The game field of infinite moves

Frank Noschese just posed some questions about “just trying something” in problem-solving, and why students seem to do it intuitively with video games but experience “problem-solving paralysis” in physics.  When I started writing my second long-ish comment I realized I’m preoccupied with this, and decided to post it here.

What if part of the difference is students’ reliance on brute force approaches?

In a game, which is a human-designed environment, there are a finite number of possible moves.  And if you think of typical gameplay mechanics, that number is often 3-4.  Run left, run right, jump.  Run right, jump, shoot.   Even if there are 10, they’re finite and predictable: if you run from here and jump from exactly this point, you will always end up at exactly that point.  They’re also largely repetitive from game to game.  No matter how weird the situation in which you find yourself, you know the solution is some permutation of run, jump, shoot.  If you keep trying you will eventually exhaust all the approaches.  It is possible to explore every point on the game field and try every move at every point — the brute force approach (whether this is necessary or even desirable is immaterial to my point).

In nature, being as it is a non-human-designed environment, there is an arbitrarily large number of possible moves.  If students surmise that “just trying things until something works” could take years and still might not exhaust all the approaches, well, they’re right.  In fact, this is an insight into science that we probably don’t give them enough credit for.

Now, realistically, they also know that their teacher is not demanding something impossible.  But being asked to choose from among infinite options, and not knowing how long you’re going to be expected to keep doing that, must make you feel pretty powerless.  I suspect that some students experience a physics experiment as an infinite playing field with infinite moves, of which every point must be explored.  Concluding that that’s pointless or impossible is, frankly, valid.  The problem here isn’t that they’re not applying their game-playing strategies to science; the problem is that they are. Other conclusions that would follow:

• If there are infinite equally likely options, then whether you “win” depends on luck.  There is no point trying to get better at this since it is uncontrollable.
• People who regularly win at an uncontrollable game must have some kind of  magic power (“smartness”) that is not available to others.

And yet, those of us on the other side of the lesson plan do walk into those kinds of situations.  We find them fun and challenging.   When I think about why I do, it’s because I’m sure of two things:

• any failure at all will generate more information than I have
• any new information will allow me to make better quality inferences about what to do next

I don’t experience the game space as an infinite playing field of which each point must be explored.  I experience it as an infinite playing field where it’s (almost) always possible to play “warmer-colder.”  I mine my failures for information about whether I’m getting closer to or farther away from the solution.  I’m comfortable with the idea that I will spend my time getting less wrong.  Since all failures contain this information, the process of attempting an experiment generally allows me to constrain it down to a manageable level.

My willingness to engage with these types of problems depends on a skill (extracting constraint info from failures), a belief (it is almost always possible to do this), and an attitude (“less wrong” is an honourable process that is worth being proud of, not an indictment of my intelligence) that I think my students don’t have.

Richard Louv makes a related point in Last Child in the Woods: Saving Our Children From Nature-Deficit Disorder (my review and some quotes here).  He suggests that there are specific advantages to unstructured outdoor play that are not available otherwise — distinct from the advantages that are available from design-y play structures or in highly-interpreted walks on groomed trails.  Unstructured play brings us face to face with infinite possibility.  Maybe it builds some comfort and helps us develop mental and emotional strategies for not being immobilized by it?

I’m not sure how to check, and if I could, I’m not sure I’d know what to do about it.  I guess I’ll just try something, figure out a way to tell if it made things better or worse, then use that information to improve…