Tuesday, December 17, 2013

But Seriously... Is Algebra Necessary?

A friend tagged me in a FB post with a link to a New York Times article by Andrew Hacker Is Algebra Necessary? I need to process this, so here goes....

I saw the article as having two distinct parts. Here are my reactions to each part.

Part The First: Math Is a Useless Pain

The first half or so of the article indicates that math causes high dropout rates and is basically useless to everyone not bound for MIT or Caltech. Well, if math causes high dropout rates, then I think there is a reasonable discussion to be had about how we address the issue. What should we do?
  1. Prepare students more effectively from the beginning. That is, should we fix our elementary and middle school math programs so that students can have more success later in their math careers.
  2. Fix the high school math curriculum so more students can find success and gain the math skills they need for life and for later mathematical study.
  3. Give up. Stop requiring so much math.
The eye-grabbing headline and some of the arguments in this first part seem to imply that Hacker is suggesting a focus on option 3, but after reading the second half of the article, I think he is making more of an argument for option 2. I believe that we need to focus on options 1 and 2.

By the way, the Common Core standards should  help with option 1. A coherent curriculum that focuses on important mathematical practices and covering fewer topics, but with more depth is a great place to start. It isn't a panacea, but spending more time on fewer topics can help everyone out. I think the Common Core standards do a pretty good job of mapping out a coherent mathematical progression from elementary school through the end of grade 8. Then, we come to...

Part the Second: The Traditional Algebra 1-Geometry-Algebra 2 High School Math Sequence Is Mostly Useless and Should Be Improved

OK. This is where Hacker and I agree. In an earlier post, I said that we drive too many kids (like cattle) on the pathway that leads to Calculus. As I said in Math Illiteracy, everyone needs to master some math skills and understand some math concepts, but these don't necessarily map well to the cattle drive to calculus that I think is over-enrolled. By pushing just about every kid through the same cattle drive, we are driving kids away from math and putting up barriers to later pursuits that should not be dependent upon relatively esoteric skills such as learning how to factor cubic polynomials.

Maybe most kids should take a (perhaps more applications-oriented) course in Algebra, but maybe fewer kids need to take geometry and Algebra 2. Maybe a course in Practical Math (the actual title of a course on which I am working) could help. This sort of course can help students see how math can be a tool for solving problems. It can still be a pretty rigorous course, though it certainly wouldn't prepare anyone for calculus. But then again, not everyone needs to take calculus.

From my perspective, the tricky part centers around mobility. If we have a math pathway that prepares potential engineers, scientists, and mathematicians with the math skills they need, and we create a separate pathway that helps the general non-mathy population acquire the skills they need, then how do we ensure that a student who starts on a less rigorous pathway can change his or her mind and switch to the mathy pathway? How do we make sure that the less rigorous pathway doesn't become a dumping ground for students who are ill-prepared for the more rigorous pathway? These are very real concerns. Perhaps I'm being a paranoid Black man, but I know that this sort of dumping ground mentality has been wide-spread in the past, and I'd hate to create a two-tiered curriculum that institutionalizes it.

The Bottom Line

As Hacker says:
Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.
Here, he is talking about how medical schools (and other post-graduate programs) use calculus as a way to identify students who have the right academic stuff. Honestly, I can't see that changing any time soon. Also, I'd be interested in a study about this. Maybe being able to learn calculus has a high correlation with the ability to survive and thrive in medical school. Maybe this extends to undergraduate studies as well. As the author of the A Mind for Madness blog says in Thoughts on Nicholson Baker’s Case Against Algebra II:
... if a high school diploma is meant to indicate some level of readiness for college, then algebra is probably a good indicator. This does not mean that you will use it, but will just point out that you have some ability to do some abstract things. I’m not saying it is the only way to test this, but it is probably a pretty good one.
Regardless, I think we need to:
  • Prepare more students for success in mathematics more effectively. We shouldn't focus solely on the cattle drive to calculus, but then again, we shouldn't ignore it either.
  • Do a better job of creating math courses that engage all students. We need to have students wrestle with more authentic real-world applications and see how math can help solve real problems.
  • Help students see the beauty in math in addition to the utility it affords in problem-solving contexts.