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This study proposes a teamwork cognitive diagnostic modeling framework to address the limitations of traditional individual-level cognitive diagnostic models in team collaboration contexts. Building on higher-order latent structures, the model simultaneously assesses individual/team-level cognitive attribute mastery and collective cognitive ability through conjunctive diagnostic mechanisms. Empirical validation using a dyadic teamwork matrix reasoning test and two simulation studies were conducted. The framework reveals specific cognitive factors influencing team performances. This work bridges critical methodological gaps by extending cognitive diagnostic assessment from individual cognition to team cognition, offering novel analytical tools for diagnosing collaborative problem-solving mechanisms in educational and organizational settings.