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Archive for March, 2009

What Can You Do With This? is the most fun I've had this school year. I could do week after week of times table review if my students and I were allowed just thirty minutes per week to sharpen our minds with mathematically rich multimedia1.

I have received two suggestions recently I wanted to address, two suggestions that would put us off a useful trail and into the bramble. Here is one.

FlickrCC Won't Work

Scanning Creative Commons-licensed photography databases for math media simply isn't a scalable solution. These media must be unaffected. The student must lift the heavy weights. The student must decide for herself what is important about an image, audio sample, or video. Most photographers, meanwhile, are very interested in artistic expression, in affectation, in imposing their own point of view on a scene, rather than stripping the scene of their point of view entirely, which is essential for classroom work. So instead of something unaffected, and artistically value-neutral like this:

You get expression like this:

… with the camera positioned at an artistically interesting but academically unhelpful angle. You can't model a parabola onto this. You can't model a circle onto this. The photographer was (naturally) unconcerned with measuring the scene, which rules out basic photogrammetry. It begs the question, "who shot this?" rather than an interesting question about the parabola itself.

This is a generalization, true, but a useful one. You can't find the really effective WCYDWT? media. You can derive surface-scratchers like "what shapes do you see here?" from Creative Commons-licensed Flickr media but if you're looking to propel a meaningful discussion or a rigorous activity, you have to make it yourself.


  1. If you're the sort who sees potential in these blog things for professional development then the fact that I developed this classroom fixture organically, spasmodically, like a wobbly baby giraffe, here on this blog, in full public view with full public input, might be a useful data point.

I pick up a huge static charge whenever six words, paired with the right a/v material, can motivate an hour of mathematical exploration.

Here is the opposite of that static charge, a loud sucking sound as my brain deflates, the old way of doing real-world relevance:

As a student, I'm like "cool, volleyball, volleyball's fun" but the problem is already dumping questions and formulae and mathematical structure on top of me before I have ever once considered the reality that projectile motion follows a parabola.

You have to earn that.

So I shot four of these images [partial, full] — one that ultimately went long, one that went short, one that went in, and one that looked like it went in, but really veered to the side, provoking a discussion of errors in 3D projections onto a 2D plane.

I shot 'em plain. Nothing fancy, plenty of room along the edges, no soundtrack, no narration, nothing overtly helpful. I set them up so I could ask the students a clear, visceral question: "Will the ball hit the can?"1

Because this is a question which everyone wants to answer, regardless of mathematical ability. Everyone has an opinion. Everyone gets invested. It's also a question that has a visual answer, one which we can compare against their predictions. So the first thing I had the students do after they paired up in front of laptops was divide a piece of paper into quarters and make a bet on each throw. I gave them the digital files, next, on top of which they modeled parabolas in Geogebra, revising their guesses afterward.

Then we played the answer videos and called it a pretty good day.

Perhaps now that they're really, really invested into the idea that projectile motion follows a parabola, now that they're comfortable with Geogebra, we'll take Geogebra away. We'll change the constraints now, superimposing a grid or a protractor, deriving the parametrized equations, but I just want to impress upon you, if nothing else, that this is a very deliberate, very sacred (to me) process, a process which most textbooks desecrate whenever possible.

If one of my students could successfully answer that scanned textbook problem above, but hadn't on her own wondered, "What if we knew the equations of the parabola, what then?" I really don't know how accomplished I'd feel.


  1. These guidelines are all in the manual.

Look carefully.

Download high quality here. See the pilot for instructions.

BTW: Lotta good stuff in the comments. I can't prove any suggestion is better than another, but Jackie hits the one I intended all along, the one that packs the most punch per word, the one that rides into class alongside a student's intuitive understanding of the world, the one that will do the most good as a introduction to parabolas:

Will the ball make it into the can?

Any question heavier than that and the picture starts to get a little wobbly under the weight.

BTW: Here are the still photos we imported into Geogebra and the full videos we used to confirm our answers.

This is the final hand of the 2008 World Series of Poker.

Click through to view embedded content.

Download high quality here. See the pilot for instructions.

BTW: Chuck has precision on his side:

I’d stop the tape after the turn comes down and have them figure out the chance that the guy with 2 pair wins

ESPN makes a running calculation of these percentages, of course, so I blacked out that information in the clip. Have the students make the calculations and then play the unedited clip.

The cool thing, to me, is that there are varying levels of difficulty, depending on how many community cards are still unknown.

The other cool thing, to me, is that the problem functions pretty well as just a photo. In the thumbnail image, for instance, you have all the information you need, with just enough panic in Eastgate's face to motivate the problem.

Two minutes into his MGFest 2009 presentation How To Be Creative And Get Paid, Nick Campbell summarizes my concerns about cigotie's technically proficient mimicry.

Campbell tells the crowd to learn what doesn't change.

design, storytelling, animation, typography, composition, color theory

We are awash in shiny cheap tools, a reality which is both wonderful and maddening. These creative disciplines have changed very little in the last several centuries and yet when edubloggers talk about creativity in 21st-century schools they talk overwhelmingly of the tools and, occasionally, of who found the tool first.

I paint with a broad brush here but for every 100 posts celebrating the easy-bake aesthetic of Wordle and Animoto you'd think I could find one celebrating the use of color toward easier, more satisfying communication.

Just gotta make it look new maybe. Like maybe we lose some vowels, rename it colrthry or something. We'll give it a logo with a gradient, add some social networking functionality, and if our district IT guy blocks it maybe then we'll start talking about what's more important to art than the tools we use to make it.

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