Confusion = Conflict (and I mean this in a good way!)

When telling a story, there are certain things that you need to have. Characters. A setting, or multiple settings. Things that happen (i.e. a plot). Without these fundamental building blocks, you don’t have a story to tell.

However, just putting the building blocks to paper doesn’t mean that you have a story; just as piling a bunch of bricks and mortar together doesn’t mean that you have a wall. The way that you put these items together is what dictates your end product.

And to be perfectly honest…all of the writing “rules” can be broken (so long as they’re broken well). But there’s one thing that just HAS to be there for a story to take place. Without this, nuh-uh, ain’t happening.

Conflict.

A story without conflict is like a bird without wings. I’m not sure what it is exactly, but it’s definitely not a story. Could be an amusing anecdote; perhaps a lovely vignette. But it isn’t a story. No way. No how.

I’m sure we’ve all read stories that were boring. I’m not talking about stories that were annoying, irritating, or that you just didn’t like. I’m talking deadly dull, nothing is happening, this-book-is-putting-me-to-sleep booooring! Why were these stories so painful to read? Because there was no conflict.

I believe in my heart that math teaching can draw from and be informed by storytelling. And, if I am correct, this means that there must be some sort of conflict that takes place in our teaching, and our students’ learning, of mathematics. As teachers, we probably hate conflict and avoid it at all costs. I know this is true for myself, and I’m willing to bet that more than a few of you out there feel the same way. But, to tell a compelling story there HAS to be conflict. Sorry; that’s just the way it is.

Right now, in the interwebs, there has been some amazing thinking and talking going on about the role of confusion in the classroom. The teaching strategy of making your students grapple with ideas that leave them frustrated and bewildered…but not too much of either of these things. And not forever, but for long enough that this is a meaningful activity. For teachers out there who aren’t already knee-deep in student-centered, constructivist, complex-instruction style teaching, this is probably a jaw-dropping, gasp-inducing, holy shitake mushrooms what-the-hell-are-you-thinking idea.

But for a storyteller, this methodology makes perfect sense. In fact, it fits into my storytelling/math teaching analogy so well I’m kicking myself that it took me so long to see it. Confusion is the mental conflict that students must go through in order to make learning math akin to experiencing a narrative.

Think about the basic structure of a story:

  1. Alice is innocently minding her own business, when WHAM! Something happens to change her life.
  2. Confronted with a BIG PROBLEM, Alice doesn’t know what to do at first. But, she comes up with a plan to solve her BIG PROBLEM, and begins to take action.
  3. Along the way, Alice encounters difficulties in solving her BIG PROBLEM, but makes progress—little by little—towards her goal. She adapts her initial plan to fit where she is in the present moment.
  4. Eventually, after much trial and tribulation, Alice resolves all of her little issues, allowing her to finally solve the BIG PROBLEM.
  5. Much rejoicing is had by all; they live happily ever after.

Here’s how Alice’s story might play out in the math classroom:

  1. Stanley traipses into class nonchalantly, plops down his backpack and looks up to see a question written on the whiteboard/overhead/LCD projector/SmartBoard/WTF.
  2. Stanley has NO IDEA how to solve this problem. Stanley (mentally) says a word we don’t want him to say in class. But…Upon further inspection, he notices one little step he could take to get himself started, perhaps after a nudge from his teacher.
  3. One step leads to a new idea, which leads to a new idea, which may or may not dead-end on Stanley. He gets stuck, he struggles; he turns to Sally and asks her what she thinks about what he’s done so far. They discuss the problem, get some more ideas and move further along.
  4. Eventually, after much trial and tribulation, Stanley–and Sally–figures out how to solve the problem.
  5. Much rejoicing is had by all; they live happily ever after (or at least until the next school dance).

Contrast this with the lecture-style lesson.

  1. Here’s a problem.
  2. This is how you solve it.
  3. Okay! Now you get to do fifteen problems exactly like it.

This is like flipping to the back of the book to see who-dun-it before reading a mystery novel. I have known people who do this, and I have never understood why they would want to. Why on earth would you want to know who commits the crime before you know what the crime is? But direct instruction prior to student exploration presents the same problem. It gives away the ending too soon, before students have an opportunity to puzzle things out on their own. It takes away the joy of discovery, leaving the class with nothing but an empty exercise, devoid of conflict.

It may feel nice. Students may feel successful, like they “get it”. But they’ve lost out on the good stuff. And will they remember what they’ve “learned”?

I don’t know about you, but I can pick up a book off of my shelf and by the end of the first chapter, sometimes by the end of the first page, I remember what happens in the book[1]. If I only read the first chapter and the last, and maybe the Cliff’s Notes version, I don’t think I would recall the story as well.

Once you know the resolution, or the solution, do you really care about solving the problem? Are you that geeky[2]? Do you truly expect your students to be excited by figuring out the answer(s) if you’ve already shown them exactly how it all works out in the end?

When the only conflict in a math classroom is in students who don’t want to do the work and the teacher who is trying to make them do the work, or between students who are arguing over (non-mathematical) issues, there is an issue. The teacher is telling the wrong story. The students are telling the wrong story.

The mathematics is telling the wrong story.


[1] I only keep books I really love, so I have reasons other than “what happens next?” to re-read them.

[2] This is meant as a complimentary term.

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8 thoughts on “Confusion = Conflict (and I mean this in a good way!)

  1. Pingback: dy/dan » Blog Archive » The Three Acts Of A Mathematical Story

      • What! You’d better not tell people how to do stuff in the next installment! :)

        Seriously though, it’s been interesting watching our curriculum and its effect on teachers — especially teachers using it for the first time — because of exactly what you describe here. “But … but … I can’t give my kids things to work on without telling them how to do them.”

        Oh yes you can! And you’d better! It’s not going to be that way in college or careers (well, the good careers, anyway).

        And a few months later, some of these same teachers are shocked to find that kids CAN do this. They want to do this. They become good at actual mathematics by doing this. And they’re way more adept at thinking about and solving new problems, a huge goal.

        I await the next part. Hope you are doing great.

  2. Pingback: In Which It Is Resolved | The Space Between the Numbers

  3. Pingback: Story Interrupted | The Space Between the Numbers

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