While design processes have been studied for many years, relationships among design team characteristics, teamwork, and team performance have not yet been fully understood. As such, there is no consensus on how to form design teams or enhance teamwork. In this paper, we propose a conceptual design-team effectiveness model based on team effectiveness theory in which we divide team process into two components: team member collaboration and design process. Built on this model, we then present a six-step research roadmap towards enhancing teamwork in engineering education by 1) improving methodology to form design teams and 2) finding a team-building design exercise to promote team member collaboration. We propose to improve team formation methodology by 1) comprehensively studying associations among team factors and team performance and 2) investigating how associations among team factors and team performance change with team-building design exercises. Together, we expect both team performance and team member collaboration to improve, which should lead to a better teamwork experience in engineering education.