Thursday, January 21, 2010

Teaching probability

This semester I am teaching an undergraduate introductory class on probability. I don’t typically announce my courses here, but teaching probability is a special enough task to deserve mention -- for me at least.

As a high school student, I used to dread questions about blue, black and red balls drawn at random from an opaque box. The typical question went like this: if the first three balls are blue, what is the chance a black one will be next? The initial questions were innocuous enough, but they quickly got complicated. They also tested your ability to count – to figure the number of permutations or combinations, without which you couldn't answer. At the incredibly difficult mathematics examination for admission to the prestigious Indian Institutes of Technology (IITs), there were quite a few of these counting questions. Let’s just say that I did not even attempt them.

College contributed nothing to my knowledge about probability (college, to be frank, was a four year vacation and I have no regrets). It was only during graduate school, where I took a number of statistics courses, that I was introduced to the mathematics of randomness. And over the last few years, much of my research has involved probability models – some very sophisticated ones at that, thanks to my colleagues who have majors in math and physics. Even now, my early lack of aptitude for the field and poor undergraduate training comes back to haunt me.

But there’s no better way to drive insecurities away than by teaching. The cliché that the best way to learn is to teach is very, very true. Which is why I am excited about my class this semester. The material itself is not difficult, since it’s an undergraduate class. But even the simplest topics in probability can cause confusion; and what better way to tackle them than at the foundational level.

Last week, I went to check my classroom. It was late in the afternoon and the campus was empty. The classroom was in the Chemistry building, and had tiered, auditorium style seating; the seats were bright red. It was a grand setting, and I could imagine it bustling with sophomore year students -- there are ninety students enrolled at this time. And for the first time I’ll be using what is called the PRS clicker system: I will ask students multiple choice questions during each lecture. Students will choose what they think is the right answer on their personal clickers (they’ll press a button, in other words). A slide will immediately display how many clicked each option, as in a game show. Wouldn’t it be fascinating to have this type of instant interaction – and, importantly, feedback on how well the class is understanding the material – especially in a class about probability, as slippery a topic as any in the whole of mathematics?

Fancy embellishments aside, the real grandness of probability lies in its elusive, mysterious quality. Everything we do in life is governed by chance. Our instinct toward religion partly stems from the uncertainty that always seems to stalk our futures. The theory of probability lends mathematical formalism to uncertainty. But it also makes us think of some very vexing questions: What does it mean when we say things are truly random? Why do things turn out the way they do?

That’s the charm of it: it’s more philosophy than mathematics.

5 comments:

SternMystic said...

Nice insight into your life and interesting last minute attempt to tie it up with philosophy :) However, I was very interested in learnign about the PRS (game show) methodology being used in classrooms, had nto heard about this before and think it is indeed a wonderful idea. Its greta that went to check otu the room beforehand, shows dedication. I remember my first class - Technically after that embarassing one hour, I should have faded away with self-pity :(

Hari said...

Thanks, SternMystic! The PRS bit is indeed interesting. Let's see how it works out. I am hoping it will especially good to have it in this class.

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Dev said...
This comment has been removed by the author.
Dev said...

I've been starting to think of probability as a mathematical description of decision making. Decision making relies on some sort of belief in your foresight, a sort of trust in the psychic intuition that you have. This psychic intuition could have a factual or logical basis, but not necessarily, and as always requires some trust in that your knowledge is applicable and accurate enough to base decisions off it.

Probability and statistics, in my opinion, are very philosophical, and I'm glad someone of your stature has recognized that actually. These are just observations I've made in my undergraduate courses (I'm a senior undergrad majoring in applied math and stats). I just stumbled upon your blog and I'd love to see more posts like this, explaining the philosophy behind mathematical subjects, and will scour through your page for these kinds of posts.

Also, I found your experience in Yogyakarta Indonesia very interesting, as I am also from a Hindu background but of a Bangladeshi ethnicity, which is a primarily Muslim country. Contrary to Indonesian Muslims, Bengali Muslims have forgotten that they also had a Vedic history and culture, before and even during the times when Islam came to the region through conquering armies and Sufi saints. This is why there is a rapid radicalization of Bangladeshis, and I'm curious as though how the culture-loving part of Indonesian Muslims came about and still (relatively) hold strong today.