In a comment on a recent post, Steven Gubkin pointed out that in doing mathematics he likes to develop stories. This motivation for mathematics is perhaps familiar to many practicing mathematicians. Calculations can even become stories. I do not mean, necessarily, that we tell the story about the mathematician who developed a bit of mathematics…which may be part of the story…but that the drama of the mathematics itself is a focus for continuing to investigate. The development of the story, with unexpected mathematical plot twists and seamless interface with humans engaging with the mathematics, as well as the cultural setting of the mathematics, seems to be front and center for mathematicians. This is perhaps because we have a developed mathematical cultural identity.
Please note that I am not asking about the role of writing in learning mathematics. It is possible for traditional mathematical writing, even when such writing is of decent quality, to completely avoid the aspect of mathematics as story.
I confess that this question, like many of my questions, arises because I am rather ignorant of sources in mathematics education. (Sorry!)
Q: What are some good studies and references that explore the role of developing mathematical stories as a central approach in mathematics education?
I am interested in all levels, here.
P.S.: The recent passing of Umberto Eco brought on this question, in part. An observation in his book on literature, together with Steven Gubkin's observation mentioned above, points directly at this question in our domain. Particularly, Eco observes that storytelling and narrative writing is not illogical or unstructured, but that there is a strong need to maintain the reality and consistency with what has been written. In some sense, I think this is the kind of consistency and logic that rules (and delights) the lives of practicing mathematicians. We have an idea and follow it up in our calculation and writing, and find out where our idea is wrong or inconsistent with what has been established. Thus unfolds a rich reality to which we respond.
Edit: Here are a few things that might be helpful. One is a book introduction writtend by Bill Thurston, and the other is a book on teaching mathematics as story.