Grading work during class - it's not "lazy", it's pedagogically effective

It's late February.  At this point, my classroom culture has been well established.  Students work independently on the list of tasks for the day - predictions, experiments, simulations, analysis, etc.  They know to ask each other for help when stuck, then to come see me with their work to get checked off.  This is the "come and show me" approach that's worked very well for me.

So well, in fact, that as often as not I have little to do during class.  I have lots of prep to do outside of class, creating the list of tasks and ensuring that all materials are ready for each task.  But once we get going, I sit at my desk waiting for students to see me.

When students turn in a problem set at the start of class, it's tempting to put the stack of papers in my bag to look at later.  However, as the year (and my career) has gone on, I've found it ever more worthwhile to start grading these problem sets in class, while students are working on other things.

I'm sure I'd lose significant marks on a teaching evaluation rubric if some administrator or ed professor were to observe me while I grade at my desk during class.  "Your students deserve your full attention all the time," they'd say.  "Grading papers should be done alone, during planning period or in the evenings, when it will take your mental energy away from your colleagues and your family and will grind you into a hollow shell of yourself before the next school break."

I object on several counts.

Firstly, my students deserve a teacher who does not hover, who does not give away answers, who does not do any heavy intellectual lifting for them.  Part of success in physics and in all academic pursuits is making and recovering from mistakes; is figuring out for oneself how to start a problem, not just how to finish.  If I'm walking around the classroom, students can and will ask me a "quick question" - one they would figure out for themselves if they took but a moment to think carefully.  My physical separation from the class as they work is very definitely a feature, not a bug.

Secondly, consider the purpose of grading papers to begin with.  I'm not merely trying to put a number into a gradebook.  I'm providing my students with an authentic audience for their work.  The actual number that I write on their paper is almost immaterial.  My students need to know that I'm paying attention to what they submit, that I'm going to find the things they've done right and wrong.  

Of course, we all know that students never read comments we write on their papers, except in the manner of a defense attorney looking for a legal loophole.  Writing comments takes an enormous amount of time.  I don't recommend writing anything on a student's paper beyond an occasional X or checkmark.

But students need feedback, right?  Right.  Often our daily quiz is based on the homework; going over the quiz provides the necessary feedback.  Other times, I grade a problem set at home, and I later bring in students who did really poorly for consultation later in the week; at that consultation, I have students redo the problems they missed from scratch, giving feedback in the moment.  And if a significant fraction of the class makes a similar mistake, I'll address this mistake in class or in an email thread, always with followup in the form of a quiz or a similar question on a future problem set.

Grading work in class provides perhaps the best opportunity for feedback that I've discovered.  Teenagers live in the moment.  The effectiveness of a problem set has a half-life measured in minutes.  The clock ticks starting when the problem set is turned in; even feedback the next day is often too late to effectively address misconceptions (or to effectively address student apathy).  

A projectile is launched horizontally at a speed of 30 m/s from a cliff, and hits the ground 2 seconds later.  What is the vertical height of the cliff?  

Jimbo solved using the equation d = v^2/2a, with a = 10 m/s/s, and v = 30 m/s.  If I address Jimbo's issue in class a couple days from now, he'll have forgotten how and why he used these values; and he'll do it again.  It's not like I haven't emphasized separating vertical and horizontal velocities in projectile problems before. 

But if I call Jimbo to my desk and show him the problem statement that says HORIZONTAL speed of 30 m/s, and then ask him whether the question asks for a vertical or horizontal distance... then I can show him directly and immediately that he's used a horizontal speed in a vertical context.  This is generally an entirely good-faith mistake, born of an incomplete understanding of projectile motion.  And Jimbo is less likely to make this mistake again.

Kearney solved using the equation d=vt.  His mistake is less about true understanding of projectile motion, and more about insufficient attention to detail.  We don't learn by doing, we learn by thinking about what we do.*  Kearney wasn't thinking about what he was doing.  He knows - because our fact sheets say, because we've dealt with these equations in class in multiple contexts for months - that d=vt is only for constant speed, and vertically a projectile is changing speed.  When I call Kearney to the front of the room and circle the word "vertical" in the question, he generally hangs his head and says "yeah, I know, I didn't read carefully."  In the rare case in which Kearney doesn't immediately see his mistake, I can help him.  I discovered a student who didn't understand the meaning of the words "vertical" and "horizontal" this way!  But no matter why Kearney got this wrong, he got the feedback he needed, at the right time.  He's less likely to make this mistake again, if only because he knows I'm going to find out and say something if he does.

*Apparently that's a Dewey line.  I've been using it a lot lately, as a variation on my old band director's "Practice doesn't make perfect, perfect practice makes perfect."