Tuesday, October 7, 2008

Math Illiteracy

On his Uncertain Principles blog, Chad Orzel provides an interesting look at the problem of our culture's math illiteracy in The Innumeracy of Intellectuals. Professor Orzel's essential point is that people are generally ashamed of a lack of knowledge about art or culture, but can have a sense of pride about their lack of mathematical knowledge.

Epsilonica has this post: Lockhart, Jenkins and compulsory maths about how he wishes he had been taught math.

I don't think that everyone needs to love math any more than everyone needs to be an artist or a musician. On the other hand, here are three reasons I think everyone should master some key mathematical skills and concepts:
  1. We are constantly bombarded by information and much of it requires some analysis. Sometimes, we need a solid grasp of logic, and at other times, we need to understand some basic statistics or probability. Math helps us make sense of many situations.
  2. Math is a great problem-solving tool. The more math you know, the more ways you can see that it can be helpful as a way to model real-world situations.
  3. Math is beautiful.
Point 1's implications: I think everyone needs basic knowledge of algebra, probability, and statistics. That's it. No calculus. No trigonometry. Nothing too fancy.

Points 2 & 3's implications: These are a bit trickier. You need teachers who really have used math and teachers who are passionate about math's beauty. Neither of these is a slam dunk. In my experience, most math teachers are academics who have lived their entire lives in schools. Some of them really love math, but most have never really used math to solve real problems in the real world to make a living. Not every teacher needs to have earned a living with math, but I think most schools would benefit from a broader mix of backgrounds. Some academics, some turbo geeks, and some practical mathematicians should be in every math department from high school on down to at least middle school.

I will complain about elementary school math, arbitrary timelines for learning algebra, and the inflated importance of calculus courses some other time. Those are big topics unto themselves.


Kaz Maslanka said...

Hi Reston,
Had maths teachers focused on the idea of maths as a language as opposed to teaching it as a system with rules that one needs to memorize. I would have used it as a language for poetics much earlier.


reston kid said...

Actually, the right way to teach math is to intertwine all the different aspects of math. The rules to memorize (AKA facts and procedural fluency), problem-solving skills, and conceptual understanding all buttress each other.

I would go on with this response, but I don't want it to be burried in comments. Look for a post on this topic very soon.

Kaz Maslanka said...

The point that I was trying to make, was that I believe the best way to teach is to figure out what concepts excite a student to desire and focus some individual attention in that area and the rest will follow.

reston kid said...

I agree that individualizing the approach has value when it comes to motivation. Finding out what excites a kid and using that as a way to draw them in is very powerful.

My point is that many folks end there, but research indicates that you need to bring all the different aspects to bear when you teach math. If a student likes to view math as a language, then that's a great hook, but we shouldn't feed that kid that perspective to the exclusion of learning the rules and procedures. Similarly, kids who like the procedural stuff need to see it as a language as well.

I like the idea of a great, personalized hook to draw a kid in, but don't want it to become the entire story.

Anonymous said...

Thanks for the link (and sorry I took a while to spot it).

The only quibble I have with what you say is that the knowledge of probability and stats needed to unpick potentially misleading information (particularly in health and science journalism) is rather more than would be called "basic".

I may be atypical in this (I did grow up to be a pure mathematician after all) but I think getting an accurate picture of what correlations mean is actually rather harder than calculus (and certainly much harder than trig). I think our intuitions steer us badly wrong on the meaning of stats and it's hard to correct.


reston kid said...

Matt: Thanks for the comment.

I agree that identifying misleading statistics is often not simple, but sometimes it is simple. Perhaps I am overly optimistic, but I think it is possible to at least imbue more people with a sense of skepticism so they think to question what they are being led to believe.

Anonymous said...

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