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The Many Misconceptions About Algebra

I've been thinking a lot lately about why the national reaction was so strong to Andrew Hacker's op-ed in last Sunday's NY Times, "Is Algebra Necessary?"

After engaging with various blog posts and comments on the subject, I've identified a couple of reasons.

First is "tl;dr" syndrome—"too long; didn't read." Relying too heavily on the headline, thousands of readers simply fail to engage with Hacker's substantive and thoughtful argument. For example, many readers seem to think he's advocating for the end of all advanced math instruction, a scenario that would leave our society with a crippling lack of engineers and other STEM professionals.

Another significant factor is the seemingly pervasive misconception that most adults use algebra and calculus on a daily basis. For example, I was pointed to this NPR article on the need for stronger math skills in manufacturing workers as evidence of algebra's usefulness in the workplace. I can only conclude that most adults simply don't remember what algebra is, and think of high school math when they hear

today's manufacturing work requires strong math skills—not just adding and subtracting, but a good grasp of fractions, decimals and basic trigonometry.
But that's 4th grade math, not advanced algebra. This goes to show just how little of high school math most adults have retained—and I would suggest we lose it because we don't use it.

Harvard's Tony Wagner writes in his book The Global Achievement Gap: Why Even Our Best Schools Don't Teach the New Survival Skills Our Children Need—and What We Can Do About It:

So-called advanced math is perhaps the clearest example of the mismatch between what is being taught and tested in high school versus what's needed for college and in life. It turns out that knowledge of algebra is required to pass state tests ... because it is a near-universal requirement for college admissions.

But why is that? If you are not a math major, you usually don't have to take any advanced math in college, and most of what you need for other courses is knowledge of statistics, probability, and basic computational skills. This is even more evident after college.

Graduates from the Massachusetts Institute of Technology were recently surveyed regarding the math that this very technically trained group used most frequently in their work. The assumption was that if any adults use higher-level math, it would be MIT grads. And while a few did, the overwhelming majority reported using nothing more than arithmetic, statistics, and probability. p. 92 (as quoted in Abundance, by Peter Diamandis)

This of course raises the question of why we don't teach statistics as a core subject in high school. Certainly, students are exposed to probability and some basics of statistics in elementary and middle school, but full-blown stats is reserved for college. Who could argue that advanced algebra is more essential for work and citizenship than statistics? Hacker suggests that a required course in "citizen statistics"

would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.

It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted -- and include discussion about which items should be included and what weights they should be given.

This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry. More and more colleges are requiring courses in "quantitative reasoning." In fact, we should be starting that in kindergarten.

Many of Hacker's critics view the problems with advanced high school mathematics as a pedagogical issue. If students are not passing algebra and becoming prepared for college math, teachers are to blame, this argument says. We need to strive harder to serve our students, not lower our standards. Of course "lowering standards" sounds like a bad thing.

But what if—to Hacker's point—our standards aren't the right goals?

To consider this possibility, I just looked over the Algebra section of the Common Core State Standards for Mathematics. I found most of it comprehensible, even after many years with no formal math instruction, and I would say useful in career and citizenship.

The problem is that we don't expect all students to merely master these standards; we expect them to master them in 9th grade and move on to more difficult, less useful material. This is what we should think seriously about changing. The standards are fine; it's the needlessly aggressive course sequence that's harming kids and making them less prepared for adulthood. (Here's some interesting research from Chicago's CCSR showing that making Algebra I a requirement for all 9th graders did nothing to improve their odds of graduating or going to college.)

Far more students can master algebra during high school if we don't try to cram it all into 9th grade. I'm interested in exploring the pedagogical angle more; as the CCSR abstract notes, changing the way we support students is also an important consideration. If you have a perspective to share as a math teacher or teacher educator, I'd love to hear from you.

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