Goal-less problems

One of the things I do like about the flipped classroom I teach in is the use of goal-less problems.

If you click through that link, you’ll see that on exams, Kelly O’Shea asks students to:

(a) list which models apply and explain why

(b) draw useful diagrams or graphs

(c) use diagrams to help you find interesting unknown quantities

Here’s an example of the kind of written goal-less problem that have been built into the flipped classroom I teach.

Here’s an example of a video goal-less problem that I think would also be good (perhaps better) for our class.

I think for the video-goal-less problem, I could easily edit the video to cover up the odometer, and then an interesting question is, “How far does the car get?” or “Does the odometer change numbers?” A perhaps less compelling question, at least initially, would be “What’s the average acceleration?” And a higher level question would be, “How well does a constant acceleration model do here?”

There are lots of different ways to find how far the car gets:

(1) We can make an educated estimate for the average velocity, and use the average velocity idea to calculate the distance.

(2) We can break up the motion into pieces, and use speedometer reading at different times to estimate the distance of each piece, perhaps applying the constant velocity model to each section. I imagine a careful strobe diagram (or motion map) could work here, but algebra or graphing would work, too.

(3) We can calculate an average acceleration just using the initial and final speedometer readings, and then apply the constant acceleration model. You could also plot some data points for velocity at different time, make some inferences about a best fit line to either estimate the average acceleration and/or find the area under the curve.

Of course, 1-4 don’t represent completely independent thinking or processes.

I’m curious to run a mini-teaching experiment where some students get the written goal-less problem with the original directions and other students get the video goal-less problem with something more like Kelly’s directions.

I just want to see (1) how these two different scenarios “launch” in terms of engagement and (2) the extent to which these different activities lead students to make contact with important disciplinary ideas (not just equations).