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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.

Question:

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.

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    $\begingroup$ You might check out some of my previous answers, e.g., MESE 1380 which contains Brown & Walter as well as Joseph O'Rourke's suggestion of Silver. $\endgroup$ – Benjamin Dickman Mar 20 '15 at 0:41
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Nice question! Let me add one reference to your list:

Silver, Edward A. "On mathematical problem posing." For the learning of mathematics (1994): 14(1) 19-28. (PDF download link.)

Silver cites Hadamard's famous book, The Psychology of Invention in the Mathematical Field, as recognizing that isolating key research questions is a sign of exceptional mathematical talent, but then focuses most of his article on fostering problem-posing as part of inquiry-based learning in elementary education. In his conclusion, he says,

"The process of personalizing and humanizing mathematics for students through the use of open-ended problem-posing tasks invites them to express their lived experiences, and this can have important consequences for teachers and for researchers."

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    $\begingroup$ Maybe also worth pointing to earlier work by Kilpatrick (1987) on problem formulation and Duncker (1945) in which problem solving is viewed as involving problem posing. $\endgroup$ – Benjamin Dickman Mar 20 '15 at 0:43
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The answer to your question is yes. Check out the recent textbook:

Singer, F. M., Ellerton, N. F., & Cai, J. (Eds.). (2015). Mathematical problem posing: From research to effective practice. Springer. Google Books.

In particular, Part III, which contains 10 chapters, is described as:

enter image description here

Here is the beginning of the first chapter in that section:

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See the actual article for their theoretical framework, as well as the rubrics developed for problem-solving (Appendix B) and problem-posing (Appendix C).

There are various theoretical frameworks and methodologies described in the several chapters in this section of the textbook, though many connect back to the work of Silver and colleagues. You may also appreciate the review chapter included later on in this section:

enter image description here

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