This article from a 1993 edition of the Phi Delta Kappan somehow summarizes hundreds of pages of a digest of hundreds of research studies that wasn’t written until 1999 in only seven pages—and a drawing takes up most of the space of the first one. I agree with almost everything in it, except the bit about math movies at the end. Also, I might take issue with some of the suggestions curriculum reform. For example:
In addition, topics not previously explored in traditional curricula must be added. Changes from an agrarian society to a technical/information society demand the literate citizens be familiar with such concepts as mathematical modeling, discrete mathematics, and data analysis. An example of discrete mathematics would be the decision process whereby a street sweeper is routed through a town so that the fewest number of streets possible will end up being swept twice.
Now, sure, we ought to rethink what we teach our kids. The author is absolutely correct. The standard American math curriculum hasn’t budged much in the past century despite radical changes in American society, culture, and technology. To ignore the passage of time is stupid. But I’m not entirely sure what the author is proposing here. To me, she’s suggesting we load up our kids with graph theory and Fourier analysis. This is great if we want all our kids to go into algorithmic optimization, data compression, and signal processing. Maybe that wouldn’t such a bad thing. In my experience, Fourier analysis can be hard. But such a suggestion presupposes that everyone, everywhere will end up in the high-tech sector. Even then, my friends who do lots of computer science [most of whom actually work in finance] don’t rely on mathematics proper so much as things in computer science, and then, that they picked up in college.
Also it’s worth mentioning that we can’t just continue to add things to the curriculum and expect a change in our students’ abilities or understanding of the subject matter. Right now the curriculum is too broad and lacks substantial depth. As is, kids have to memorize lots of seemingly unrelated, mathematical facts. They’re presented in isolation and learnt in isolation. If you’re going to revamp the curriculum, fine: just don’t tack on more and more things and then look for a miracle. But moving on.
The author cites a statement by the Mathematical Sciences Education Board. Following fold, it’s reproduced for your benefit and my scrutiny in part below:
Almost no time is spent on estimation, probability, interest, histograms, spread sheets or real problem-solving, things which will be commonplace in most of these young people’s later lives.
I agree. We pay little attention to any of those things; it’s a shame, too. Probablility and statistics are perhaps the most important “real-life” mathematics we could be teaching. I’ve always found it funny that calculus has dominated as the capstone math course at many high schools. College freshmen use it as a measure of their peers mathematical prowess. You’re especially frightening if you took a multivariable calculus or linear algebra class. Statistics isn’t as nearly frightening. Too bad, because if it were, maybe more people’d offer and take it. I routinely run into Ivy-league educated people who don’t know “correlation is not causation.” I’m a bit worried and confused by their inclusion of “real problem-solving.” I don’t know what it means, but I can guess.
They want our kids to pretend that they’re the CEO of a juice company, and they need to figure out whether to make more cranberry juice or more grape juice according to a number of contraints. Maybe they’ll do the linear programming themselves, or maybe they’ll plug it into a computer. In any case, these sorts of highly contextualized, so-called real world problems are, in researched fact, a bad, bad, bad idea. Not only do they not interest most children—most children are not, nor do they dream of being the CEO of a juice company—these sorts of problems actually hinder transfer of abstract principles and problem solving structures to other types of problems and disciplines. What does go, however, are abstract relationships.
With a little practice and a lot of thought, it’s not hard to come up with motivating questions that live soley within the realm of mathematics. There’s no need to introduce confusing and distracting details from the physical world.
But, if you must, I could see the addition of more mathematics into the school day. What if we had two math classes, but disguised one of them as “real-world problem solving”? Then we wouldn’t have to compromise learning how to think through problems in an abstracted way that promotes the formation and understanding of relationships, and we’d have a venue for an integrated approach science, math, and technology with applications that is so hot nowadays.
Anyway, I’m meeting with the author sometime next week to talk about these sorts of issues in person. I’ll let you know how it goes.
[…] Musings on whether and how to include more applied math in high school math curricula. […]
I was just hopping around the web looking for recommendations on changes to math curricula to make them a bit more interesting to more kinesthetic learners. I also happen to have a Harvard connection. What have you discovered?…Can you recommend any open-minded math folks at Harvard?
I am graduate student in Tallahassee, FL, working on a project to help a local middle school transition toward an integrated and applied approach to math & science instruction–with a STEM (science technology engineering math) model as the ideal. Are there any curricula or implementation models that anyone can recommend? Gratefully yours, Mark