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Teaching, Mathematics and Teaching Math.

Posts Tagged ‘Research’

Why is Mathematics a core subject in school?

Posted by forumjoe on January 1, 2011

Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it.

– B. Mencken, 1715

In order to get my students to think a bit more about what they’re studying and why they’re studying it, I’m going to ask them the above question… Why do we study mathematics?

And I’m going to get them to really think about this. First individually, then in groups, but not in the way that can be brushed of with “Because its important”. However, if I’m going to ask my kids this question, I’d better have some idea about what the answer is, so I decided to do some research and discuss the results here.

It is my belief (though I can find no factual evidence of this) that 90% of careers and occupations use no maths higher than Year 8 level. Beyond addition and subtraction (which cash registers and calculators can do anyway) how much maths do you really need to survive in society these days? Why do we force students to study maths beyond this level? Sure, there should be maths classes covering calculus and algebra and trigonometry in highschool for those students who WANT TO BE THERE, and these should be wonderful, happy places where students creatively solve problems and learn about the world, like Lockhart envisioned.

Mathematics is looked at by society at large as a “necessary evil”. Why is it necessary? Do schools make Mathematics a compulsory subject because society sees it as necessary? Or does society see it as necessary simply because “everyone has to do their dues” in the mathematics classroom as a child. Parents expect their children to study maths because they themselves studied maths as a child. But if they’re not going into a career that requires maths, why do they need to study it?

The SIN rule
The Mode of a dataset
The Volume of a right prism

When will people ever need to use these things unless they get a job in a field that requires it? The only reason to understand these concepts in maths is because they’ll need to build on their understanding next year. It’s a repeating cycle. “You need to learn [x] because it will help you learn [y] next year”

Cut The Knot’s manifesto – http://www.cut-the-knot.org/manifesto/need_it.shtml – has a great collection of quotes on this issue from throughout the ages, for both sides of the argument. Here are some interesting ones that I’ll be showing my kids to start discussion on this:

J. B. Mencken, De Chralataneria eruditorium, 1715 (quoted in C. Fadiman, The Mathematical Magpie, p. 256):
Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it.

Has anything changed since 1715? I think many people would agree with this statement today.

Fran Lebowitz (b. 1951), Social Studies, “Tips for Teens”, 1981.
Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.

Phwoar, no such thing as Algebra!? But what about… oh. How about… hmmm. Surely… no, ok. Maybe you’re right.
Algebra is a great mathematical tool. It’s great for solving mathematical problems and it is a fundamental building block for many subsequent mathematical concepts. But if someone doesn’t learn it, or doesn’t understand it, will it affect their ability to contribute to society?

R. P. Boas, Jr., If This Be Treason…, Amer Math Monthly, 64(1957), 247-249.
When I was teaching mathematics to future naval officers during the war, I was told that the Navy had found that the men who had studied calculus made better line officers than men who had not studied calculus. Nothing is clearer (it was clear even to the Navy) than that a line officer never has the slightest use for calculus.

So now, perhaps, we are approaching the crux of the problem. Why is this so? Why does studying calculus help in an occupation that has no use for calculus? I can think of a whole bunch of possible reasons, but I don’t really know. Hopefully this is where my research will lead next.

There are lots of great quotes in Cut The Knot’s manifesto, and I encourage you to check them out. Many have anecdotal evidence about how studying mathematics helps develop the mind in ways useful for many careers. I shall leave you with one of my favourites. Benjamin Franklin, in 1787:

It seems to me, that if statesmen had a little more arithmetic, or were more accustomed to calculation, wars would be much less frequent.

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What sort of gamer are you? (Research Paper)

Posted by forumjoe on August 13, 2009

From a Slashdot article I found a research paper that I find interesting enough to be my first Gaming post on this blog. (I’m more interested in gaming research that mainstream gaming news, so must of the stuff I post here will be research related)

Player Modeling using Self-Organization in Tomb Raider: Underworld (Anders Drachen, Alessandro Canossa and Georgios N. Yannakakis, 2009)

Using statistics about player deaths, game completion time, and the number of times (and places) a player asked for help, the researchers were able to categorise players into four different categories:

  • Veterans
  • Solvers
  • Pacifists
  • Runners

Obviously these four categories are specifically related to Tomb Raider: Underworld, and aren’t necessarily directly transferrable to different types of games.  But if you consider TR:U to be the tool for gathering statistics, rather than the entire focus of the study, you can still get a lot out of it.  There are plenty of other online quizzes and stuff (usually related to MMOs) that determine the sort of gamer that you are, but this paper is the first I’ve read that uses solid data analysis to create the categories, rather than just asking questions about what the player enjoys and aims for.

Myself?  It’s been a long time since I played a Tomb Raider game (though I have been intending to check out one of the newer ones recently).  I generally didn’t like the combat (though was still able to do it) because I came from a FPS background.  If I want combat, I’ll play quake, I played Tomb-Raider for the adventure and the puzzles.  It appealed to my Prince of Persia mindset.  I guess that puts me in the Solver category, but really I could be a veteran or a pacifist too.  Who knows?

It’s an interesting paper.  Check it out.

Addendum: I’ve been shown http://www.mud.co.uk/richard/hcds.htm which talks about similar stuff, only was written 15 years ago and uses MUDs as its statistical tool.  Quite Interesting. (Richard Bartle, 1995)

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