Teaching WCYDWT: Storytelling

2011 May 12: I gave this post another pass a year later.

The job of the dramatist is to make the audience wonder what happens next. Not to explain to them what just happened, or to suggest to them what happens next.

David Mamet

Once you’ve learned something, my experience is that if you do something with that learning, if you turn your learning into something else for somebody else, it starts a flywheel spinning awfully quickly where you start learning more and then doing more with that learning and then you’re on CNN.

A recommendation: turn your learning into a story for somebody else.

Why a story rather than a persuasive essay or a pillow sampler? For one, the story is a medium that runs on greased rails between very different people. It’s an efficient transaction, even between me and my grandpa. For another, it’s hard for me to ignore how many elements of good teaching have their predicates in the three acts of a good story.

The First Act

Consider the opening shot of Star Wars, a movie which is nothing if not a story well told.

The moons. The tiny ship pummeled by the huge ship. The chase. The symbolism of the green and red lasers. The camera rolling just inches from the huge ship’s underside so it (the huge ship) appears to go on forever.

I’m not saying every lesson needs to (or can) open this way. I am saying there are obvious advantages to opening a learning moment with a series of clear, intriguing constraints (again: the tiny ship, the huge ship, the chase) that invite speculation and curiosity.

I’ll leave the injection of poor teaching onto the opening sequence of the first Star Wars prequel as an exercise for the reader. Hint:

The Second Act

During the second act of a story, your protagonist encounters allies and antagonists and uses the former to help resolve problems created by the latter.

During the second act of our lesson, students seek out the limits of the problem and try to determine valuable information and skills for resolving it.

The storyteller / teacher needs to assist the viewer / student just enough to make the viewer / student wonder what’s coming next and enable her to put that answer together on her own. It’s almost easier in these instances to help too much, to nudge a viewer or a student too forcefully, than it is to help too little.

Here’s an example from television where that goes right and wrong. These two shows both feature armed standoffs between criminals and cops. One show asks you to work hard to determine the motives and capabilities of the characters, the tone and possible outcomes of the scene. It’s a satisfying, tense experience. The other show signals all those answers awkwardly, and loudly, elbowing the viewer in the ribs with some ominous strings on the soundtrack.

You should be able to determine one from the other.

Click through to view embedded content.

Obviously, I need a better illustration with fewer adult themes here. Perhaps think about those sloppy literary adaptations where the writer couldn’t describe the source text visually so she has the main character narrate all those thoughts on the soundtrack.

The mandate for filmmakers is show, don’t tell.

Question, don’t tell is far from the worst mandate you could choose for the second act of your lesson.

The Third Act

Consider, now, a) great movie endings alongside b) Ben Blum-Smith’s Pattern Breaking series. If we allow the relationship between storytelling and teaching, Blum-Smith’s broken patterns represent the third-act twist: Rosebud is a sled; Bruce Willis is really dead; Darth Vader is Luke Skywalker’s father; 2, 4, 8, 16, 31. These patterns lull you into a false sense of certainty before yanking the rug out from under you, leaving you scratching your head, wondering what you missed, sending you back through the narrative again, scouring the story for other clues, conjuring up new theories.

Other movies choose to set up a sequel in their final minutes, like Batman Begins positioned the Joker as The Dark Knight’s next villain. Do you see how neatly that fits into Avery Pickford’s definition of great problems:

The problem should be deep. It should be rich enough to spend hours, days, weeks, months, or years working on variations, generalizations, and extensions.

Great problems and stories lead to more great problems and stories.


“Perplex them,” one of my old high school math teachers advised me when I told him I was going into teaching. Perplexity isn’t the same as confusion; rather, it’s a very, very productive form of confusion. My favorite teachers and storytellers perplex me repeatedly throughout a lesson or movie.

How do you teach people to tell perplexing stories? Even harder question: how do you teach people to tell perplexing stories about math?

My fear is that this skill, more than most others in my practice, reduces to character traits that can’t be taught. Storytelling requires empathy, an understanding of an audience’s expectations, their current knowledge, and their prior experience. I don’t know how you teach empathy. Perhaps it can only be modeled.

Certainly, here are fair pre- and post-assessments of storytelling:

  • Tell me about something you learned recently that exhilarated you. Tell me about it in such a way that I understand your exhilaration. ie. “Holy cow. ‘Oman’ is the only country in the entire world that starts with an ‘O!'”
  • Tell me about something you learned recently that exhilarated you. Tell me about it in such a way that I experience that exhilaration for myself. ie. “What is the only country in the entire world that starts with an ‘O?'”

It’s the assessments in between that mess me up.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Maybe it’s because my summer started over a week ago and my mind has already shut off, but the pre- & post-assessments of storytelling aren’t clicking for me.

    I don’t really understand how they work. Perhaps if someone could give another example?

  2. Take any interesting thing you’ve learned recently. It’s one thing to describe to me what you learned in a way that makes your exhilaration clear to me. It’s another, harder task to put me in a place to experience that exhilaration for myself.

  3. While I love the storytelling analogy, the Second Act has me puzzled. I’m still not sure which episode you like better. I think the second is superior but for reasons that don’t jive with how you describe things in the text. I also don’t know how you are translating “your protagonist encounters allies and antagonists” into pedagogy. I would like to see a “shot-for-shot” match with some actual teaching here.

  4. I feel that just like only certain movie producers/screenplay writers can achieve this, only certain teachers can do this. Like if I was smart enough to write Harry Potter or Lord of the Rings or Star Wars or Star Trek, then why would I be doing what I’m doing now?

    I don’t think I have the foresight to see the ending I want to get to, and then the creativity to build up the story to a climax that results in said ending. I either have the beginning, middle, or end but putting it all together would require me having a producer, director, cast, etc.

    Which hasn’t worked out for me yet.

  5. Great minds think alike:

    Grace on storytelling:

    Adam with an awesome indictment of textbooks and a teaser on a future storytelling post:


    Extended excerpt:
    Our students read textbooks, refined over the years to be ruthless, efficient and deadly. The story is missing, the context is missing and the connections are missing. The textbooks are a reference, not a teacher. It is then the teacher’s responsibility to add the missing ingredients, to tell the story, to explain how experts actually think about these things and, most importantly, to teach the students how to read (or understand) a subject non-linearly. Mathematics is structured so poorly K-12 partly because we keep treating the learning of mathematics as a well-ordered system and it isn’t

  6. A few years ago, I brought a friend along to my Calc 3 class (in college, obviously). My friend is mathematically-minded but doesn’t know very much actual math. He doesn’t know calculus at all.

    We were doing a problem involving a rectangular solid, each dimension of which was increasing or decreasing at a particular rate. The question was, at what rate was the length of the diagonal inside the rectangular solid changing?

    Once all the math was done, it turned out that the length of the diagonal was constant.

    My friend laughed and laughed at what he saw as the punchline of a really great joke!

  7. Dan I think this post explains a lot about the way you teach. A number of comments throughout your blog talk about how not every teacher would be able to pull off your lessons. I think you’ve hit the nail on the head as to why that may be. You present your lesson as if they were stories. These stories include drama and suspense which make them appealing to students. This is what hooks them and gives them a stake in their learning. I think any teacher could deliver the material you present on your blog as long as they approached it as telling a story. Thanks for making this explicit. It gives me a lot to think about.

  8. Barry Lewis

    June 4, 2010 - 5:39 am -

    When I get to the part where I actually have a classroom, I, like probably everyone in this region of the digisphere, want my students to become atomic-powered, self-guided, knowledge-seeking rockets of goodness. I’ve known for some time that teacher school can’t guide me into all the ideas that are going to help me do that, and as much as I’ll learn there can only ever be like getting so many crisp, folded sails that I take with me onto my first boat ever.

    So, space flight and sea journey metaphors behind me (carnival still ahead), I’m wondering about the role that these impassioned, guerrilla fierce tactics for student involvement and learning play with respect to the textbook based curricular delivery system that the school that hires me will provide (and will expect me to deploy). Granted, I’m pretty sure already that the first 1, 2, or 9 years of teaching are mostly about not succumbing to the fumes and the dizziness, like I might on a runaway, diesel powered carnival ride, but I’m wondering how I’ll be able to design opportunities for my kids to create these kinds of experiences for themselves, assuming even that I can, when it seems like there can be a ratio of about one week creative+production time for every one hour of classroom time, or in cinematic terms, a ratio of time to image that’s more like that for animation than for live action. I’m not necessarily referring to the tech overhead, if there is any, but to the whole process of seeking out and following recklessly intuitive and innovative ideas in the quest for meaningful learning.

    I was pretty sure I had some questions here. I guess one of them is this: how does storytelling (here broadly used to represent any kind of inspired, off-road approach to true and vital learning that probably involves the elements of story as you’ve described them) fit with what I imagine most teachers responsibilities to be? If we tell more stories and my kids do fewer textbook assignments one year than the year before, then is that a good (enough) year? Gradually is the only way I can see this transformation happening, but it feels like cold turkey is the needed approach to an urgent problem.

    And thanks for letting us see the pictures inside your head.

  9. I’ve been musing some more, and I believe part of the issue with the second act is in a discovery context it can be highly nonlinear. The paradigms for linear storytelling don’t apply as well, and it might be more fruitful to look at interactive media.

    For example, Emily Short has an essay on how she formed the story tree for the interactive fiction game Bronze. One could imagine a lesson plotted the same way (I may take a crack at my Giant Ants of Doom lesson I was never able to fix).

  10. Wow. This totally blew my mind. I’m a math teacher, but I’m also a writer and, while I have been catching glimpses of some of the parallels between those two aspects of myself, never have I seen them so clearly laid out. And in a way that they could be used in the classroom. I’m feeling the warm-fuzzies.

    I think one of the things that has always bothered me about math textbooks (and your typical math class) is the lack of any narrative arc. It’s one of the reasons I liked IMP when I taught it during my student teaching. Though I like Dan’s vision where the math itself contains the narrative, not just having a narrative to tie together mathematical concepts.

  11. Well dangit! It only takes a generation for stories to be forgotten. In all of our systemization (is that a word?) and standardization of education, we’ve lost sight of a time when almost all knowledge was passed down by story.

    I blame abstraction and specialization. Math in general has suffered plenty at the hands of these two vile side-effects of progress. Teachers are going to have to fight the herd mentality if we ever want to get back to… umm… effectiveness?

    And Dan, no shame for the Star Wars reference. Whatever gender bias whispers from it are dwarfed by the rapport we develop when we share our personality and passions in the classroom.

    Rock on.

  12. Jason D.: I would like to see a “shot-for-shot” match with some actual teaching here.

    I’ll try, though it seems like you more or less answered your own question farther down the page. Let’s say the student is struggling to solve the watertank problem. The student doesn’t know where to start. At that point, I can either say a) “Find the area of the base, multiply it by the height to find the volume. Then divide by the constant rate of flow,” b) nothing at all, or c) something that’s just helpful enough to get the student moving and invested.

    It’s in “just helpful enough” where I find common cause with the storyteller.

    Jason B., maybe I saw Adam’s teaser and decided to fast-track my own storytelling post. Maybe I didn’t.

    Barry: I’m wondering how I’ll be able to design opportunities for my kids to create these kinds of experiences for themselves, assuming even that I can, when it seems like there can be a ratio of about one week creative+production time for every one hour of classroom time

    I can only assure you that this process gets a) less time consuming, b) easier, and c) more fun as you engage the flywheel I mentioned above. Take something you dig about math. Tell a story about it that opens with a clear, simple question. Repeat. Watch the smile on your face get broader.

    Barry: how does storytelling (here broadly used to represent any kind of inspired, off-road approach to true and vital learning that probably involves the elements of story as you’ve described them) fit with what I imagine most teachers responsibilities to be?

    I’d rather not conflate math storytelling with off-road discovery-type learning. What I do most days isn’t that special.

    We did a few problems with standard form lines yesterday, for instance. I put up an empty graph, a table with coordinate pairs, and a standard-form equation. “Who is the imposter?” I asked. “Who doesn’t belong?” The students then had two methods (graphing or evaluating) to determine the outsider.

    That’s probably the smallest unit of math storytelling I can offer. I shot no video, took no photographs. I just made sure to present my textbook’s activity as some kind of dramatic scenario.

  13. . . . it seems like you more or less answered your own question farther down the page.

    Well, sort of. Here’s my attempt at applying the story tree to a real lesson.

    Nonlinear lesson design vs. Giant Ants of Doom

    I still would like your own take, especially since the devil is the details even finer-grained than I discuss in the blog post. How do you teach a teacher to say the right thing?

  14. Jason: Dude, that’s hard. I have NO IDEA what makes ants able to live anyways! (That’s me channeling a high schooler’s first instinctual answer. They probably wouldn’t even be able to verbalize it that far.)

    Maybe if you held their hand by saying stuff like “Well, let’s look at the question…*read question*…So what do we need to live? Food? Air? Hmm, what do we know about “. Hmm, I don’t know, it seems like a very exotic thought experiment that most kids at that age wouldn’t be able to run with. I do like the multimedia parts though.

    And man, that is a horrible, complexly-worded problem (the textbook, not yours). If I were a high school student who didn’t like math, my brain would freeze at that onslaught of science babble. Like, “….0_0…(what do I do)…”.

    Good effort though, and nice creativity!

  15. @Chris, the hook portion works pretty well. The science is informal so there’s no pressure. I even had one student give a brilliant answer involving breeding ants in the right environment to increase their size. It’s the math where they went loopy.

  16. “That’s probably the smallest unit of math storytelling I can offer. I shot no video, took no photographs. I just made sure to present my textbook’s activity as some kind of dramatic scenario.”

    Dan, thanks for relieving the worry that every lesson need not be an Oscar-winner (in 2nd grade I plan about 12 20-minute chunks or mini-lessons for every day). I tend to build things up in my mind, and tend to beat myself up if I’m not a rock star every chunk of the day. Your example of low-key was perfect…it simply comes down to presenting the “textbook’s activity as some kind of dramatic scenario.”

    Phew (or, as one of my kids spelled it the other day, “fyou!”).

  17. @Doug ~ I am curious…you seem impassioned for gender equity, yet assume because I’m a girl that Star Wars doesn’t speak to me. It’s ironic that this type of stereotype should lead the discussion on gender-based engagement techniques.

    I would suggest that knowing our students is more important than knowing their labels. I can’t assume that no girls like Star Wars (or gaming, for that matter) any more than I can assume that none of the boys in my class enjoy gardening. Or glitter.

    It’s as ridiculous as assuming that all black students prefer rap music. There is no generic replacement for actually knowing what your students find engaging.

  18. @Mia, just because there will be outliers does not make it gender-neutral. Obviously not ALL girls dislike Star Wars, and to suggest that something can’t be biased if at at least one person likes it is nonsensical. I would hope Dan, as a young male teacher, takes into account his biases when using examples to teach to his female as well as male students.

  19. Either:

    a) Doug didn’t read my post very carefully, or
    b) Doug doesn’t understand what an analogy is.

    Either way, it’s tough to know how to respond. Suffice it to say, at no point in this post do I suggest using Star Wars to teach math, not that I’d be opposed to such a thing.

  20. Ok, sorry, I was wrong since the post did not describe a Star Wars problem. Mia is still wrong, too, and I still think questions/storytelling which may be biased towards one gender should be taken into consideration. But this has nothing to do with the original post so feel to delete my replies.

  21. *grin* I like that I have to be wrong too! My point is only that I don’t *feel* like an “outlier” just because I’m a girl who likes Star Wars. The point I’m making is only that *everything* is a potential outlier when we’re not basing our teaching decisions on what we know about the actual students – in all their complexities – sitting in the room with us. I don’t actually disagree that we need to be fully aware of gender (or any other bias), just pointing out that we can’t know if it’s a good or bad storytelling opportunity until we understand the students and relationships in the classroom.

  22. My simplified Hero’s Journey for Teaching:
    * Act One:
    — call to action (compelling problem, posed in a way that sparks curiosity)
    — refusal/skepticism (but… but… but…)
    — no choice / we’re in
    KEY FOCUS: build curiosity, almost against their will…

    * Act Two:
    — mentors, allies, sidekicks, enemies, problems
    — backstory
    KEY FOCUS: tools, twists, turns, increasingly-challenging problems. Surprises.

    * Act Three:
    — we’ve solved the problem (mostly)
    — but we’re SO not over… new issues arise
    — ultimately, return to the village with the new elixer
    KEY FOCUS: overcoming big challenge, THEN looking into what new vista/possibilities open up as a result

    We try to do this in our books (often not successfully, but… we try) at two levels of scale — the book/course as a whole, and to some extent at the chapter level as well. Each chapter spirals through a “imagine you had to do [x]…” and on it goes, with each chapter’s end a resolution of one problem that opens up new possibilities (either challenges/problems we hadn’t seen before or really cool new capabilities). Tools/sidekicks are introduced just-in-time, and mentors and allies are there for guidance, also just-in-time or sometimes AFTER you failed the first test but learned something valuable.

    Why they don’t teach screenwriting techniques to teachers is beyond me. We used to make all the authors in our tech book series read the screenwriting book “Save the Cat”, by Blake Snyder, and build storyboards for each topic using that simplified framework. It’s not an answer to bad teaching, but it’s a way of structuring a lesson that feels more like a hero’s journey for the learner rather than–as so often happens with difficult topics–the learner feels like the textbook author surely must be an orc, not an elf. ;)

  23. This is great. The art of story telling dates back for centuries, that’s how events in history were passed down. I’m even thinking back to watching a group of small children listening to a story. Story telling in Math is an excellent way to hook our students. There are several math experiences we encounter that can be used in math to make math more real and meaningful.