Tuesday, September 27, 2005

More samples from statistics class, not necessarily random or independent

If you're going to give an example, pick a good one: For many mathematical methods, there's an easily-understood example that illustrates why the method is important ie why anybody bothered to come up with it in the first place. Unfortunately, many math professors seem to either not know about those examples, or forget about them when introducing a new method. For instance, compare these two introductions to Bayesian parameter estimation [to an audience that's never heard of it]:

1) "Suppose I have a probability distribution for the parameter p in a Bernoulli distribution, based on, well, just about anything. If I then observe some data drawn from the distribution parameterized by p, how should I update my probability distribution for p ? Bayesian parameter estimation is one way of doing this".

2) "Suppose I want to figure out the chances of a particular coin coming up heads. I could toss it a bunch of times and count the number of times a head appears. However, suppose I toss it 3 times and I always get tails. Does that mean the coin will never come up heads ? Our intuition says no, and Bayesian parameter estimation is one way of formalizing that intuition and taking into account the fact that we have some ideas about what the chances of coming up heads should be before we even toss the coin."

I know my reaction to approach #1, as my first introduction to the topic, would have been "Wha' happen ?"; #2, on the other hand, made sense as soon as I heard it. Unfortunately [for people who hadn't heard it before], #2 is not the way this particular topic was introduced in class today -- approach #1 was the one chosen and I don't think many people really grokked the whole point of it.

Somebody really should pull together intuitive examples like this from all areas of math and professors should be required to memorize them. The chances of that actually happening are, of course, arbitrarily close to zero [a prior belief I will be happy to update should I get some data ;-)].

"Periodic sampling coupled with lazy updates": This is a phenomenon exhibited by a poor sleep-deprived undergraduate student: she'd fall asleep for five minutes, return to a semi-awake state, look at what had been added to the board since her last period of wakefulness, scribble down the new stuff and then fall back asleep.

Given the fact that her notes looked pretty chicken-scratchy and that her memory of the class is probably a series of 10-second sound samples along the lines of "... and the Bayes estimator for this is ...", "... the Beta is a conjugate prior distribution ...","... the mean of the posterior evaluates to ...", I'm not sure that I would advocate this as an effective learning strategy.

2 Comments:

Anonymous Anonymous said...

[So this is a, umm, frequent poster posting today anonymously on the subject of your first observation.]

So say there's this new class on campus. It's very interdisciplinary, and involves cool biology and computing and all sorts of engineering ideas. And it's turning out to be very popular, with maybe 80 or 90 people signing up for it, because it sounds so very cool.

And the faculty member nominally "in charge" of it is very smart, and could teach it very engagingly. But he's a big-hearted fellow, and instead lets three random first- and second-year grad students have their way with it: class planning, presentation, discussion, the whole nine yards.

So all the diverse 80+ people in the class hear explanations of subjects as complicated and esoteric as signal theory, high-throughput screening, stochastic oscillator differential equations and the dynamics of the lac operon from people who have never taught, and appear never to have explained anything at all to a student. Or anybody.

This leads to the same sort of situation as you note, in spades: On explaining the lac operon, we have two attempts at leading a pedagogically fruitful discussion. One begins, cold [with no introductory material at all], "So who can come down here to the board and draw a picture of the lac operon in its 'off' state? Anyone? No?"

After five minutes of mumbling and silence (even from your correspondent, who was dumbstruck), one of the other grad instructors (a biology student) got up, and started to draw the genes of lac on the board. But they're connected with those little pointy-ended activation and square-ended inhibition arrows one sees in genetic regulatory diagrams.

Which of course leads to even more and deeper silence. Nobody but the pros in the room have ever seen such a thing, and the first student instructor hasn't ever seen one: he is a signals guy, and was thinking somebody would come down and draw some zeroes and ones to indicate the binary state of the genes....

I'm guessing there needs to be a lively critic on hand.

9:20 PM  
Anonymous Andre said...

The periodic sampling method probably isn't a great learning strategy but I don't think lectures are a good teaching strategy. At least not with a subject like statistics. It's just no good to have someone talk statistics or physics at me. Not only can I not think fast enough to watch and write the material that's usually covered, I certainly can't understand it. Maybe I have ADD, but I get sidetracked every few minutes - in a bad lecture it's due to boredom and in a good lecture it's because something the lecturer says sparks an idea that I end up following for a while. In either case, I end up a little further behind each time and it doesn't take long for my priority becomes staying awake while I watch someone practice their Greek alphabet.

I would respond much better to a course consisting of assigned reading with lectures serving to clarify difficult concepts. I don't need someone to re-write the book for me. Of course going into a lecture and just waiting for questions from students that have actually read the material is hard on the teacher and takes a level of knowledge and confidence that is surely not common.

12:21 AM  

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