So here's one where no one gets any credit for guessing the question. The question is obvious. The question is scattered throughout this entire clip (from the fourth season of The Office). I made the question explicit in the post title.
Will the DVD icon ever ricochet into a corner?
But what are the supplementary materials? How do you make this experience real to your students? What do they have in front of them? How are they getting their hands dirty with the math?
It doesn't matter if you don't know how to make the supplementary materials. Just name them. This is a big-hearted community. We'll find someone who does.
Here’s what basically has to happen to make a successful WCYDWT lesson:
Lighting strikes (you observe something).
You recognize that lightning has struck (you say “holy *&^%”).
You investigate by building layers of abstraction on your observation.
You realize that that particular abstraction fits in your curriculum.
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.
You rebuild the abstraction in a way that will support the questions you successfully predict they will ask.
You make attractive keynote slides out of it.
You extend your original abstraction to questions that they will want to pursue to enhance their understanding.
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:
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.
I read stuff like this, and the first thought that goes through my mind is, “Man, I suck at teaching math.”
#2
I’m with Steve. I realize how far I am from where I should be.
#3
I’m with Steve and Craig- I can’t teach this way yet because my brain isn’t aware/smart/intuitive/mathematical enough to first notice these things, then develop a lesson, and actually deliver and make sense of it.
#4
I’ll echo Steve’s comment, I read this site and I feel like a fraud. I don’t know anything about teaching math.
I don't teach to disempower students and I don't blog to disempower teachers.
My largest point with these WCYDWT features, way above any other, has been that compelling, interesting math is everywhere. That you can capture it, mount it, and bring it into your class in such a way that students will also find math interesting and compelling and, in the process, become a little less intimidated by their own imaginations.
But I really suck at teaching that to teachers. Both off comments like those quoted above and off a recent, gruesome experience teaching online, it's clear that I'm missing some key piece(s) of scaffolding.
Course Prerequisites
I'm trying to determine the prerequisites for this kind of coursework and — correct me here — I'm pretty sure there are only two:
You like math. You weren't forced into this job.
You use math. You're high on your own product. This isn't a game to you. Math has made your personal life richer, easier, or more meaningful in the last week.
From there it's a simpler matter of teaching:
process — how to flip an interesting thing around into a challenging thing, detailed somewhat in my last post.
technique — how to (i) capture photos / video, (ii) copy and paste images from the web, (iii) rip DVDs, (iv) download TV shows, (v) layer measurements on top of photos/videos, and (vi) post all of the above online.
Once the process becomes intuitive and once any three of those skills become easy, I think you fall quickly into this virtuous cycle of seeing interesting things > teaching interesting things > seeing more interesting things. The coefficient of friction falls to zero. It's like skating on ice.
Case In Point
Kate Nowak, on the bite-sized opener clip I ripped from Parks and Recreation and posted two weeks ago:
This is cute, and totally slipped by me even though I watch this show.
I see little daylight between me and Kate as educators, which makes her comment all the more illustrative of the skills I'm talking about, skills which I use often enough that my antenna is on auto-scan for these passing mathematical moments. If I had to guess, Kate has never (iv) used BitTorrent to download a digital copy of a TV show and excerpt a clip in QuickTime, which means there is a certain degree of interference between her antenna and those moments.
Does That Make Sense?
If I allow myself any charity here it's to acknowledge that this process is as much lifestyle as it is technique, and blogging — or any kind of asynchronous forum where dialogue plays out slowly — may be the wrong forum for teaching it. The right forum has proven pretty well elusive, though.
[Correction: an oil barrel contains 158,987.295 ml.]
Nat Torkington writes the Four Short Links column for O'Reilly's Radar, highlighting interesting articles around the web on a daily (or near-daily) basis. Recently, he's pitched me a few links via e-mail under the heading "WCYDWT?" which, due to my fallen nature, I have taken as a challenge to my sacred honor.
Here's one: the relative price of different liquids which illustrates the disturbing fact that HP printer ink is several orders of magnitude more expensive than crude oil.
So I opened our first day back from winter break with a learning moment built around Nat's link and then recorded video of the moment which you'll find below. My apologies in advance for the pitiful production value. Initially, I was going to forward this only to Nat as some kind of retort but I found the experience so difficult, messy, and exhilarating, I had to debrief myself here. Notwithstanding the video quality, you're welcome to pummel me for anything you see.
Synonymous with "What Can You Do With This?" is "How Do You Turn Something Interesting Into Something Challenging?" I have asked educators that question on this blog, in online classes, and in several conference presentations over several years. Here is — by far — the most common answer:
"I'd put it on the wall and we'd talk about it."
Which is a weak start. A certain kind of student inevitably dominates these pseudo-Socratic discussions and then invites another kind of student to disengage. But Nat has dealt us a strong hand. If we play those cards right, we can retain and empower a lot of those (mathematically and conversationally) reticent students.
1. Calm down with the math for a moment. Invite their intuition.
At one point in my career, I would have led this off by giving them all the data and asking them to compute the ratio of cost to volume. but my blue students are poorly-served by that approach. So many of them have been burned so badly by math that if I open the conversation with terms like "ratio" and "volume," pushing numbers and structure right at them, I'll lose the students I want to keep. Moreover, this confuses master with slave. We use math to make sense of the world around us more often than the reverse.
So I put seven liquids on the wall and asked them to rank them from most expensive to least. Simple speculation. Nothing more mathematical than that. Please imagine, here, how much more fun it is to walk around and talk about the question, "Which do you think is the most expensive?" rather than the lead balloon "Which has the highest ratio of cost to volume?"
Ask a student to come up and share her ranking with the class. Argue a bit. Entertain opposing opinions. Ask a student if he'd trade a can of Red Bull for a can of his own blood. Student investment at this point is very nearly 100%. It's mine to lose.
2. Slowly lower mathematical structure onto their intuition.
"Here's the answer," I told them, but students know at this point to triple-check me. Several went straight for Red Bull, which totes does not cost $51.15.
"So you're saying that how much you get matters as much as how much it costs."
Fine.
We used cell phones to text Google and ask for unit conversion. This always strikes my students as magical and suspicious.
And here, finally, we talked about the ratio of the cost of blood to how much blood you get. I asked them to visualize one milliliter of blood. "What does .40 mean?" We talked about the cost of one milliliter and how it's useful to compare that cost across liquids.
The rest (hopefully) writes itself, though, for the record, I kind of hate how explain-y I get in the last third of the video.
Transform that interesting thing into a classroom challenge.
Help your students develop tools to resolve that interesting challenge.
[Optional] Blog about it.
Repeat.
The feeds in your reader then spiral upwards and out of your control. WCYDWT ideas begin to pile up faster than you can capture them. It'll freak you out and you'll wish you could turn it off for just a few hours while you're watching TV but you realize this a rare ancillary benefit in an occasionally tortuous job and you accept it gratefully.
