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This study examines how pre-service math teachers (N=30) develop problem-solving competence through AI collaboration. Using Bloom’s taxonomy, we analyze cognitive integration and gender differences via cognitive network analysis (ENA) and lag sequence analysis (GSEQ). Key findings show: (1) Gender-differentiated cognitive networks—males prioritize "analysis→creation" paths, females emphasize "understanding→evaluation" loops; (2) High-scorers form synergistic "application→analysis→creation" networks versus low-scorers’ "understanding→application" cycles; (3) AI strengthens higher-order behavioral chains but cognitive fragmentation persists.