I know there is a fair bit of literature on mathematical problem solving (e.g., Polya, Schoenfeld). I am wondering if anyone can direct me toward good sources on mathematical problem posing.
More precisely, I'm looking for any studies, articles, or expository essays on what goes into writing a good math problem.
Ideally, I'd like literature that answers/tackles questions such as:
-How does one come up with a good math problem?
-How does one modify an existing math problem/result to pose a new problem?
-How does one sequence several related problems so as to be most effective pedagogically?
I'm particularly interested in problems at the gifted high school level or undergraduate math major level, but would welcome most any references. Thanks!
Edit: Without trying to define too precisely what I mean by "problem", think of questions akin to what you would see as A/B 1/2 on the Putnam.
Edit 2: I think now that the best way to answer this question is by taking well known literature on problem posing and seeing who cited it. For example, one could use google scholar to check who cited the book "The Art of Problem Posing" by Brown & Walter (see here) or the article "On Mathematical Problem Posing" by Ed Silver (see here). At some point I will build a fairly extensive bibliography on mathematical problem posing, creativity studies, and the literature lying at the nexus of the two; if there is interest, I will make that list available here on math.SE.