Last week, Mike Dunford was struggling with some teaching issues, relating to what level of effort he should expect from his students. His original decision drew some harsh criticism, both in his comments and from Sandra Porter, leading Mike to reconsider matters.
I meant to comment at the time, but I gave an exam last Thursday, which kept me kind of busy, and then there was the SAT Challenge to get ready.The issues Mike raises present some tough questions: on the one hand, you want students to learn to learn for themselves, and that occasionally runs counter to their immediate impulses, which are often to avoid work at all costs. As the Dean Dad puts it:
Unlike almost any other industry, in higher ed we have a substantial number of customers who are happier if the product is shoddy, or not delivered at all.
At the same time, you need to avoid situations where progress can be completely derailed by really basic misunderstandings. This is particularly important when the entire problem could be avoided by providing a trivial amount of extra information. Students have an amazing gift for slipping through the tiniest gaps in the statement of an assignment, and taking off in wholly novel directions. They can go wrong in ways that just never occur to faculty who know the full context of the problems being studied.
Example below the fold:
For the exam I gave last wek, I needed a problem dealing with one-dimensional motion under constant acceleration. I opted to use the example of somebody throwing a ball up into the air. I set it up so the thrower was standing on a balcony, and asked students to find the time taken for the ball to go up and fall back down to ground level, and what the speed was when it hit.
As the final part of the question, to sort out those who really have the concepts nailed from those who can just manipulate equations, I asked what would happen if a second person threw a ball downward at the same speed that the first ball was thrown up. Which ball would be moving faster when it hit the ground?
Now, this is a classic problem in physics classes. The answer is that both are moving at the same speed, because the ball thrown upward returns to its starting point moving with the same speed, in the opposite direction. The two balls accelerate identically from that point on, and hit the ground with the same speed.
It's a classic question, and immediately obvious to any faculty member what it's getting at, so it didn't even occur to me that I had forgotten to specify that the second person was standing on the same balcony as the first. The question just wouldn't make any sense otherwise, so it's an obvious assumption, to me.
Sure enough, though, I had a couple of students who picked up on that missing bit of information, and arrived at a different answer. I had to give them credit for it, too, because while their confusion might not seem sensible to me, because I know the background of the question, it was ultimately my fault-- I failed to give them all the information they needed.
(Most of them got it. They're pretty sharp.)
Correctly anticipating the wrong answers is one of the things I find hardest about trying to make up quiz and exam questions. The problem I have is similar to what Mike describes-- I try so hard to avoid "babying" them, that I end up under-specifying problems. And that inevitably leads to trouble.
- Log in to post comments
Amen.
I had a revelation this summer. In my intro class, I will sometimes (as I do always) write down variables with subscripts, so that they can be distinguished from other variables.
For instance, L_A is the luminosity of star A, and L_B is the luminosity of star B.
Students with math anxienty (i.e., students) see equations, and start to freeze up. Many will say, "I just don't understand anything." This time, I had the luxury of a class of 15, instead of a class of 100, so I was able to interact with the students in class a lot more. The student asked what the subscripting was all about.
I realized that the student was thinking that this was some sort of mathematical oepration -- simliar to how superscripting usually means raising to a power. I had no clue before that this might be a point of confusion, but now that I've seen it pointed out, I see how it can be. I believe I succeeded in convincing that class that L with a subscript A was just a name, and that there was nothing particularly deep or scary about the subscript.
The thing is, the students often don't even know how to express their questions or their confusion. They statement usually is "I don't understand any of this," rather than "what does the subscript A mean? How do I do that on my calculator?" The latter would help me figure out the problem, the former doesn't. But I think that students often have a hard time getting past the former and figuring out how to state the latter.
There is education research that points out the main misconceptions students have in some fields... but as you say, there's always more. Students will always find new cracks to be confused about which faculty wouldn't realize was even a potential point of confusion. It makes the whole teaching business very hard.
(And it's harder that students are afraid to ask questions because they don't want to look stupid, and because students think that professors want to hear that they understand things, even when they don't.)
Ohhhh, I wasn't hard on him - I was hard on the attitude. :-)
I have the same problem with my students. I teach 5th/6th grade math and science and I'm trying to help them develop their abstract thinking skills. As a result, when I attemp to give them so more open ended questions, where answers may vary, I sometimes forget crucial pieces of info that may aid in their thinking. Or, like you, I don't anticipate certain answers that while wrong, I can't necessarily mark them off because I failed to be specific enough. It's a fine line to walk.
Air resistance (speed) and Coriolis acceleration (landing zone). If the ball was released spinning, Magnus effect. The situation is only symmetric in vacuum in an inertial frame. A bullet fired horizontally does not land when a merely dropped bullt hits - the Earth curves away from the fired bullet's trajectory; Sagnac effect, Special Relativity, etc. How good is good enough?
The primary teaching of math and the sciences is dreadful - dumbed down to convenient approximations. The kids then suffer the rest of their lives with defective intuition. The Devil is in the details, and not trivially so. One rail of a railroad always wears faster than the other. A child wth glasses uncouples his eyes' accomodation, convergence, and image size - all with distance. He will not be good in airborne sports. The damage is done.
Hmm... but which cardinality of infinity are they? Is the number of wrong answers countably infinite or uncountably infinite?
Strings are countable, so the number of wrong answers that can be *written* would be countably infinite, but maybe it's possible to incorrectly answer a question nonverbally...
...must...ignore...the...troll...
Ak! Failed my will roll!
Uncle Al is way off base. "Dumbed down?" If, from the very beginning, we taught and talked about every potentially relevant detail, nobody would ever learn anything; everybody would be lost in a bewildering and overwhelming array of details.
It's not just at primary education. It's in research too. I was at a talk yesterday about electric and magentic fields that should be generated in the early Universe (just pre-CMB) by the charge separation resulting from the proton/electron mass difference. And, of course, the analysis was a simplification. It was done in a perturbative manner. It restricted itself to regimes where atoms wouldn't have to be worried about, and where nuclear reactions wouldn't have to be worried about. It restrictied itself to a few linear approximations.
And results were obtained; interesting ones. You do the easy things first that only looks at the most important affects to develop an understanding of the kind of things that go on.
When you drop a ball from a balcony, the Coriolis affect is a serious second order affect. Indeed, the way Chad states the problem, it complete cancles out anyway -- but even mentioning and discussing it would only obfuscate the problem and lose the important physical understanding and intuition carried within the problem.
We should always start with the broad outlines and the general understandings, and only once those are mastered, start adding the more compliacted and hard-to-understand second order effects.
-Rob
Coin is demonstrably incorrect. Surely any real number can be an incorrect answer.
I get why a ball thrown up would be moving at the same speed as a ball dropped from the same location, but if the person throws the ball down, isn't that imparting complementary force to gravity? (or whatever the correct term is. Anyway, I think a ball thrown downward would be traveling faster than the ball thrown upward.)
Read the question again scott. The ball is thrown down with the same initial speed as the ball thrown upward. So they should have the same speed. Throwing it straight up and allowing it to fall back down only changes the direction of the velocity, not it's magnitude.
Scott: Why would you get that a ball thrown up would match a ball dropped? Would a ball pitched up at 95mi/hr be going zero when it came back down past you (and inspired you to merely drop the second ball?) Or would you have to pitch one down at 95mi/hr to make it match the first?
Okay, I see my mistake now. It's been 17 years since I took classical physics, other than acoustics. Plus I was plotting the velocity curve incorrectly in my mind. Thanks for the corrections.
This is a little off track, so I apologize up front ( I had to look up apologize in my danish-english book (yes there is a short version of that "word" but the clock says 0300 and i am going to work in 5 hours so...
I like this site und so witer, and because I feel so teribly ignorant when I read some of the stuff, I started to listen to a podcast from Berkeley University, called Physics 10: Descriptive Introduction to Physics - Spring 2006
By a Richard Muller, it is great.
My question finally :
I think he said this : It takes 30 times the energy to make a sattelite go round the world, compard to the energy it takes to get it up.
My boss says no very loud, and I really do not want to listen to Richard Muller for another 30 hours.
By the way, because I wrote out my wrong answer, it is countable. But what if I had kept my mistake to myself? Would it then prove that mistakes are uncountably infinite?