# Developing mathematical stories

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.

• Somehow, I think that the idea of mathematical story as a motivation is incomplete. It may be that the development of mathematics is actually more the following of, and contribution to, a conversation than the development of a story. Story development may be too one-sided. This, of course, is a well-travelled claim since Imre Lakatos. Just recording this as a critique of the question. I guess what I mean is that a story can be well-told and needs an audience, but doesn't wait for the audience to respond. In a conversation, the response is crucial…and the subsequent response etc. Mar 2 '16 at 23:03

With regard to "mathematics as story" in the context of mathematics education, one place you might look to is the work of Leslie Dietiker (google scholar) on mathematics curriculum as story.

For example, here is the abstract from Dietiker's (2015) Mathematical story: a metaphor for mathematics curriculum:

You might also check the more recent piece, Dietiker's (2016) The Role of Sequence in the Experience of Mathematical Beauty, which investigates a first grade lesson and its aesthetics by framing the lesson as a mathematical story in keeping with the previous article. For example, consider the following excerpt, for which the citations may be of interest, as well (pp. 153-154):

The latter article ends with a nice quotation that I interpret as being in keeping with your general query. Specifically, Dietiker writes (p. 171):

In other words, does there exist a mathematical story that would similarly captivate students with a non-special number, such as $68$? Or with a function, such as $y = -\frac{1}{2}x + 6$? In mathematics education, when a mathematical lesson is neither stimulating nor interesting, is it a result of a poorly designed mathematical story or is it the result of poor delivery?

(Rather separately, I also point back to my response in MESE 2164 on reading mathematics textbooks, and, in particular, how reading a "math book" is or is not similar to reading a novel.)

This youtube video created by the now popular "Primitive Technology" account showcases EXACTLY how a story about completing a task can be made both interesting, exciting, and informative: https://youtu.be/GzLvqCTvOQY

The goal in presenting and teaching mathematics is to achieve this level of clarity and engagement while "doing math". The path to this goal is exactly the same as used in any of the Primitive Technology youtube videos: show the concrete actions which take place and which solve the given problem. There is nothing simpler, and yet there is nothing harder to keep in mind while you're flipping madly through textbooks for "the method" or "the solution" or any other such nonsense. You must engage the senses that students have IN THE PRESENT and to do so requires that you are equally engaged in the physical actions which lead towards a solution to a mathematical problem. Anyone who believes mathematics is "abstract" is greatly confused about what mathematics is: mathematics is nothing more than the living symbolisms we use on a daily basis, it is only and solely the stories we tell about the symbols we use.