Design education has moved towards a collaborative practice where designers work in teams and with other disciplines to solve unstructured problems. Along with the cognitive skills involved in the execution of the design process, designers also need skills to work in teams, share information, negotiate common ground and reach consensus. The aim of this research is to understand the cognitive processes used during the interactions of design teams to reach consensus during the design process. Four cases were studied across different design domains during the problem definition, ideation and concept development phases of the design process. The cases involved two bio-medical fellowship programs, an undergraduate product design project and a user experience design consultancy. The team's conversations were recorded and a discourse analysis (DA) was used as the main method to analyse the data. The findings show that during team interactions design teams alternate between four main cognitive processes to execute the design task and reach consensus throughout the process. Recommendations are proposed that can guide design educators to support students during team interactions when solving design problems.