This research used Novakian concept mapping and interview techniques to track changes in knowledge and understanding amongst students and their supervisors in the course of full-time research towards a laboratory science-based PhD. This detailed longitudinal case study analysis measures both cognitive change in the specific subjects that are the topic for research, and the understanding of the process of PhD level research and supervision. The data show the challenges for students and supervisors from different national, ethnic, cultural, and academic backgrounds and traditions with a focus on how this impacts the PhD research process and development. Working cross-culturally, and often in a setting different from either the student or the supervisor's background and training, can lead to a lack of common language and understanding for the development of a pedagogically oriented supervisory relationship. Documenting change in knowledge and understanding among PhD students and their supervisors is key to surfacing what the joint processes of mutual democratic research and of supervision may entail. This study explores how one of these key processes is a student's developing sense of belonging (or non-belonging). Specifically, this paper engages the concepts of belonging, and democratic education through mutual learning, to explore the practices of working across national, cultural, ethnic, and diverse academic backgrounds, for both supervisors and students. Doctoral study is understood as a situated context in which belonging also acts as a gateway for who can join the global scientific community.