Is Algebra Necessary?

Andrew Hacker recently had an op-ed in the New York Times entitled Is Algebra Necessary?   

His answer is “no” based on an argument that algebra is hard and that people who do poorly in algebra tend to drop out and that most people don’t ever use algebra in their jobs.

(Some of) his points actually do make sense, but I don’t agree that with his conclusion that algebra should be dumped from the curriculum. First, his suggestion that the history and philosophy of mathematics should also be a focus of math classes and his desire to more explicitly teach quantitative reasoning are exactly right and there should absolutely be more emphasis on exploring math from these perspectives in class. This helps students realize that math is a field that is actually real and has a basis in something, and is not just some random set of tasks your teacher tells you to do.

He is also right that the total quantity of mathematical topics that are taught could be reduced. For me, however, this would be for the sake of actually having an opportunity to explore topics more deeply and then apply topics more deeply (as opposed to his apparent desire just to “waste” less time on math). As more and more math standards get added to the curriculum each year, students actually understand each one less and less (don’t even get me started on the harm caused by how disconnected some of these standards are from each other).

He is also right that courses in “citizen statistics” should be offered to everyone. However, I think his description of such a course is not nearly rigorous enough. For example, learning how to calculate the CPI and other similar tasks, as he suggests, fail to explore the most important concept embedded in any stats course: correlation does NOT imply causation (his conclusion that algebra should not be taught because people who do poorly in algebra tend to drop out would, itself, have benefited from a deeper focus on that particular principle, for example).

Even if it is true that algebra is a major factor causing people to drop out, if it is eliminated from the curriculum, as he suggests, this makes a high school diploma pretty watered-down in the eyes of most people, and may actually further reduce the quality of jobs available to someone with only a high school diploma. Using his employment perspective, graduating from high school without having taken algebra seems fairly similar to just dropping out in terms of the real or perceived depth of knowledge of potential employees.

Of course, the argument that employers will think that passing algebra means you have at least a basic understanding of reality is actually one of the smaller reasons why algebra is important. Here are some grander reasons:

1. Algebra is all about finding patterns in the world and then using them to your advantage to help understand a situation and make predictions about the future behavior of a system. Algebra is about developing a deep understanding of something and then using that understanding to create tools for yourself. This is a critical skill in any field of work (and life).

2. Algebra is beautiful. For example, the obvious statement “if two things are equal, they will still be equal if you do the same thing to both of them,” sounds pretty boring and obvious. It turns out to be a surprisingly powerful insight to help create tools to solve problems such as, “If I start with a number and then add 7 to it, and then multiply it by 9, and then divide it by 3, and then square it and the result is 64….what was my original number?” You could certainly do a bit of (tedious) trail and error, or you could turn it into an equation and use that seemingly trivial but surprisingly potent observation above to solve it! Cool!

3. The concept of a variable is fundamental to my understanding of the world. The idea of a box with some meaning which contains a (possibly changing) quantity is a super-powerful way of conceptualizing quantities in the real world.

4. The concept of a function is ALSO fundamental to my understanding of the world. The idea that the quantity which lives in one of those meaningful boxes described above might depend on a quantity that lives in another (or possibly many other) meaningful boxes is an even more super-powerful way of conceptualizing reality! (Next month, the number in the box called “selling price of my house” probably depends on what is contained in the boxes that describe what improvements I have made, where it is located, the value of my neighbors’ houses, and even *gasp* the current number that is in that same “selling price of my house” box.)

5. Variables and functions form the basis of all computer programming and computer science, which is currently a pretty important avenue of human progress (let alone a pretty important factor in lots of people having jobs).

6. There are probably more good reasons. Feel free to add your own in the comments below.

P.S. Let’s consider a sentence near the end of Hacker’s piece: “Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions.”   Why on Earth would he advocate that students SHOULD learn long-division, but SHOULD NOT learn algebra? I seriously cannot come up with a coherent theory which could explain this. Also, using a bunch of complicated-sounding terms to make math sound complicated and irrelevant is an unnecessary cheap shot.

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2 Responses to Is Algebra Necessary?

  1. Wan says:

    i liked YAY MATH! the best. it was funny but it also taught me alot, of cousre i doubt i’ll remember any of it in the mornin, but i watched the rest of the magician video and learned how to like multiply square routes or whatever, partially. i didn’t really like the like math playground place, i got sorta confused there, but i like the like cool math one. i played this game though called like snorzies, i have no idea how i ended up on it, but that wasn’t exactly related to math, but i saw some other things that were useful on the cool math page.

    Like

  2. totally agreed, zach. the article was just silly and he’s (rightfully) gotten a lot of blow back about it. i especially liked your correlation/causation jab at him. that crap drives me crazy.

    Like

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