That’s one of the essential ingredients for the intellectual crisis: a question that’s impossible to answer, one on which everyone can speculate regardless of mathematical ability, one that illustrates a need for more information.

Knowing that the snapshots are 1s apart makes a big difference; the lack of a clear time reference was one reason why I felt that video would be better. I totally agree that having printouts of the photos to write on is a plus, so maybe the ideal I-have-infinite-time-to-prepare-lessons version would use both.

I’m too sleep deprived to imagine exactly how this would all play out. Is there a specific intellectual crisis that these media uncover in students?

i love what you’re doing dan. and more importantly – my kids do.

the frankness and authenticity of this post in particular….thank you for that as well.

You’ll see.

But it won’t happen unless you and your cohorts keep at it.

I was really confused by the apparent time transport that occurs between photos 3 and 4. (as well as between other adjacent photographs). The fact that photos 1 through 3 are obviously a set led me to think that the photos were all related to the same race. With the help of the comments above, I now think that you didn’t intend for the photographs to be a series but to have each stand alone as an individual problem.

The information that the strobe shots were taken one second apart definitely re-sparked my interest and led me
to consider each photo as two overlaid snapshots from a separate race from which to have students make predictions as to the entire course of the race. My confusion now subsides but my interest also does. Now each problem presented becomes a pair constant rate problems presented visually.

I liked the problem better when I was totally confused.

Here’s my suggestion on how to “be less helpful”.
1) Drop the strobes.
2) Start with a wideangle of the entire course, the position of the runners and a time reference. Ask the students, who is going to win?
3) Add closeups of sections of the race course with time references. Have lots of of these and show the students only what they ask for. Give an index of the available closeups to the students and challenge the students to predict the winner by viewing the fewest number of close ups as possible.
4) Make the first problem linear.
4a) Make the second problem linear.
4…) linear again
5) Crisis – introduce a non-linear problem (have a runner stop to tie his shoe or trip and fall.)

Optional lesson. Graphing stories. Hand out a random set of snapshots to different groups of the students and have them graph the course of the race and then discuss why different groups got the same or different results.

Optional race: Have a runner race a basket ball shot. Linear versus quadratic. Do you graph horizontal versus
vertical or position versus time?

I asked myself, “WCYDWT?” and sat in the pile for a while, thinking it over. Then we devoted the whole club to “counting all the leaves in the pile” – well, estimating, really. Kids got to 100, 000 very meaningfully, and worked through a couple of important snags in the process, like counting “Ten thousand, two thousand, three thousand…” (the typical place value mistake). It was a very good math experience for six year olds, as evaluated by kids, parents, and myself.

I largely blame WCYDWT for this success. I could probably write up a journal article about it, with formal references to relevant research frameworks. However, it’s your baby, so maybe you should do that.

This is the first WCYDWT that I can recall leaving me positively nonplussed. The reason I always read the WCYDWTs, even though they never go into my classroom, is that I enjoy finding out how you’re going to turn an ordinary experience / easily argued about problem and scale it into all different kinds of mathematic principles.

The intellectual crises that these images lead to seem to be at their core just a repackaging of the good ole’ textbook word problem with trains leaving the station at different times. Really, who cares?

“Don’t just whinge, provide a solution.” -my last boss

A race is not static like photographs. I think that these would pack punch and hook students in if each scenario was first preceded by one second video clips from a similar vantage point, or even from a first person view.

Heck, get inside a track and put the camera inside the announcer’s box. Or spend ten minutes on youtube. Stop the tape of a 200 meter run as the athletes enter the final 50 meters. After the howls, ask the class, “Who’s going to win?”

Or put on that Jason mask. Seriously.

And to clarify, your vision of where this is going is that the students would plot position vs time graphs and find the intersection? In my mind I was trying to force it into an rt=rt+k make substitutions and solve for t kind of direction.