The Necessity of Algebra

When I originally read Andrew Hacker's op-ed in the New York Times calling for abolishing (or at least replacing) algebra as a core requirement, I dismissed it. It reminded me of a colleague and mentor who had stopped writing a critique of a book dismissing computers because there was so much wrong to correct. However, one of my indefatigable students found it and asked my opinion, so here we are.

Hacker's premise are these:

• Algebra is obscure
• Algebra is too hard
• Algebra is not taught well

Of these, I can only agree with the last. We as a nation produce so few talented math teachers that high schools are often unable to offer sufficient coverage for four years. As a computer scientist teaching at a large research institution, I can verify that our students come woefully unprepared in terms of math. However, the solution that Hacker proposes, removing algebra as a requirement, is not going to create more math teachers, or raise their salaries. It would gut math departments. No one likes math, because math is hard. Conversely (or perhaps perversely), everyone likes the things that math can do.

I'm not going to address the second point. The literature from mathematics education indicates that someone of average (as compared to the median) intelligence can learn algebra. The fact that many don't learn has to do more with how we teach math and fund math education.

I can address the idea that algebra is an obscure field with bizarre rules that most of us don't completely remember. Recently, some colleagues in the math department proposed adding an end-of-summer bootcamp for new freshman on math. I was skeptical; was this going to address remedial skills or advanced skills? Who needed the most help?

The profound answer I received convinced me to support their effort enthusiastically. The bootcamp was agnostic in reference to a topic; it was a bootcamp on understanding the rules of algebra. Whether the students were going into college algebra, precalculus, calculus for business, or calculus for scientists/engineers (the latter has trig), they could attend and benefit.

If you aren't in the sciences (and perhaps even if you are), you may be puzzled. Isn't algebra at type of math? The simple answer (not entirely complete, but correct) is that algebra is the fundamental unification of arithmetic that allows useful things to be done.

Being able to use the concepts from algebra effectively allows a students to learn to:

• Balance equations and predict effects in chemistry
• Program computers
• Understand statistics, calculate them, and analyze the outcome

There are others on this list. You would be hard-pressed to find a science (including the social sciences) that do not rely on algebra when analyzing quantitative phenomena (those things that can be counted).

No sane educator would tell you that students don't need to learn to write essays. I regularly push my students to develop their writing. It's not that the exact format of an essay will be used regularly in work, but the tools that it integrates are used constantly. Analysis of a problem or question, forming a response, making an argument in support of the response, adding additional arguments, and then summing up: these are all required to complete a day's worth of email I send.

The needs of our workforce are not thick looking for skills developed purely in the humanities (and I say this as someone who has studied the humanities and holds them as the ne plus ultra of academic pursuits). We need technologists and information workers, and those two need to be able to comprehend and, yes, even conduct math operations at the level of algebra.

I hope I've elucidated the importance of algebra. Hacker's idea of a "citizen statistics" course can't work, because statistics require knowledge of algebra to learn. The use of statistics on an uncritical population led to British Prime Minister Benjamin Disraeli to state "there are lies, damn lies, and statistics." Just as we wouldn't allow a student to run from algebra because it's hard, we should not as a society run from teaching and requiring algebra because it's hard.

I'm going to add another point, one that is more personal to me. The notion of a liberal education is old, and while it has been altered to suit different societies over time, the principles have been tested against hundreds of societies over thousands of years and found to be correct. Our society (along with all stable societies in the past, western or eastern) is run by the products of liberal education. To say to mathematics, "sorry, we don't accept your entry to our system" is absurd, especially when the entry is the foundation of all science in addition to further math.

Hacker is a successful scholar and educator, but I'm bothered by his willingness to dismiss the very substance of the liberal education. He's clever to not dismiss math entirely, but it is not for the political scientists to determine the necessary components of math education, any more than it would be appropriate for a computer scientist to dictate the content of a freshman lit course, claiming that students don't need Shakespeare but do need to write emails.