There is a widely acknowledged need to improve the reliability and efficiency of scientific research to increase the credibility of the published scientific literature and accelerate discovery. Widespread improvement requires a cultural shift in both thinking and practice, and better education will be instrumental to achieve this. Here we argue that education in reproducible science should start at the grassroots. We present our model of consortium-based student projects to train undergraduates in reproducible team science. We discuss how with careful design we have aligned collaboration with the current conventions for individual student assessment. We reflect on our experiences of several years running the GW4 Undergraduate Psychology Consortium offering insights we hope will be of practical use to others wishing to adopt a similar approach. We consider the pedagogical benefits of our approach in equipping students with 21st-century skills. Finally, we reflect on the need to shift incentives to reward to team science in global research and how this applies to the reward structures of student assessment.