The scourge of the physics student is the tendency to get problems done merely for the sake of finishing the assignment, without really knowing or caring whether the approach is correct. I'm asked all the time "Can I come to consultation period so you can give me more practice problems to do?" I generally have to explain that it's not doing MORE practice problems that will help their understanding, it's paying careful attention to the practice problems that I already assign.
A couple of weeks ago I assigned this classic question about dragging a block at constant speed across a table: when I double the speed, what happens to the force I'm pulling with? Most everyone generally gets this wrong on their first, individual attempt. They revert to "logic" and "of course" in their justifications. Even students who have carefully trained themselves to write facts of physics and connect those facts logically to the situation get the answer wrong -- they write a fact, yes, but then say "logically, of course, doubling the speed means doubling the force." Or they write Newton's second law, TELL ME CLEARLY that acceleration is zero in both cases, then say "since the a doubled, the force must double as well."
I'm not stating a new issue here -- all the physics teachers reading this are nodding their heads. We will never get all of our students to answer this question the right way. There's no magic, secret method that will turn all students into Newton's second law machines. All we can do is use all of our tricks to maximize the number who do it right.
Underlying all those tricks, though, is getting students to care very deeply about their prediction. I often pose the thought experiment: Will you bet $100 that your answer is right? So often, the answer is, "sure, but let me change my answer real quick." I then have the conversation about how they hadn't taken their initial answer seriously enough.
But that's a thought experiment. Everyone knows I'm not REALLY going to bet them $100. If nothing else, they know I'd always win.* My point stands: there's no purpose in doing a physics problem if you don't really believe in your answer. If students had to gamble money on the correctness of each answer, their problem sets would be vastly improved.
* I do get the occasional student willing to bet, reasoning that while I'd certainly win, they'd get their money back after I was sacked for gambling.
Given the prohibition against actually insisting our students bet money, can we instead set up a situation in which the students FEEL like there are high stakes to their prediction?
Some folks would put a grade on the line -- "this correct answer earns extra credit." Sure. But to me, that feels no different than grading their problem set. If 4/5 of the students are already getting the answer wrong on a graded problem set, then clearly grades are an insufficient motivator. The stakes have to be different. Money isn't an option... but you have other "items" of value that you can use.
Last week I used gift certificates to the school snack bar. Each certificate was for a single item -- a cheeseburger, order of fries, milkshake, whatever. I've also used homework exemptions in the past; or, the ability to leave class early rather than work on a review packet. These are all high-stakes items to my students. They covet, ninth commandment be danged. (Which is silly, when you think about it. They're all paying some fraction of the astronomical school tuition to attend here, but they go nuts over a cheeseburger worth $1.65 at our subsidized snack bar.)
Now, here's the new bit -- I didn't just say "correct predictions earn a gift certificate." No. That wouldn't give the students any skin in the game. There's not much given up if the prediction is wrong -- oh, well, no cheeseburger for me.
Instead I gave each student a gift certificate. Everyone held, in his very hand, a piece of paper worth the coveted cheeseburger, with his name on it, even.
Then, each student had to place his certificate on top of a card indicating one of the possible predictions: the force necessary to move the car will double, quadruple, or stay the same. Only the certificates placed in the correct pile would be returned.
I've never seen such investment in the results. You've heard the term "bear pit atmosphere?" I've never been in a bear pit, but I've seen the reactions around a high-roller craps table. Suddenly, my class was all nervous, excited, anticipatory... of the reading on a force probe. The difference was, with the certificate in-hand, they were worried they might lose what they already felt like they had. Why should there be a difference between "correct predictions earn a cheeseburger" and "here's a cheeseburger, now you can only keep it if you make a correct prediction?" I know I've seen Nate Silver and his ilk discuss the psychological research. I make no claims to know why this technique felt different, I only know that it worked.
When, later that week, I had students write a correction on that problem, I got immediate, thorough, and correct justifications. No more of this random wrong answer for the second and third time with a hangdog look telling me how hard physics is... this time, they remembered the answer and the justification -- because they "lost" a cheeseburger. :-)