Thursday, December 23, 2010

Calculus vs. Probability

I am trying out listening to podcasts on my – yes – iPod, during what was figuratively described to me as my “downtime”. In Zurich for me this means being on trams and trains, and walking between them or to them. So I went looking for captivating podcasts and of course ended up at the TED site, where you can download any number of interesting speakers and topics. I came across a short and poignant talk by mathematician Arthur Benjamin's on his formula for changing math education.

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His simple approach is to switch from calculus being the pinnacle of math education to actually probability and statistics, because while the former is beautiful yet little used, the latter two topics are in fact very practical and in high demand. In short we need to better understand risk. Below is the full text of his short talk, where I have highlighted a few phrases in bold

Now, if President Obama invited me to be the next Czar of Mathematics, then I would have a suggestion

The mathematics curriculum that we have is based on foundation of arithmetic and algebra. And everything we learn after that is building up towards one subject. And at top of that pyramid, it's calculus. And I'm here to say that I think that that is the wrong summit of the pyramid ... that the correct summit -- that all of our students, every high school graduate should know -- should be statistics: probability and statistics. (Applause)

I mean, don't get me wrong. Calculus is an important subject. It's one of the great products of the human mind. The laws of nature are written in the language of calculus. And every student who studies math, science, engineering, economics, they should definitely learn calculus by the end of their freshman year of college. But I'm here to say, as a professor of mathematics, that very few people actually use calculus in a conscious, meaningful way, in their day to day lives. On the other hand, statistics -- that's a subject that you could, and should, use on daily basis. Right? It's risk. It's reward. It's randomness. It's understanding data.

I think if our students, if our high school students -- if all of the American citizens -- knew about probability and statistics, we wouldn't be in the economic mess that we're in today. Not only -- thank you -- not only that ... [but] if it's taught properly, it can be a lot of fun. I mean, probability and statistics, it's the mathematics of games and gambling. It's analyzing trends. It's predicting the future. Look, the world has changed from analog to digital. And it's time for our mathematics curriculum to change from analog to digital. From the more classical, continuous mathematics, to the more modern, discrete mathematics. The mathematics of uncertainty, of randomness, of data -- and that being probability and statistics.

In summary, instead of our students learning about the techniques of calculus, I think it would be far more significant if all of them knew what two standard deviations from the mean means. And I mean it. Thank you very much. (Applause)

I could not agree more. The world is discrete for me, and very few of the problems that I encounter succumb to integration.

9 comments:

Hans-Peter said...

Interesting - need to listen to this talk. I would agree that more understanding of probabilities and statistics will help (it helps even more to understand where statistics can't help -> see Taleb's fourth quadrant). I'm just not sure whether this can be achieved by compromising on calculus education. It's not so much calculus as a topic but mathematical thinking in general. I never really did get it in school - this happened after I got to university studying physics and math! I certainly agree that I never fully got comfortable with statistics, though. I can use it but I never developed an intuition for it.

Regards
Hans-Peter

Unknown said...

Thanks for the comment, and I think the speaker is just trying to say that wonderful as calculus is understanding probability, stats and risk is very very practical and in short supply. Also useful to some extent in physics, depending on the models you use.

Luke

Anonymous said...

In terms of mathematical I really hate calculus but again thank you very much by posting this.



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anarchitek said...

Calculus is the process of applying time (rate of change, growth, expansion, etc) to a process or quantity. I'm no math genius, but it wasn't until I grasped this essential, but little-if-mentioned-by-instructors-at-all fact that I began to conquer this particular skill.

Hard to understand how taking one page out of a book (statistics are snapshots of one step, or result, of one of these processes, & probabilities are fortune-telling-as-math-exercise) could be more important than the book.

I bet you vote for republikans, too.

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