Feedback Inertia -- finding the right amount of effort necessary to check an answer

It was Matt Greenwolfe of Cary Academy who first articulated this concept to me while I was visiting last week.  He formerly used an online simulation to help his students practice translating physical motion into position-time graphs.  But he found that the instantaneous feedback of the simulation led to pure guesses about what the graph should look like.  Not enough feedback inertia.  

Then he created a programmable robot: students draw a position-time graph on the computer, plug a cord into the robot, press the download button, wait a moment, disconnect the cord, and press start.  The robot performs the motion represented by the graph.  Matt found that because there were a few minutes of effort involved in connecting and disconnecting the robot, students were more likely to think carefully about their original graph.  Just the right amount of feedback inertia.

I'll start with the obvious: Physics frustrates many good students, because it does not yield to memorization.  Other subject require learning of facts; physics additionally requires learning the processes that, in combination with those facts, produce correct answers.

Yet the answers to physics problems seem deceptively simple.  Increase, decrease, or remain the same; up, down, left, or right; speed up, slow down, or steady speed.  Even quantitative problems can be* reduced to picking the right equation out of only a few reasonable options, and then assigning one of just a couple of possible values to variables.

*Shouldn't be, but can be

Much of physics teaching, then, consists not just of helping students to find the right answers, or even of explaining the correct process.  We have go farther -- we have to put students in situations where they internalize for themselves the methods of getting answers that work.  Such internalization takes the right kind of practice, and just the right style of feedback.

Students love instantaneous feedback: when answers are available in the back of the book, by clicking on an online simulation, through webassign or its clones.  But does checking an answer instantly (and correcting it if wrong) really lead to understanding?  Sometimes... but because the negative feedback comes so quickly, the process can quickly devolve into horse games.  Students will make another educated guess, and be given a false sense of security if the next guess is right.  Even if you award a declining scale of class credit, it's still a higher priority for most students to be done than to maximize credit.  Not enough feedback inertia.

The other extreme is the extended laboratory activity.  We might have students make a high-stakes prediction, then collect abundant data to verify or de-verify the prediction.  Fabulous... but the longer it takes to collect and analyze that data, the farther divorced the students are from their original prediction.  Furthermore, their mindset becomes less about dispassionate understanding than about proving themselves right.

It's unlikely that a teenager says, after an hour of data collection, "oh, I predicted a line here, but I got a curve.  Oh!  That's because this is a sine function, which looks linear at first.  So next time I should look carefully at the relevant equation rather than assume that all increasing functions are straight lines."

More likely, the thought process is, "Come on, it sorta looks straight, can't you count this right?  Oh.  I guess I predicted wrong.  Shit."  Too much feedback inertia.

The trick is to strike a balance between these two extremes.  Students need feedback quickly enough that they have the opportunity try a new prediction before they lose mental contact with their prediction method.  But they need enough of a barrier to feedback that they don't guess, but rather pay careful attention to their prediction method.  Being wrong has to hurt, but only a wee bit.  And that's what I mean by feedback inertia: the inherent difficulty of checking an answer.

Feedback inertia can come in many forms.  Matt uses his robot.  I use my line of students at the front of the room -- because they have to wait in line to check their answers, students think a bit more carefully about what they're writing.  Or, I use simple experiments which require a few minutes of walking to the back of the room, or picking up a labquest to plug in.  

Now, longer experiments have an important place in physics courses, as do sets of multiple choice practice with instant feedback.  I'm not saying that everything that I or you do must include an ideal amount of feedback inertia.  I'm suggesting that the concept exists; and its application is most important when students are introduced to a new topic in which they have to build mental models to understand how to predict simple physical behavior.

Got another way of optimizing feedback inertia?  I'd love to hear it in the comments.

GCJ