Here are two very similar #anyqs entries fromÂ Dan and Nancy – two teachers I worked with in Grand Forks, ND. I asked my readers to decide which was the better first act and I disagreed with most of them.
Dan’s features a spigot leaking into a bucket. It’s just leaking. Drip drip drip drip drip.
Nancy’s features a faucet leaking into a measuring cup. It’s just leaking. Drip drip drip drip drip. But Nancy also includes a timer on her iPhone. And at the end of 39 seconds she draws the measuring cup close to the camera so you can see how many ounces have leaked out so far.
Why Dan Has Told The Better Mathematical Story
The first act of a good story introduces a conflict. It does very little to solve it. Think of the shark in Jaws munching on the lady swimmer. At that point, we have no idea what tools, resources, and information will be brought to bear on the task of killing the shark. We only know we want it dead.
The first act of a good story asks very little of the viewer’s intellect. It appeals, instead, to the gut. The viewer of Nancy’s first act would ideally think, “My word. How much water is that faucet going to waste?” Instead, because Nancy has already foregrounded the tools, resources, and information that belong in the second act of the story (just several minutes later in the lesson!) the viewer thinks, “Oh. This is a math problem, isn’t it?”
We need to curb our natural tendency as math teachers to burn up interesting problems on an altar to our math gods. In this case, all that means is you wait until after your students have formulated a question that interests them before offering them tools, resources, and information to solve it.
BTW: Picky? Absolutely. But where’s the fun in this job if not in negotiating the details. For whatever it’s worth, if you called me out for featuring timers prominently in the first acts of my own stories (as Bowen Kerins did recently) you’d be right on. The timers came from a position of insecurity that no one’s going to wonder “how long?” if I don’t explicitly call out time in the first act. That’s done now.
PhilJune 29, 2011 - 11:16 am -
Thanks Dan, I find my favorite questions are the ones I discover not as much those I strive to create. A lesson I’m glad you reminded me of.
Matt McCreaJune 29, 2011 - 11:21 am -
This, of course, runs right back to Jackson, et al from your last post. The addition of the timer lowers the cognitive demand of the task at hand, making this a less rigorous and cognitively demanding task than the first.
It’s nice having a bit of research to back up your gut, no?
NumbatJune 29, 2011 - 12:08 pm -
I think Dans is better because it’s more “real”. Nancy’s is clearly contrived.
Jason DyerJune 29, 2011 - 12:54 pm -
From the dept. of teaching-is-an-art-not-a-science:
I’m not wild about either; Nancy’s or the reasons you outlined, but from Dan’s I get almost no dramatic sense at all. I can GUESS that the water that I see on the left is somehow dripping to the right, but it’s too hard to see so there’s no tension.
Because of that issue if I had to pick one I would use Nancy’s. Dan’s I can’t work up enough effort to even try to solve it myself. If I’m not motivated to solve something how would my students feel?
[And no offense meant to Dan or Nancy themselves — we are being picky here.]
Matt McCreaJune 29, 2011 - 3:06 pm -
After reading Jason’s, I buy his, but not enough to switch to Nancy, just enough to want to improve it. Maybe a close up shot of the leaky faucet pans out to see the whole scene? Does that build a bit more tension?
As a further improvement, I’d want to see a bit more than just a leaky faucet, maybe a small stream. If a faucet’s leaking outside, I don’t put a bucket under it, I just let it run until I get it fixed (unlike a leaky ceiling, for instance). However, I could plausibly be filling up a bucket with that steady stream, and I’d want to know how long that would take before I have to carry the bucket to its destination. More dramatic effect for me in that situation while keeping the integrity of its cognitive demand.
Dan MeyerJune 29, 2011 - 4:23 pm -
I’m not saying Dan’s is beyond improvement, for the record. Just that Nancy’s has structural flaws.
Jay PatelJune 29, 2011 - 6:32 pm -
With one caveat, I agree with Dan’s video. The “plain Dan” video is short and does little to build a sense of impatience. For example, have you considered doing a time lapse of the video starting from sunrise to sunset? I know the prep would be demanding, but the I could see nearly ever student thinking “How much water?”.
PeterJune 30, 2011 - 4:37 am -
I’m getting it…..
In today’s modern, if uncivil vernacular, Act 1 of a lesson should be the ‘WTF?’ part. If I can get students saying, “Huh?”, or “What is this?”, then I think Act 1 is working
MarkJune 30, 2011 - 4:46 am -
You could add a little more drama. Dripping water is just not that exciting.
Maybe take that iphone and put it on the ground next to the bucket. Students would but totally bummed if the iphone was destroyed, similar to how I felt when that attractive woman was eaten by jaws.
John BerrayJune 30, 2011 - 5:59 am -
I do think Dan’s video is a slightly more natural and hence the winner of the two, although seeing the full bathroom counter top in Nancy’s scene lends an air of “this could be anyone’s house.”
The idea of a close up of Dan’s shot would be valuable, followed by a pan out, but that could get a shaky.
Here’s a crazy idea: leave out the bucket in Dan’s video. Give the impression that a passerby has noticed this leak and is catching the waste before the homeowner has. This might get students pondering “How much water is wasted every hour, day, month…?” or “How much is that unfortunate drip costing the homeowner?”
The bucket just seems like it’s already one step into the process of the solution.
Dan MeyerJune 30, 2011 - 6:09 am -
Exactly. And the real challenge isn’t to create a first act that makes students go “WTF?” You can find those all over Twitter’s #anyqs tag. The challenge is to create a second act that helps students resolve the “WTF?” from the first act mathematically.
ie. I can make you wonder a bunch of different things from an image, but very few of your questions will be resolved mathematically.
MarkJune 30, 2011 - 6:36 am -
“WTF for Math” could be a cool coffee table book (print? OMG so 80’s.)
Julie ReulbachJune 30, 2011 - 6:45 am -
I like the “picky”. You are explaining how to do this in a very illustrative way. I am still trying to figure #anyqs out so I’ll take all of the explanations that I can get, even the picky ones. Thanks and keep it coming.
Joshua SchmidtJune 30, 2011 - 1:09 pm -
Thanks for explaining this in detail. I think I can fully understand the side that you are coming from now, Dan. When explaining as the first act, I do think that (other) Dan has a better first act set up.
I would like like to note as well how cool it is to be able to be picky about videos like this because let’s not forget how much better these are than pulling problems out of the book.
John GaskellJuly 2, 2011 - 3:10 pm -
So. I’m making my budget for next month and I need to know how much my water bill is going to be if I don’t get this leak fixed. See, the plumber charges $150 to fix it. Is it worth it to get it fixed before I move out at the end of the month? Or should I just let it run?
Bowen KerinsJuly 2, 2011 - 8:46 pm -
Hey, I wasn’t picking on you, just curious about the decision — and with most Internet videos coming with timecodes now, may as well include it.
What about taking Nancy’s version and replacing the “Act I” with the water dripping into a half-full plugged sink? The measuring cup could be useful in “Act II” but also needed is some information about the size and shape of the sink.
I suppose this becomes a little reminiscent of the famous “fill the octagonal thingy” video, but the question “How much longer is there until this sink overflows?” adds tension and interest.
richJuly 12, 2011 - 6:38 pm -
A dripping faucet can lead to an open-ended discussion with students. For example, a fellow teacher saw that the water fountain in the hallway outside her classroom door was always dripping at what seemed to be a constant rate. She started a discussion with her middle school students with regard to the dripping faucet without talking about math. The students responded with the idea that the fountain probably wasted a lot of water and then the students drove this idea into a project to determine how much water (and money) was being wasted by the drip. After determining the amount of water and researching the actual cost of the water, the students were able to determine the loss of water (and cost) for the district. The teacher arranged to have the class present their findings to the district administrators. As no surprise, the long-time leaking fountain was repaired. The teacher never lead the students into a math problem and the students were truly engaged. More meaningful, applied, and not contrived.