I’m very impressed by the commentary in the kick-off post. The default WCYDWT stance has the eager math teacher stroking his chin and musing that “we should really tie this into gas prices somehow … ” while studiously avoiding the essential, practical details of constructing a framework for that learning. Instead, at freaking last, our commenters are starting to attack those logistics with a certain thrilling mania, developing full-bodied worksheets, manipulatives, and Geogebra appletsHats off to: Steve Phelps, Jack Bishop, Josh Giesbrecht, Dan Schellenberg, Nick Hershman, and Justin Lanier. Great work..

I’m not exactly sure of the best route through this problem. In fact, the one that interests me most is one I don’t know how to solve. I hope you can help me with that. I only know one thing:

We can’t learn much from an obscure background element of a video clip unless we drag it into the foreground. We need our own copy of that bouncing DVD screensaver. So I made one in AfterEffects. [download clip]

DVD Screensaver – Plain from Dan Meyer on Vimeo.

Your goal with these intro clips should be to infect your students with as much of PB&J’s anticipation as you can:

Take bets: will it hit a corner with five minutes? Ten minutes? Put a few students on record.

Now ask your students, “what matters here?” There are nearly ten variables you can define together. Ask, “what are good ways to measure what matters?” Pixels, angles, speed, time, etc.

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Albert Einstein:

The formulation of a problem is far more often essential than its solution, which may be merely a matter of mathematical or experimental skill.

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Play this clip. It features information that should, ideally, surprise no one. Your students have abstracted all this information already. You’re just taking their hard wor and pressing play. [download clip]

DVD Screensaver – Gridded from Dan Meyer on Vimeo.

From there, take your pick. You could give them something fairly explicit like this [download image]:

Or you could just give them this grid, 720 by 480 with ten-pixel increments, go frame-by-frame through the movie, and pick out some data points together. [download image]

The awesome observation they should make, regardless of what route they take, is that, once that icon starts moving, the rest of its natural life is foretold. It’s totally predictable in this frictionless environment.

By my count, we’re still missing a clip.

We need video of the solution. It’s one thing for you to consult your answer key (the full measure of your authority) and confirm a student’s answer. (A: lower-left corner at 1:34.) It’s another thing entirely to say, “It doesn’t matter what I think. Let’s check the tape.”

So here are five minutes of the DVD screensaver.

DVD Screensaver – Gridded, Five Minutes from Dan Meyer on Vimeo.

Now will someone teach me how to solve this algebraically?

Kate Nowak:

Here’s what basically has to happen to make a successful WCYDWT lesson:

1. Lighting strikes (you observe something).
2. You recognize that lightning has struck (you say “holy *&^%”).
3. You investigate by building layers of abstraction on your observation.
4. You realize that that particular abstraction fits in your curriculum.
5. You strip away all those layers to a core question interesting to a 15 year old, who (I’m sorry and draw whatever conclusions you will about me or my school system) are the least interested people on the planet.
6. You rebuild the abstraction in a way that will support the questions you successfully predict they will ask.
7. You make attractive keynote slides out of it.
8. You extend your original abstraction to questions that they will want to pursue to enhance their understanding.

mg:

there seem to be two corners of necessary student experience here. first, engaging with the instructor in “recreating mathematical reasoning”…using cooperative examples to learn how to ask useful questions, and making visible the math already there to find solutions. but those presented scenarios, in turn giving birth to the useful questions, are still coming from the heart/experience of the teacher, even if covertly. the most valuable part of WCYDWT to me is giving students the confidence and skills to recognize within their own spherespassionsinterestsloves specific places where those useful questions can be posed.

Let me be clear, first, that Nikki Graziano’s Found Functions are beautiful, subtle invocations of math and nature. They make me happy.

But two people have forwarded Graziano’s work my way in the last 12 hours under the heading “WCYDWT?” so I’d like to point out, for whatever it’s worth, that this is significantly narrower in scope than what I’ve been proposing for the last few years. The same goes for most tweets tagged #WCYDWT, which typically link to:

1. a picture of a mathematical shape.
2. an article that deploys mathematical analysis.

Meanwhile, I am trying to:

1. recreate mathematical reasoning for my students as I find it in the world around me.
2. involve students in both the solution to and the formulation of meaningful questions.
3. exploit my students’ intuition and prior knowledge in the solution of those questions.

I don’t have any problem using Graziano as a classroom conversation piece, but there isn’t a question here. I don’t know how to turn this interesting thing into a challenging thing.

Yes, I could go out and take a few photographs and have students model different equations also. But in the service of what higher-order question? It’s like asking “what shapes do you see here?” It isn’t worthless but it isn’t far from the bottom of Bloom’s taxonomy either.

I’m trying to get this blog feature to a place where teachers ask themselves, “what extra resources do I need to create to make this question accessible and challenging for students?” but, for the most part, teachers aren’t even asking themselves “what is the question here?” They’re applying this #WCYDWT tag to an exhilarating feeling of connection between math and the real world. Which is great, but it’s an entirely different (and entirely more difficult) task to translate that exhilaration into something a student can discover and experience for herself.

I’m frustrated. I have no idea how to make this any clearer.