Math Curriculum Remix

I don’t know why this is tripping my fuses so hard. I’ve seen it hundreds of times in the most straightforward textbooks: obscure one set of inputs, then reveal another, and you have a totally different math problem. Simple stuff, right? This visual proof-of-concept is really freaking me out, though.

(You know where to press pause, right?)

It’s the same footage. But the original was California-grade-six rates and the remix is California-grade-eight systems. What?

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. RudeDude

August 11, 2010 - 10:28 am -

I see what you did there! (I think.)

Pause at 00:39. You’ve obscured the base walking rate by the escalator rate. So now the “simple” problem from before has become a more difficult “back out the escalator rate” problem. It also helps to remove the music beat since the stepping rate (difference) is less obvious.

Certainly a perplexing problem. :)

2. Frank Noschese

August 11, 2010 - 10:58 am -

I don’t want to be a Debbie Downer, but I can still solve this one without systems. The physical mechanics of the set-up blow your cover.

For 10 seconds, I counted the number of taps I heard as you went up the down escalator, because each tap meant you placed your foot on the next step. You took 26 steps. Then I paused the video when you were at the bottom of the stairs and counted the number of stairs to the top as best I could. I counted 35 steps.

10 sec / 26 steps * 35 steps = 13.5 seconds to climb the stairs. (Pretty close!)

The simplest solution is the best solution.

Even with the sound off, I could still watch your feet and count you taking steps. Perhaps using a moving sidewalk would be better at forcing the kids to use systems? And maybe replacing you with a battery operated toy that moves at constant speed? It would remove “cheats” like step counting. But toys aren’t as engaging as people.

Thoughts?

3. Rob

August 15, 2010 - 6:29 pm -

Frank, do you still then have to use systems to find the speed of the elevator itself?

Maybe I’ve been out of eight-grade math for too long (I’m not a math teacher), or am making the problem more difficult than it really is, but I have to admit, this is a really challenging problem for me!

4. Frank Noschese

August 15, 2010 - 6:53 pm -

Rob: If I am interpreting Dan correctly, the gut question is “How long will it take Dan to walk up the stairs?” I was able to solve this without knowing any distances or speeds because Dan moves up/down the same number of steps every second (though, b/c some stairs are moving, he doesn’t move up/down the same number of meters every second). All I have to do is watch/listen to his footsteps, count them and time them. It doesn’t matter which escalator b/c his step rate is the same (in time to his music, right?).

If you wanted the speed of the escalator, you just need a distance traveled and time interval for one 1 stair. No systems necessary.

I hope this makes sense.

And Dan, am I interpreting the purpose of this video correctly?

5. Dan Meyer

August 16, 2010 - 1:41 pm -

Frank: And Dan, am I interpreting the purpose of this video correctly?

Proof is in the pudding, Frank, and you nailed the time it took me to walk up the stairs. Your idea to use a moving sidewalk to conceal the footsteps is sharp. Logistically challenging, also, which makes it all the more fun.

6. Colin Graham

August 25, 2010 - 4:41 am -

Going down the up escalator would be fun too, if a little more dangerous! I wonder if it would be possible to do a side view so we only see the top half of your body as you go up and down. You might then be able to juxtapose the three ‘strips’ (four if you have down the up) similar to the Scott Haluck video. You could maybe just throw out the question “How long would it take to go down the up escalator?” as final problem.

Oh and the English teaching part of me says to tell you that the proof is in the eating, not the pudding!

:)

Colin

7. Vince Muccioli

October 13, 2010 - 2:42 am -

Dan, I love the material you are putting out. I find the original version of this video much easier to follow for the students. It seems like the remixed version ends before students would have a handle of what they are watching. The problem is that the original video is no longer available. Could you possibly make the original available on vimeo again or something? Thanks.

8. Maria Droujkova

October 22, 2010 - 12:08 pm -

Dan, here is a weird Russian page on what is apparently a tongue-in-cheek schoolchildren sport/web meme there called Escalator Running (transliterated from English): http://lurkmore.ru/%D0%9C%D0%B5%D1%82%D1%80%D0%BE%D1%8D%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BA%D0%B8%D0%BD%D0%B3/%D0%AD%D1%81%D0%BA%D0%B0%D0%BB%D0%B0%D1%82%D0%BE%D1%80_%D0%B3%D0%B5%D0%B9%D0%BC%D0%B8%D0%BD%D0%B3

I thought about you when I ran into that page. Check out the video of the girl walking up the down escalator, absolutely packed with people: http://www.youtube.com/watch?v=oFFfs3K6Tjs&fmt=18

9. Christopher Danielson

March 12, 2011 - 10:57 am -

My question hasn’t come up here, which is “How long if Dan rides the escalator like a normal person?” I suppose this is the same as asking about the speed of the escalator, but it feels more engaging to me as a learner.

Thanks for offering this twist. I am planning a session with future teachers here at my community college in which we solve the escalators problem together and think about what the process can teach us about teaching and learning. This second video adds productively to the work we’ll do.