Argument A: It would be much harder to swim to the other side of the river in the fast-moving water as in still water.

Argument B: It would be just as easy to swim to the other side of the river in the fast-moving water as in still water.

I hope this gets as out of hand for you and your students as it did for me and my wife.

Featured Comment

Scott Farrar:

This excellent question exhibits a quality that is not found often in math curricula: it has the “specificity sweet spot”: it is specific enough for a student to answer, but non-specific enough for every kid to agree on the answer. Students making different assumptions will have different responses, thus creating a real mathematical argument.

Let’s say he wants to assess the impulse-momentum theorem, which is the theorem that explains why boxers roll with punches rather than against them. ie. If you double the duration of the impact, you halve its force. (Cut me some slack here, science-buds. Everybody knows I have no idea what I’m talking about.)

He gave me permission to share with you three versions of the same assessment of a student’s understanding of the impulse-momentum theorem. Let me invite you to assess the assessments in the comments. List some advantages and disadvantages. Ask yourself, “What is each option really assessing?” Greg will be along shortly to offer his own commentary and to assess your assessment of the assessments.

Option 1

An 80 kg stuntman jumps off of a platform high in the air and lands on an airbag. The stuntman hits the airbag with an initial velocity of 45 m/s downward. 0.1 s elapses between the moment the stuntman first touches the airbag and the moment the airbag completely deflates and he comes to rest. Assume that the maximum force that the stuntman can experience and survive is 39200 N. Does the stuntman survive the fall?

Option 2

A stuntman jumps off of the top of a crane extended high up in the air. Below him is an airbag–a large inflatable cushion that has a thickness of 3 meters. When the stuntman comes into contact with the airbag, the impact deflates the airbag over a period of time, compressing the airbag from 3 meters thick to 0 meters thick while slowing him down to a stop. Explain, making reference to the impulse momentum theorem, why the stuntman is able to survive.

Option 3

Explain, making reference to the impulse momentum theorem, why the stuntman is able to survive the jump.

BTW: xkcd on the same issue.

BTW: Not for nothing, this is exactly how my mind worked. When I was ten.

Though neither of the following two curricula have any kind of public outline, they seem extremely self-consistent and they track (unintentionally, of course) extremely closely to the vision I’m chasing.

Problem Pictures

These CD-ROMs (which you can preview here and which Mr. K reviews here) are stocked with images that are each, on some level, “interesting,” and each of which beg a different mathematical question. Mercifully, that question is rarely, “what shapes do you see in this photo?” which is the lowest level of some pyramid which has yet to be named.

Principle Failing: No video, which makes the next entry particularly essential to my investigation.

The Hypertextbook

“Edited by Glenn Elert, written by his students.”

Their investigation of Mario’s acceleration due to gravity may have cropped up on one of your Internets, recently, and was certainly worth your attention. The recipe is consistent throughout Elert’s curriculum:

1. Extract some video from pop cultureTalkin’ about Batman Begins, Madden 2006, Jackass – this Elert guy is out of control in my opinion..
2. Use physics, math, Wikipedia, photogrammetry, and estimation to answer an interesting question.

Principle Failing: This document is designed more as a record of student learning than as a curriculum for teachers. The media which would propel this thing into classrooms around the world is either absent (as with the Mario investigation) or was uploaded to YouTube which dutifully scrubbed it (as with the Hulk investigation).

To proliferate as fully as they deserve to, these investigations need a complete multimedia supplement, starting with high-resolution captures. In Mario’s case, you would need:

1. a clip showing Mario falling from the same height from every Mario game published, edited into a multi-panel split screen. The students would then ask the obvious question, “Why does Mario hit the ground sooner in some games than in others?”
2. an individual clip for each jump, no decoration.
3. The same clips with a grid superimposed over the footage for measurements.
4. A lesson plan with analysis.

Again, we’re working on different projects here, but Elert only includes #4, which means his work will find its way only into the classrooms of the most digitally savvy physics teachers. How many more teachers would benefit had he included the first three? My guess is: a lot.