After the students made their predictions, I abandoned the water tank problem and moved on to something completely different. In each one of my classes, eventually a few of the students made a comment along the lines of “you never told us how long it took to fill the tank.” Sometimes the comment came only a few minutes after we had moved on. Other times, it came much later. More convincing evidence of the students’ level of engagement in the exercise came at the end of the lesson when I played the rest of the video.

That reminds me of a time (back in the early 70’s) when I boldly told my class that there were more VW bugs on the road today than another specific brand/model of car. Of course, I was wrong, but…

Later during lunch I watched as several of my students skipped lunch and were counting cars to prove me wrong!

Imagine telling kids today that their assignment is to count how many times a particular brand of car passes during their lunch hour? I would have to threaten with fire & damnation to get them to do it.

-Ihor

PS VW bugs were quite popular in those days. So they did count quite a few.

With their focus on the screen, you would have thought they were watching a summer blockbuster at the movie theater, not a tank filling with water in a classroom.

That’s of course assuming that the student buys into it. What makes it pseudo is not whether math is its own context or not, but whether the student buys into it and wants to do it.

With all due respect to DLB, the problem that Dan start’s with is interesting only if the student thinks so. Which means the teacher has to use it in a context that is appropriate for his/her student(s).

I think there are contexts that are more intrinsically interesting to more kids than others. (That’s why I didn’t think the pouring water into the tank problem was all that much.) The trick is to come up WCYDWT ideas and build a pedagogical context with good math engagement that will work for most of your kids.

-Ihor

As a title I math resource I like to give problems like these to students in the hall. Most just blow it off, but for one or two kids a year they come back every couple of days or so and try to give an answer just so they can get a new question.

Mark E: I would be curious as to your take on Paul Lockhart’s “A Mathematician’s Lament”

I read it on the plane en route to NYC for TEDxNYED. I finished rehearsing my talk silently to myself over Nevada and then read Lockhart over Colorado. Afterward, I could only think, “… this guy already said it all.”

I concede the dissonance between our work – I love finding math in the world around me; he emphasized math as an end to itself – but where we line up, I think, is behind a) the power of a visual, and b) the importance of problems that announce their constraints quickly and clearly.

Also, Sam has a sharp eye, especially with the last bit: “Give your students a good problem, let them struggle and get frustrated. See what they come up with. Wait until they are dying for an idea, then give them some technique. But not too much.

Breedeen: I’m a little bit in love with Deborah Ball. In fact, just about every math teacher I know is a little bit in love with her. And I don’t fully trust the ones that aren’t.

Ha!