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23 March 2009

Secrets of grading homework

In order to get your students engaged on a nightly basis, you absolutely must make some pretense toward grading homework. If you expect your class to make an effort “for their own good,” without you checking their work at all, you’re deluding yourself – teenagers are not known for accurate evaluations of what’s good for them.

Let’s disregard philosophical issues of self-determinism vs. paternalism and note that even the most diligent student needs feedback on his efforts. Spending three hours doing 15 problems incorrectly is worse than useless; on the other hand, just 15 minutes of serious, careful thought about physics can be extraordinarily productive. A first-time physics student doesn’t know the difference between good effort and wasted time. Grading homework helps the student see that difference.

That said, there’s no need to grade every problem every night in tremendous detail. The purposes of grading homework are to inspire effort, and to provide useful feedback. Let’s say you assign two problems each night. Just knowing that one of the problems will be graded will be sufficient to inspire effort, as long as the students don’t know which problem will be graded. As for useful feedback, some of the most common mistakes in approaching physics problems are poor problem presentation, not checking the reasonability of answers, writing five paragraphs when one sentence would have been sufficient, or not explaining anything at all. Chances are, if the student is making these errors on one problem, he’s making them on both; there’s no need to grade every single assignment.

Near the beginning of the year, I find it important to grade a problem every night. Ideally, I grade it in time to send a brief comment to the class email folder:

"Good job explaining your reasoning on the normal force problem. The most common mistake was that a normal force requires a surface. You can’t label “normal force” for any old upward force!"

I’m establishing a tone. Those who are inclined to slack learn quickly that I will notice. My expectations become crystal clear right away.

As the class progresses, just the fact that I do some grading on a regular basis is enough to maintain the class’s focus. After a month or so, I can save up some problems to grade for my nights on duty. Or, I can grade the problems only every other night, or even every three nights. As long as they still know I’m watching, as long as I catch the egregious attempts at slacking1, I keep my class with me.
[1] And, because I graded a problem every night for a month, I know exactly who might make these egregious

What my homework grades mean

Different teachers take all kinds of different approaches to grading homework. Many are perfectly reasonable – please don’t take my ideas as gospel.

I grade each problem on (usually) a 10 points scale, just like an AP free response question. In principle, I have in mind a loose rubric. In reality, though, I am grading holistically.

On the top end of the scale, I want 10/10 to be reasonably tough to obtain. That means the student has presented the problem neatly and clearly, with explanations or annotations so that I know he understands what he did thoroughly.

I do occasionally give 11 or 12 points out of 10. Such bonus scores are given for outstanding presentation, for a clever explication of the meaning of a result, or for something out of the ordinary that I feel bears recognition.

The students’ overall homework grade is assigned based on a square root curve, where 81% is an A, 64% is a B, 49% is a C. Therefore, on an individual problem, 8 points is essentially an A, 6 or 7 points are a B.

Below that, the minimum passing score is 4. If I feel like the problem does not merit a passing score, I don’t even differentiate between a 0, 1, 2, or 3; I simply stamp VOID1 on the problem, and assign the student a time to come discuss the problem with me.

[2] Yes, I actually purchased a red and blue “VOID” stamp. It’s effective.

So what am I looking for when I grade?

It is critical that a stack of homework problems not take me all night to grade. I have to grade as fast as possible, which is not conducive to evaluating every aspect of the problem. If I know before I start what mistakes students might make, and what aspects of the problem require annotation or explanation, then I can move quickly.

For example, consider this problem, which I assigned last Thursday:

In a double-slit experiment it is found that blue light of wavelength 450 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same location? (Hint: figure out which variable must be the same in each case!)

Here are the solution steps I expect to see:

• Writing the relevant equation, dsinθ = mλ.
• Recognizing that d and λ must stay the same
• Using a half-integer for m in the second case, because the light will be at a minimum
• Recognizing that while any half-integer m will work, the correct m will be the one that gives a wavelength in the visible spectrum

Now, what do I actually look for? I want to see some evidence that the student has not only done the steps above, but that he knows why he has done these steps.

For example, many folks start their work with the statement that m1λ1 = m2λ2. That’s technically and mathematically correct, and will lead to a correct solution. But that equation is not on the equation sheet, and so is not a legitimate way to begin a problem. Where did that equation come from?

If it’s the first equation I see, then most likely it came from a friend’s advice. That’s fine, as I encourage collaboration. Nonetheless, collaboration isn’t a substitute for individual thinking. It is critical that I catch students when they are using classmates’ ideas without an attempt to justify them with reasoning. So, this student will lose several points.

However, if this student says m1λ1 = m2λ2 “because d1sinθ1 = d2θ2, then I see what he’s doing. If he further mentions WHY the angle to the screen and the distance between slits does not change, then that’s worth full or extra credit.

Similarly, I expect to see some kind of annotation when it’s time to plug in m= 3/2: “Because of the destructive interference” or “because the light is at a minimum” works for me.

And finally, to earn full credit, I have to see some writing about the subtleties of choosing m. They should show that they tried other m’s besides 3/2, and that they gave wavelengths outside the visible spectrum; or, at least, they should tell me that they could have tried these other m’s. Saying that m= 3/2 for an illegitimate reason (for example, “because m was 2, so now it has to be less”) does not earn full credit. Failure to justify the choice of m earns the same points as if the justification were incorrect.

Beyond these four issues, I don’t really look at the solution. If the answer is wrong but the student explained the four bullet points clearly, I’ll probably just call is 9/10 and be done with it. After all, this is not a math class. It’s far more important to be able to explain the physics than to plug in correctly to the calculator. Throughout the year, my grading sends this message, as the class certainly shares stories of what they lost or gained points for. They see that I’m looking at their words far more than I’m looking at their numbers. And, since I know exactly what I’m looking for, it doesn’t take me very long to figure out whether I’ve seen the words I want to see – saving me time in the grading process.


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