Like the Batman problem a few posts down, there’s another classic failure which has reached internet fame and glory by virtue of its spectacular flameout.
Wonderfully eccentric, but the sad part is that the problem is literally one line away from a correct solution. The block starts off with a gravitational potential energy mgh. This is turned into kinetic energy as it slides down, and then into the potential energy of the spring as the spring slows the block to a halt. The potential energy of the spring is (1/2)kx2, so when the spring is fully compressed all the gravitational potential energy has been transfered to the spring: mgh = (1/2)kx2. And the student has all except the equals sign written down! All that remains is to solve for x:
x = √(2ghm/k)
And of course for part b, the block will return to its original height since no energy was lost to friction.
Which brings us to the real question: does the student’s incomplete answer deserve a 0? Most people who study physics in grad school or go on to become physics professors have to do a lot of grading. I myself am a TA; last semester I taught the E&M half of the intro physics class for engineers. A lot of times you’d see students solve problems with the shotgun method: write down every equation that contained the variables in the problems and hope something stuck. Most of the time it didn’t work. Sometimes it resulted in some truly wild but correct solution methods. Usually the professor would give us TAs pretty good guidelines for how strictly we were to grade, but sometimes we had to use our judgment. This particular student picked the exact two correct equations. This showed understanding that energy was involved. But what wasn’t understood is that energy is conserved. That is, the fact that both forms of potential energy were equal was not explicitly mentioned. And that’s one of the most important concepts to master in an intro physics class. But one line shy of the answer… I’d feel pretty bad taking off too many points. In the absence of other guidance from the professor, I think I’d give a 5/10. Half credit for an answer that’s halfway there seems legitimate.
Those of us who are used to physics sometimes lose sight of just how deeply unnatural physics is compared to the vast majority of other things people do. It’s a beautiful subject though, and in our efforts to teach both the beauty and methods of natural law we should remember that students won’t grasp everything at once. What’s trivial to my professors is not necessarily trivial to me, and what’s trivial to me is not necessarily trivial to my students. And if partially correct solutions take the longest to grade, well, that’s why we TAs get paid. Even if more money would be nice!
5 responses so far ↓
1 Åka // May 29, 2008 at 10:26 am
This reminds me of something one of my fellow TA:s said. She remembered how she used to struggle with some of her lab reports, and pictured how the people who were grading it would laugh at some of the things she didn’t get together. And now that she was on the other side of the process, she knew that it was true! This post is an example of how we preserve the funniest “wrong answers” and show them to eachother, and occasionally laugh at them… And then, many of the students grow up to eventually become TA:s and even professors themselves.
2 CCPhysicist // May 29, 2008 at 11:06 am
That comment by Aka reminds me that I really need to work on a pair of blogs about labs and lab reports. And that the student should have just circled “x” on the picture.
First, you must have a grading rubric for every problem, making one up yourself if you are not given one by the lead instructor. This is essential if you are going to produce fair grades across a small class (say 30 to 50), not to mention a large one (I have in mind grading one problem on a final taken by 750 students), and justify your grading decisions.
I would not give half credit for a problem that showed no evidence of anything more than trivial equation grabbing. In particular, whatever partial credit might be set aside for correctly calculating the potential energy would be discounted due to a failure to provide correct units for that part of the work.
That goes double when the student gets part b wrong, since correct conceptual understanding of this problem would make that part easier than part a. The “No” in part b is almost worth negative points toward the problem. It remains at rest with a net force acting on it?
However, I would not give full marks for a correct answer that simply set them equal and produced a correct value for x, and less if all I saw was an equation grab of the x = sqrt() relation you give in your article.
A correct solution starts with Ef = Ei + W, and I’m always pleased when the student also writes “Conserve energy” right before that equation. All correct solutions start at the beginning. If the people taking your class are going to go to engineering school, it is extremely important that they learn to start their solution at the beginning.
3 Matt // May 29, 2008 at 12:09 pm
I had a physics professor who gave no partial credit. Which resulted in some ridiculous grade distributions (tests were only 10 questions).
His rationale (repeated over and over again throughout the class in a high nasal Chinese accent), “No partial credit! You engineer, you make mistake, bridge fall down, people die!!”
I think a no partial credit policy (with a standard distribution grade curve) is an acceptable (and more clear cut) way to grade physics.
4 Carl Brannen // May 30, 2008 at 10:44 am
When multiple people grade the same test, it should be done by assigning each problem to a particular grader, assembly line style. Then your students won’t complain that, by the luck of the draw, their test got submitted to the guy who was giving no partial credit that day.
Also, I tried to break my tests into simple problems so I could more easily grade them. To get it really right, take all the tests and examine the 1st problem. Put them into different piles according to the mistake. Then assign a grade to each pile.
Afterwards, when you go over the test, you can make little comments like (I taught calculus) “a lot of you left off the minus sign when differentiating cosine. That error cost you 1 point.” Your students will look down at their tests to see if they made the error. A few will groan. All of them will know that they were graded fairly.
After I fully implemented “fair grading” policy, my complaints about inaccurate grades dropped to zero. The students were graded fairly and they knew it. This is about 33% of the road to making a classroom of students happy with your class.
5 CCPhysicist // May 30, 2008 at 5:39 pm
I see that Carl and I learned a similar system for grading. I wrote about my approach in the recent past:
http://doctorpion.blogspot.com/2007/12/efficient-grading-physics-and-math.html
Rather than go into detail here about the relationship between exam design and partial credit choices, I decided to blog it instead:
http://doctorpion.blogspot.com/2008/05/exam-design-and-grading.html
Thanks for stimulating those thoughts. There are ways to make grading less of a pain, and some of it starts with the exam design itself.
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