Trading and Grading Homework Problems In Class: The Context of Your Feedback Matters.

Years ago I described how I grade nightly homework assignments quickly.  Point of emphasis: I don't write on the students' papers.  No one reads my comments carefully.  I just put a number on the paper, record that number, and give it back the next day.

I've also suggested that it's not effective to "go over" a homework problem in detail in class.  Johnny might have asked you to go over the problem, but he'll tune out once he finds where he thinks he lost points; he won't learn a lasting lesson.  And everyone else in the class has tuned out, because they either got the problem right to begin with, or they just don't care right now.

The purpose of grading homework, for me, is NOT to give detailed feedback.  It's to be sure that students are keeping up with the assignments, that they are practicing their problem presentation, that they are engaging appropriately with the material.  If I don't grade homework, the homework doesn't get done properly.

It's reasonable to ask, then: If I'm not writing more than a number on a homework problem, and I'm not discussing the problem in class, how should a student who wants detailed feedback get it?

Timing matters.  Your students have a bobzillion things going on in their lives.  Like it or not, physics just isn't a constant priority.  In order for feedback to be meaningful and useful, it has to be given at a time when the student is ready to receive it.  

One effective time for feedback would be as the student is struggling with the homework problem, immediately after he's completed the problem.  Thing is, you're usually not present at just the right moment; and, if your student is actually doing the homework problem in your presence, he's going to want the feedback* before the time is right.  

* And you're likely to give him the feedback too early, too.  Students must engage with the problem.  It's a good thing for them to get stuck.  One of the more important physics teaching skills is to find a way to politely yet firmly deny assistance to a working student until the time is right.

One way to provide appropriately-timed help is to set up part of class such that the time will be right for feedback.  Have the class solve a problem while you sit in the front of the room, encouraging students to see you after they've completed each step.  Just the fact that there are twenty other students needing your attention will usually convince students to keep working until they're well and truly stuck.  Then the faster workers can experimentally verify the answer to the problem while you help the slower folks.

But as for homework, students need to learn to rely on their classmates.  Whether the students are working in small physics parties at night, or whether they just send questions to each other via text, email, facebook, etc, they are helping each other become un-stuck.  That's the whole point of collaboration -- not only so everyone can make appropriate progress on tough problems, but so they develop the experience of teaching the problems to someone else.

Context Matters.  So Set Up A Useful Context For Feedback.

Imagine you've talked to a student explicitly about how Newton's third law force pairs can't act on the same object.  Perhaps you said so in class, and perhaps you also helped this student get un-stuck on a homework problem where he was trying to have the force pairs "cancel" each other to equilibrium.  And then, on the test two weeks later, he made the same mistake again.  Aarrgh!

Think about this student's response when you helped him.  In class, he listened attentively, maybe even wrote down some words; on the homework, he nodded, said "okay," and corrected his mistake.  Remember, everything we do in physics class is fleeting.  We like to think that students are motivated by their grade or their love of the subject to remember everything we say and everything they're asked to do.  But really, once the problem set is done, so is the student.  Even if the timing of your feedback to this student was right, the context wasn't.  

I like to create multiple contexts, each of which has some level of import.  For example, I give a quiz every day.  On the quiz, I might ask directly: "Can Newton's Third Law Force Pairs act on the same object?"  or, "The earth pulls on an astronaut, and an astronaut pulls on the earth.  What is the acceleration of the earth-astronaut system?"*  Even though the student had to use this fact on the previous night's homework, he might not have really internalized what he was doing -- after all, students are answer-focused, no matter how hard we try to change them.  This quiz provides the same question in another context.  When we go over the quiz, now the student hears the answer, and hopefully will make the connection to the homework problem.

* Expecting the answer "It can't be determined," knowing that too many folks will say "zero."

And finally, I've taken to having students grade homework problems to a rubric once every week or two.  While generic "going over" a problem is ineffective, describing the solution in the context of awarding points to a friend's paper is extraordinarily effective.  Without my prodding, students often write detailed explanations on their classmates' papers.  After the in-class grading exercise, students have done the problem, seen my solution, applied my solution to grade a friend's problem, thought about what score they themselves might have earned, then seen their friend's detailed commentary.  Now THAT'S context.