students. Convergent thinking was measured through pattern generalization and claim evaluation tasks scored for correctness and argumentation quality. Divergent thinking was assessed through problem-posing, redefinition, and problem-solving tasks scored for fluency, flexibility, and originality. Results revealed substantial individual variation in both thinking types, with students showing particular challenges in mathematical argumentation. Convergent and divergent thinking demonstrated a moderate positive correlation, consistent with theoretical models positioning them as related but distinguishable cognitive abilities. Component-level analyses revealed that argumentation quality showed stronger associations with divergent thinking dimensions than simple correctness. Both convergent and divergent thinking were significantly associated with mathematical achievement across all models, with age and gender as non-significant predictors. These findings establish baseline performance patterns for domain-specific measures and suggest that mathematical convergent and divergent thinking are linked but not redundant. The results have implications for mathematics education, suggesting that fostering both convergent reasoning and divergent creative thinking may support mathematical achievement.

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