I've read some articles about it and those papers show us that there are some facts to understand the mathematical competence in problem-posing. Besides that, those investigations show that there are some indicators to assess the competence.
Brown, S. I., & Walter, M. I. (Eds.). (2014). Problem posing: Reflections and applications. Psychology Press.
Malaspina, U., Mallart, A., & Font, V. (2015). Development of teachers’ mathematical and didactic competencies by means of problem posing. Proceedings of the 9th Congress of the European Society for Research in Mathematics Education (in press). Prague, Czech Republic.
Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149-158.
Also, some researchers agree that mathematical competence in problem-posing is part of another great competence, it's problem-solving.
Is there a framework to study the mathematical competence in problem-posing for prospective teachers?
I'm interested in figure out how we can recognize and propose specific indicators to assess this competence, if it could be studied.
I hope your help to collect some articles or thesis which could answer this question.