Tuesday, March 18, 2008

Math Wars, The Pre-eminence of Algebra and the Presidential Math Panel

The blogosphere has been abuzz with opinions about the Presidential Math Panel report. Five good ones are found at the Pulse blog. Gary Stager's opinion includes the following:

Not only is the progression from arithmetic manipulation of fractions to Algebra tenuous, but neither of the assumptions underlying the value of teaching fractions or Algebra are ever questioned. The President’s Math Panel, like most of the math education community maintains a Kabbalah-like belief in an antiquated scope and sequence. Such curricular superstition fuels a multigenerational feud in which educators fight over who has the best trick for forcing kids to learn something useless, irrelevant or unpleasant.


The Report of the National Mathematics Advisory Panel
does not dispute that teachers spend lots of time teaching fractions. The report merely urges that teachers do even more of the same while hoping for a different result. A definition of insanity comes to mind.

I wonder if Math teachers are so unwilling to question the supremacy of algebra because they are worried that they will lose market share in the high school curriculum and lose sections at summer school.


Terry said...

Are you saying that the teaching of Algebra is useless? I find that surprising,if you do.

In my work environment, I would think we would be less productive if we had less education in algebra. Not that everybody needs it, but we certainly need lots of people who understand it.

Maybe an argument could be made for less theoretical instruction and more practical instruction on spreadsheets.

Likewise does everybody need to know Lambda calculus? Nope. We have hundreds of programmers who use it everyday and haven't even heard the term. But the few of us who understand it have an edge.

Ross Isenegger said...

Hi Terry,

I didn't say much, just quoted Stager! But since you ask...

I find the teaching of algebra largely uninspiring and begrudge the way algebra and functions have completely taken over the curriculum, displacing geometry, logic, math history, finite mathematics, financial mathematics etc.

I also wonder, in my most cynical moments, whether math education is hiding behind the unthinking acceptance of numeracy as a basic skill and using that as an excuse to make the mathematical experience of so many students (both talented and not) entirely mediocre or completely frustrating. Add protracted to that - requiring 3 to 5 courses in grades 9-12 for everybody.

Once a student has mastered fractions we move them on to the gripping study of trinomial factoring, the graphing of parabolas and the simplification of rational expressions. That sucks the life out of most of them before they ever start to see the beauty of Calculus or the subtlety of data analysis.

Oh but I am sounding like someone out of the classroom too long and almost as self-righteous as some of the commenters on the Kitchen Table Math blog I have been following.

What is Lambda calculus? I am very happy for my math lens - just yesterday I used the idea of a normal vector to place some text around a point on a moving ray. I can't think of one time, in practical application, that I had to factor a trinomial though - is that a hot skill in the financial services industry?

Anonymous said...

what ross said.
it breaks my heart "teaching"
these poor blighters this weird
stuff (which they've usually
tried and failed at--often
more than once--by the time
they come to me) when there
are so many start-at-ground-level
topics with hugely much more
relevance to their lives just
sitting there begging.

lambda calculus, as far as i know
(which ain't far), is church's
technique for importing the concept
of a "function" into mathematical logic.
you find about it when you learn lisp.

now to check wikipedia
and see if i'm right ... not bad.


Ross Isenegger said...

I read two interesting posts related to this today.

The first is from Robert Schank. He presents eight 'facts' and concludes:
"I know this is a hopeless fight, but algebra really matters not at all in real life and the country will not fall behind in any way if we simply stop teaching it. That is not a fact, it is just a former math major’s, UT graduate’s, and Computer Science professor’s, point of view."

I found this via dy/dan's blog where he quotes Deborah Meier, who advocates replacing Calculus with Statistics and then comments, "I'm convinced the Algebra I > Geometry > Algebra II > Precalculus > Calculus train is useful only to the students who ride it all the way through Calculus, where all of Algebra II's abstract gamesmanship finally pays off.". Is this true of the march in Ontario schools through linear functions, quadratic functions, advanced functions to Calculus too?

Ross Isenegger said...

Another empassioned treatise indicating that it is about reasoning not about weak, contrived real-world applications: http://www.ams.org/notices/201005/rtx100500608p.pdf

Terry said...

We have identified two discussions and both are useful. One if the usefulness of math and the other of math education.

I'll bow out of the math education discussion.

Is an understanding and capability of math important in financial services. Absolutely. And I don't mean just basic arithmetic. We employ and use PhD's in math.

Those with opinions regarding the recent financial crisis might think FI's use too many PhDs(quants), but I suggest that proper understanding of the limits of the quantitative analytics was the problem.

One thing that I think is there are two key parts of mathematics education (and many other domains as well).

1. Learning the mechanics and the application of the subject material.

2. Learning how to use the tools at hand to formulate and understanding of the problem space and then applying that to a solution. Algebra, Calculus, Geometry are all different tools to solve problems. An old math teacher of mine told us, "If you don't know three ways to solve a problem, you don't understand the problem." I believe this to be very true.

I am embarrassed to admit how much of my advanced (or intermediate) mathematics ability I have lost. But when I encounter a situation which could benefit from an application of such, I know it. And can usually refresh the topic in my head or find somebody better equipped.

I regularly find applications for simple algebra, simple linear programming, and statistics. I can't think of a situation where geometry was helpful.