[Download the goods]
As you’ll recall, I take kind of a dim view towards superfluous movie soundtracks, which is to point out that the music here serves an important purpose.
- Play the video.
- Ask the students for questions that perplex them.
DimDim doesn’t save the entire chat transcript so I can’t quote the class’ questions exactly. Several concerned speed. One student asked, “If a crowd of people is standing on the escalator, would it be faster for Dan to take the stairs?” A conciser (though less interesting) phrasing of the same: “Is Dan faster than the escalator?”
The dominant question was, “How long will it take Dan to go up the down escalator?” This was, of course, an expected outcome of the video.
- Ask the students to guess at the answer to our question.
- Ask the students to set an upper bound on an acceptable answer.
- Ask the students to set a lower bound on an acceptable answer.
I think our highest estimate came from Sheng Ho who gave me two minutes to walk up the down escalator.
- Ask the students to define the information they’ll need to solve our question.
Jason: length of escalator
abarkley: your speed, speed of escalator
alemi-thevirtuosi: how many steps on the escalator
Mark Kola: rate of movement of elevator, avg step in length, and the number of steps in the escalator
Sandra Miller: speed of the escalator, speed you run up the stairs
At this point, I asked, “Which of these is easy to measure? Which of these is difficult? Which of the difficult measurements can we decompose into easier measurements?”
For example, the length of the escalator is difficult to measure — it’s too long — but counting steps is easy and measuring the height and depth of each step is easy. My speed up the stairs is difficult to measure — do I have a speed gun? — but its components — time and distance — aren’t.
And so it goes. I wonder what effect textbook problems like this one have on our teachers’ conception of mathematical problem solving.
It’s interesting to me, also, that no one answered, “nothing,” when asked what information they needed.
- Give them a pile of information to use as they see fit.
- Stairs — Depth
- Stairs — Height
- Stairs — Long Stair Depth
- Stairs — Video
- Escalator — Depth
- Escalator — Height
- Escalator — Video
- Give them time to work.
This is the electric classroom moment, the payoff for all your groundwork in the first four steps. Your students formulated their own question, guessed at the answer, set two bear traps for wrong answers, and discussed relevant and irrelevant information. This is useful preamble and no one is jumping into the hard work without a sense of direction, or at least a sense that we value experimentation here. No one is calling you over saying, “I have no idea where to start,” like they do when you assign “problem twenty-five on page sixty.”
This is also the moment where the DimDim experiment failed. It was maddening, feeling separated by a glass monitor from all the interesting student work out there. It was maddening, watching students try to explain their work in a constrained little chat box when it would’ve been clearer and easier to slide that work beneath a document camera, or to bring the student up to the front of the classroom to explain it. Students could have been lurking in the background but holding an amazing method or a productive error and I wouldn’t have known.
I had no idea who was finished and who needed more time. (I called us back together too early it turns out.)
Group work was impossible, also.
- After they compute their final answer, ask them to compare it to their error bounds from step two.
- Play the answer video.
- Compare the answer to our guesses from step two. Determine who guessed closest.
- Discuss sources of error.
- Discuss follow-up questions.
- My intent was to transform this kind of problem into something less abstract. I didn’t. It’s interesting to me how drastically you can change the skill you’re practicing depending on what information you obscure and what information you reveal. I think I sorted myself out but I’m interested if anyone knows how I should have presented this problem if I wanted to assess systems of equations.
- I should have used Google Forms for the first two steps.
- In the second draft of this problem, I added the teaser footage where I start stumbling up the down escalator. In the third draft of this problem, I added the song I was listening to in my earbuds. Both revisions resulted from test feedback from Jackie Ballarini. (Thx, JackieB!)
- A debt of gratitude to Scott Farrar, whose awesome idea I totally ripped off.
- A debt of gratitude, also, to the manager of the local multiplex, who let me run around on his escalators.
- If you attended the live session, please post a review. Did it make this WCYDWT thing clearer? Less clear? What was satisfying or unsatisfying about the experience?
2011 Mar 13: I updated the problem package to include video answering Christopher Danielson’s question, “How long if Dan rides the escalator like a normal person?”
2012 Jun 16. Brian E:
By this time, the students were dying to see how close their results were to reality, so in addition to checking the answer video Dan provides for the actual time, we also used it to check their position equations.