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:
recreate mathematical reasoning for my students as I find it in the world around me.
involve students in both the solution to and the formulation of meaningful questions.
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.
Several students tallied the left half of the pyramid, doubled it, and then added the middle column. One student not only counted the circles one-by-freaking-one but kept a current tally inside each circle.
There are 324.
He was somewhere in the low hundreds when I drew his attention to the numbers at the end of each row: 1, 4, 9, 16 ….
"What do you notice? How can we use that to save ourselves time?"
The tedium of busy work can motivate student invention.
In advance of their EduCon presentation, Dean Shareski and Alec Couros put out the call for brief interviews on teacher education, addressing these two questions:
What are your general views on the status of teacher education in preparing teachers, especially in regards to innovative teaching? What positives, negatives, or general views can you share? Please do pull in your own experiences if applicable.
What is the ideal role of teacher education in developing teachers who are media literate and technologically savvy?
For whatever reason, they decided to bury the submissions at the bottom of a wiki, which taught us all a valuable lesson. Here is mine:
Specs.Hardware: Mac Pro / 2.66GHz Quad-Core / 8GB ¶ Software: Excel 2004, Photoshop CS4, After Effects CS4, Final Cut Pro 7.
Workflow. I sketched an outline on paper, then ordered it in Google Docs and turned that into sixty Photoshop compositions. That took about two weeks. Then I sequenced those compositions into a slideshow of still images and synced them in Final Cut Pro to a Creative Commons track. After Effects doesn't play nicely with music so I spent the next two weeks working deaf, working exclusively off the timecodes from Final Cut Pro. (ie "Okay, the pie graph needs to finish its rotation at 2:41:20.") The first day I saw it with music was January 31, the same day I posted it.
Music. I'm not saying I did anything fantastic to the music track, but I did have to sync the slides to the rhythm, making adjustments for longer segments (any of the "top five + other" bar graphs, the travel maps), cutting and blending the song so it complemented the content of the video. I am saying that Animoto won't do this automatically. iMovie won't do this automatically. And teachers consistently overrepresent the capability of those tools.
Data Sources. I maintained active records in Google Tasks before transferring them to an Excel sheet biweekly which I backed up fastidiously over the course of the year. Perish the possibility I might lose it. ¶ I collected all music records passively through last.fm, which became significantly more accurate after I outfitted my car with a 30-pin iPhone cable and began tracking car audio. ¶ I also collected my mobile phone statistics passively through AT&T's online billing system, which kindly exports data to Excel.
Mathematical
I don't see any of my students buying this pitch but here it is anyway: I would have had to release this video somewhere in April if I didn't have a working knowledge of a) the degree measure of angles, b) proportions, c) percents, d) coordinates, e) 3D space, f) modular arithmetic, and g) linear interpolation. I even calculated an integral.
Here's just one example. You noticed the little animated counters running all throughout the project? Problem: you want the counter to read "0″ at 773 frames into the composition and "44651″ at 795 frames:
Solution: a linear equation!
Math.round(timeToFrames()*2029.59-1568872.77)
Miscellaneous
Guilt. I watched a continuous 20 days and 23 hours of television and movies. I could slap qualifiers all over that statistic but you're still talking about nearly a month spent proximate to a flickering light.
Battlestar Galactica. Not worth it.
Guilt II. 18 gallons sounds like kind of a lot of beer when you put it that way.
Margin of Error. I'll put the average margin of error for the project somewhere below 1%. And I'll wager the sleep statistics are the worst. I had to remember to take a screenshot of my iPhone's clock wallpaper twice a day at the two times of the day that I was the least likely to remember to take a screenshot of my iPhone's clock wallpaper.
2.5 Minutes. I'm really happy with the length of the piece. That's, like, 2.4 days per second!
Editing. For every statistic I included there were two I cut. There were albums and songs; incoming calls, outgoing calls, outgoing messages, fastest rising message recipients as well as fastest falling; places where I drank beer, number of people with whom I drank beer; repeat vs. first time movie viewings, number of people with whom I watched movies; plus a host of Twitter statistics and a Wordle visualization of my 2009 text message content which were, predictably, pretty dull. ¶ The most poignant graph that I cut for length was this one, which features both my father's cancer diagnosis and, relatedly, the fact that I drove the length of the US in one month without leaving California.
What a strange project.
2010. It's been two years and I can't see quitting this kind of introspection. I'm already anticipating my decade retrospective where I hope I'll see a lot of huge life changes reflected in microscopic daily statistics. That'll be great. ¶ My goal for next year is to post my completed annual report video no later than January 1, 2011. I don't think this is impossible. Andrew Kramer recently composed a convincing tutorial explaining dynamic bar graphs in After Effects, where you just enter the final data and Javascript recomposes the entire project. The trick will be extending that process across an entire video and several different infographics. In any case, I need to publicly throw down this gauntlet.
Throughout 2009, I recorded several dozen statistics about a) the pop culture I consumed, b) the people I talked to, c) the beer I drank, d) the places I visited, e) the vehicles I took to those places, and f) the amount of sleep I enjoyed each day. Those statistics spread across several thousand cells of a spreadsheet, which I then condensed and animated into the 2.5-minute video clip embedded below. That process took about a month, all told, which isn't a ratio I'm proud of, even if I'm happy with the result.
My name is Dan Meyer and I like to teach.
