Teamwork relies on collaboration to achieve goals that exceed individual capabilities, with team cognition playing a key role by integrating individual expertise and shared understanding. Identifying the causes of inefficiencies or poor team performance is critical for implementing targeted interventions and fostering the development of team cognition. This study proposes a teamwork cognitive diagnostic modeling framework comprising 12 specific models—collectively referred to as Team-CDMs—which are designed to capture the interdependence among team members through emergent team cognitions by jointly modeling individual cognitive attributes and a team-level construct, termed teamwork quality, which reflects the social dimension of collaboration. The models can be used to identify strengths and weaknesses in team cognition and determine whether poor performance arises from cognitive deficiencies or social issues. Two simulation studies were conducted to assess the psychometric properties of the models under diverse conditions, followed by a teamwork reasoning task to demonstrate their application. The results showed that Team-CDMs achieve robust parameter estimation, effectively diagnose individual attributes, and assess teamwork quality while pinpointing the causes of poor performance. These findings underscore the utility of Team-CDMs in understanding, diagnosing, and improving team cognition, offering a foundation for future research and practical applications in teamwork-based assessments.