I talked about my use of goal-less problems on my physics semester exam. The essential idea is that the question is actually just a description of a situation. The student’s job is to model the situation as best they can using the physics they know. First step: say which models apply and why. Second step: draw (and annotate) the graphs/diagrams that go with those models to represent the situation. Third step: use the diagrams to analyze the situation.
“This problem doesn’t ask for anything.”
We start to plant the seed of this concept in the third unit (Constant Acceleration Particle Model) with “baby goal-less problems.” At that point, they can really only draw the kinematics graphs. And if there is enough information to solve the problem, they can probably only calculate about two pieces of information about the problem. They usually feel uncomfortable that there isn’t a specific question asked, but they also soon realize that there aren’t a lot of solvable questions to ask given the information. They just don’t know a lot of physics yet. I tell them that later in the year I will be able to give them a situation like these and they will fill up an entire page with physics, and that seems unlikely to them (at the time).
By the next unit (Unbalanced Forces Particle Model), they start using this tool to compare small changes in a situation. The honors class starts with a block sliding down a ramp with various descriptions given of the motion and amount of friction. The regular class starts with a block pushed then released along floors with varying amounts of friction.
At some point, I started making the background of the page a 50% opacity fine graph paper to try and really encourage them to use careful diagrams/graphs as part of their solution.
What do students actually write?
The second half of the semester exam presented students with 5 goal-less problems and asked them to choose 2. Here are a few of those problems. I chose some of the most thorough responses as well as some sparser ones.
A couple uses of goal-less problems
One use that I really like is starting a new unit with goal-less problems when the new model is really an application of old models (projectile motion is constant velocity and constant acceleration, uniform circular motion is a special case of unbalanced forces). It all but requires them to make connections between what they learned earlier and the new special case that we are considering, and it reinforces the idea that they can model new situations using the tools that they have already developed.
Here is the start of the Projectile Motion Particle Model packet. In Honors Physics, I let them dive in with this without trying to prime them for free fall at all. With the regular class, we spent around 30 minutes analyzing the first half of take 1 of Dan Meyer’s basketball videos, drawing graphs for the motion of the basketball, and generally defining free fall as the-only-force-acting-is-Fg. We kept our discussion very qualitative leaving the quantitative analysis to happen when they struggled through the first line-up of problems.
The next two questions are identical, but the ball is changed to an aluminum ball then to a ping pong ball. After that, the ball is rolled off of a 1.5 m tall table, then launched off the end of the same table. In both classes, when they started to calculate numbers on the various problems, they had lots of disagreements at their tables and started looking for objects to roll and drop to see if their answers could actually be true.
And later, in the Central Force Particle Model unit in my honors class, we started out with spirited discussions about how to model this situation (after we had played with vectors and geometry a bit to derive some relationships for objects going around a circle at a constant speed):
Another great use for goal-less problems this year has been as reassessments. Usually, I take a piece of paper, draw a picture onto it, label it with some numbers, and ask them to show me the skills the want to reassess. It usually keeps them from cherry-picking the skills because they generally have to show them in context. If they are prepared, they can demonstrate mastery on a lot of objectives at the same time (and I don’t need to carry around a ton of problems specifically tailored to each objective).