This question is part of a project funded by the International Council for Science, supported by the IMU (among other bodies). Answers gathered here on mathoverflow may be included in the final report.
The question is NOT "How can maths researcher training be improved?" It is, rather, "What questions should the relevant social and human sciences investigate, in order to establish knowledge useful for policy aimed at improving maths researcher training?"
The project will use the method described here to group and prioritise questions.
Here is text from the first link, describing the project:
IUHPS (DLMPS): Cultures of Mathematical Research Training This project aims to mobilize the energies of a currently very active research area (the study of Practice and Cultures of Mathematics) to provide the theoretical and empirical resources for designing improvements to the training of the next generations of mathematical researchers and the improvement of research education in developing countries.
Work on mathematical research cultures will focus on the perspectives of new entrants to mathematical research and develop a theoretical framework for further discussions on various levels, including the policy level. We anticipate that analytical tools developed in cultural studies and cultural anthropology (such as power-distance, or grid-group analysis) will help the identification of research cultures and their associated obstacles and opportunities.
During the course of the project, we will develop a concrete plan for a survey project of various mathematical research-cultures that is of common interest to both academic researchers in mathematical practice and the societal stakeholders (e.g., funding agencies, universities, research policy officials and international bodies such as the IUHPS and the IMU).