As educational organizations face difficulties in providing personalized learning material or individual learning support, pedagogical conversational agents (PCAs) promise individualized learning for students. However, the problem of conversational breakdowns of PCAs and consequently poor learning outcomes still exist. Hence, effective and grounded communication between learners and PCAs is fundamental to improving learning processes and out-comes. As understanding each other and the conversational grounding is crucial for conversations between humans and PCAs, we propose common ground theory as a foundation for designing a PCA. Conducting a design science research project, we propose theory-motivated design principles and instantiate them in a PCA. We evaluate the utility of the artifact with an experimental study in higher education to inform the subsequent design iterations. We contribute design knowledge on conversational agents in learning settings, enabling researchers and practitioners to develop PCAs based on common ground research in education and providing avenues for future research. Thereby, we can secure further understanding of learning processes based on grounding communication.