Tuesday, September 4, 2012

Pre-what?

This summer, I was a TA for a (awesome and super-fun) pre-algebra class.  One of the questions that my students asked me frequently is what exactly IS pre-algebra?  This was a question that I never had a good answer to.  I could tell them what's in the curriculum, but that's what the textbook's table-of-contents is for.  There's no mathematical discipline of "pre-algebra."  You can't be a pre-algebraist (though I suppose you might be a post-algebraist some day.)*

*The "pre-____" class titles in general rankle me.  They devalue whatever you're actually trying to teach.  

This brings me to the Pre-Calculus Dilemma, or what do we put in-between geometry and calculus?  I certainly don't remember what I took in those two years.  It clearly wasn't anything that fueled a passion for mathematics (how that started is another story.)

Certainly some parts of the alg2/precalc curriculum are valuable and necessary as prerequisites for further studies.  But a lot of it is just silly.  Particularly if you're a student who doesn't plan to go on to take calculus.    One way to fix this might be to shift the balance towards modeling real life situations - NOT fakey from-the-textbook "application" problems, but real situations.  In this way, mathematical understanding can be rooted in the physical world.  Using math to model real-life situations gives it meaning.  A learning cycle in such a class might look like:
  • Look for questions around you
  • Develop the math necessary to form a model
  • Look for other situations in which this new math can apply
  • In those situations, find a need for more new mathematics.  GOTO 1.

A natural source for situations to model is in science, but there's also opportunities for analysis in the social sciences, or literature, or problems in the school's community at large.  

I think that such a program of modeling and investigation, combined with some of the traditional elements of the classes could be much more successful at giving students an understanding of what mathematics is and how it is used.  And isn't that the whole point?  




4 comments:

  1. Kyle, what you are describing sounds a little like a physics class ;)

    In lots of ways I think you are right. Good applications do motivate inquiry, which is essential in establishing a strong learning cycle. I like that idea.

    I do think though that there is a place for abstraction and symbolic manipulation. Sometimes it's helpful to let the mathematics motivate the model, rather than the other way around.

    Serious food for thought though. As teachers, it's hard to motivate anything if even we cannot see the overarching purpose for it!

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    Replies
    1. I agree, it sounds like a science class :) The funny thing is that I'm definitely a pure math kind of guy, and I would love for all my students to be able to appreciate math for math's sake. But I know that doesn't work for everyone, and that some folks are more motivated by using the math to solve practical problems. If I'm going to do applications, they'd darn well better be REAL ones - hence the emphasis on mathematical modeling.

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    2. Kyle, I am already with you. This was my major frustration with k-12 mathematics as a student. Now, I am working on a free math problem bank for teachers, and I would love the bank to feature a heavy dose of mathematical application. The issue is that it is so much harder and more time-consuming to come up with good applications (as opposed to "pure math" problems) when your starting point is a mathematical skill or standard. Have you found any helpful resources in this regard?

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