I was grading a test for my students, and I was surprised -again- by some of the answers that they can give.
They are happy to measure velocities in units of action, and energies in apples and oranges.
I also get answers of the form
a couple of orders of magnitude faster than the speed of light, or of wavelengths of the form
for an optical transition in the UV. This is only a couple of orders of magnitude smaller than the size of an atom, at distances that we have not yet been able to measure in any lab.
I wonder if there is a cure for this out there: some way to get the students to understand on their own if an answer is nonsense or not so that they can double check their work, rather than believe blindly the result of a bad computation.
I think the problem is that your students need to be trained to think about their answers and not just the questions. As a programmer, I often have completely functional programs that will contain invalid calculations (or invalid data) resulting in nonsensical output. A jr. programmer in my organization would have difficulty spotting this, simply because they are not familiar with what constitutes a sane and valid answer.
there is a cure! It is called a university education….
I agree.
I was hoping there was a way to make it happen more naturally than plain ole `survival of the fittest’ in a class (failing those who don’t get it).
Since this was for exams than I think that many times, during exams, students don’t have time to logically examine their results. If this is also the case with homework assignments than I think it is significant, but I think that the time pressure of exams makes this phenomenon understandable.
Every mistake is a learning opportunity. Except during finals, because you never know what you got right or wrong, you just get a rough idea of how much you’ve retained from the semester. You never even get to find out if you’ve retained the important stuff or just enough ephemera to squeak out a C.
OTOH, no matter how much you remind the class that you can’t exceed the speed of light, some people wont think about that when they’ve got a beer, bong and party waiting when it’s all over.
I’ve taken to requiring students in the intro class to write a short sentence at the end of every problem handed in for grading stating some reason why they think the answer makes sense. This isn’t infallible– I get some bizarre justifications of very wrong answers– but it cuts down on the incredible whoppers.
I think it is a failure, in general, of science and engineering classes at the lower levels (college wise) to promote understanding the physical situation as opposed to the mathematical situation.
Let me ask this – do you teach your students any rules of thumb? Back of the envelope or in the head ability to estimate -ball park- is something every student should be able to do.
Ask your students next time how many atoms come off tire with each revolution. Any that have the entry level physics of science or engineering should be able to do that in their head or at least quickly on paper.
I’ve had students tell me that the speed of an inch worm (unit conversion problem) is 500 meters per second. When I asked the student if this was reasonable it seemed like he understood that it wasn’t. I like the “short sentence” idea.
By the way, the first time I had a student get a 0 on a multiple choice physics exam (they answered every problem, maybe 10 questions 4 choices each), I worried that it meant I was unable to teach the subject. The second time I cut to the chase and just burst out laughing. At us both.
I think a part of this problem is that students have no natural sense for what units mean, or how large they can be.
I mean, if they were calculating how much something costs, and get, e.g., they spend a billion dollars on food a month, they’d probably realize there was a problem.
But ask them, “how fast is a meter per second” and I bet they can’t tell you, without a lot of thought, what things could move at that speed.
And, it’s not much of a surprise to me you’d get crazy things like velocities in units of action, either. What is action anyway? It seems a lot like something happening, and velocity seems like a perfectly good kind of action!
I’ll bet you most undergrads (and many grad students I’ve met!) can’t even tell you what action represents.
I mean, if you calculated that the capacitance of something is ten million Jars, would you think that was big, small, or just right? Who the hell knows? But you don’t use Jars in your every day life any more than your students use meters per second. Even in the case for, e.g., speed limits posted in m/s, that’s just a meaningless number to them, “go faster until the needle gets to around this number.”
Really, in order to do sanity-checking, they need more than just an understanding of what units mean, they need a reasonably intuitive sense of scale to compare them to.
The cure is, as Lenin would say, to learn, to learn, to learn.
I am also irritated if some people can’t see that something they hear – or “find out” – is complete nonsense.
On the other hand, the “intuition” is a double-edged sword. Intuition may fail, too. So sometimes it’s a damn good idea to trust the calculations even if the results are/look surprising.
Of course, surprising is something else than manifestly inconsistent with logic or basic principles of physics. But the difference may often be blurred and hard to see.
I thought I posted this last night, perhaps it didn’t make it through..
I think generally the problem is that most students of engineering and physics are not taught the physical side of things and instead the focus is too much on the mathematical equations attempting to describe reality.
Do your students have a grasp of the units which describe everyday (macro or micro) phenomena (there was a great xkcd comic on this)?
Time should be taken to teach students to be able to ball park or do back of the envelope calculations as this forces them to consider if their answer is, well, in the ball park.
As an example, any student who has made it through the normal series of introductory physics lectures should be able to tell you the approximate number of atoms which are lost each time a car tire makes one revolution. They should be able to figure this in their head, at worst quickly on paper or with calculator (perhaps these should be taken away too?).
Sorry:
I’m slow reading comments sometimes.
Day’s lecture was on specific heat. Particular example, why it takes a lot less heat to warm up the pot than the water inside it. Metal is much easier to warm than water.
So I ask the students, “which would you prefer to have to warm up with your body heat on a cold day, a kg of ice or a kg of steel.” They all wanted the ice. Arrgghhh.
The 10 digit accuracy on the faster-than-light velocity also sticks out for me.
The data he was using must have come from a very good experiment.
Do what Uncle Al did when he taught lab sections of pre-meds: award them their earned grades. Allow the unknowledgeable and especially the ineducable and the clueless to prosper of their own hands. Never allocate additional resources to the doomed at a university level. They had 12 years of chances, plus libraries and Google.
http://www.diversity.umich.edu/programs/
90+ programs for
moronsdiversity.http://www.giftedstudy.org/residential/michigan/index.asp
The Summer Institute for the Gifted is not associated with the University of Michigan.
Objective certification of the able reduces narrow end supply to job market demand, which is small. The unable are, as soon as possible, productively rerouted to careers in which they are able. Empirical observation tells us not everybody can be in the top 10%. Paradoxically, diversity enables 90% to be in the bottom 10%.
Somebody should look.
I had a professor tell us that a student once calculated the height that a whale (?) jumped out of the water to be about 1600 meters. Perhaps such anecdotes can help the students remember.
(Though the truth is that someone like me, who loves physics and is entertained by horrible miscalculations is destined to remember them and think critically about my answers, while someone who is less interested will invariably forget, or just not care so much.)