A Mind for Madness

Musings on art, philosophy, mathematics, and physics

Thoughts on Nicholson Baker’s Case Against Algebra II

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The debate over standards in high school math has been going on for a very long time, but things seemed to come to a pretty nasty head last year when the New York Times ran the article Is Algebra Necessary? Bloggers and educators were outraged on both sides and started throwing mud. In the most recent issue of Harper’s (Sept 2013), Nicholson Baker wrote an essay basically reiterating the arguments from the NYT’s piece and responding to some of the criticisms.

I’ve been trying to stay out of this, because I honestly have no idea what high school is designed to do. The real argument here doesn’t seem to be whether or not algebra is “useful in the real world,” but rather about whether or not we should force students to learn things in high school that they are not interested in. Is the purpose of high school to teach students the basics in a broad range of topics so that they have some fundamental skills that will allow them to choose a career from there? Is the purpose to allow students to learn topics that are of interest to them? Something else?

I don’t know, and it is impossible to participate in this debate without clearly defining first what you think the purpose of making students go to high school is (of course, the arguments are muddied by the fact that no one actually defines this first).

Here is Baker’s main argument in a nutshell (he is a fantastic writer, so you should read the full thing yourself if this interests you). Algebra (II) is unnecessary for most people, i.e. the 70% of the population that do not go into a STEM field. It causes excessive stress and failure for basically no reason. Why not just have some survey course in ninth grade where some great ideas of math throughout history are presented and then have all future math courses be electives?

I assume for consistency this means that since English, foreign languages, history, and all other subjects taught in high school are also not directly applicable to most people’s daily lives that basically you’ll do ninth grade as a taste of what the subjects are about through survey courses, and then literally everything is an elective afterwards.

Honestly, I agree with Baker that this would probably make high school a lot more enjoyable and useful for everyone. A lot more learning would take place as well. It just boils back down to what you think the purpose of high school should be, and since I don’t know, I can’t say whether or not this is what should be done.

Here’s two thoughts I had that don’t seem to be raised in the main discussion.

1. How do you know whether or not taking algebra will be useful to you? Having core standards in some sense protects the high school student who isn’t equipped to make this type of decision from making a really bad decision. I’ll just give an anecdote about my own experience as someone who really loved all forms of learning and went into math and who still made a really bad decision when given a choice of electives.

When I was going into my senior year of high school, I knew I wanted to be a composer. I knew this so confidently that despite being advised against it, I decided to not take physics since it was an elective. My reasoning was that I would never, ever need it for my future career as a composer. Let’s ignore the fact that I didn’t realize that understanding the physics of sound is an extremely important skill for a composer to have and so made a poor decision for that reason. Let’s assume that physics really was useless for my intended career.

After my first year of undergrad I switched to a math major. I really regretted not taking physics at that point and ended up loving physics in college so much that I minored in it. Here’s the point. Almost no one in high school knows what they are going to do. So how in the world are the going to know if algebra is necessary for their career? Even if they know what they are going to do, they could still end up mistakenly thinking that it is unnecessary.

My guess is that if we switch to a system where practically everything is an elective, then when people get to college and their interests change they won’t have the basic skills to succeed. They’ll have to fill in this lacking knowledge on their own, because math departments definitely cannot offer more remedial classes. We have so many students and classes as it is we can barely find enough people to teach them all.

2. This seems much ado about nothing. What I’m about to say might seem harsh, but algebra II is not that hard. You don’t have to be good at it. You don’t have to like it. But it isn’t a good sign if you can’t at the very least pass it. Baker himself points out that Cardano in the 1500’s was able to do this stuff. Since then we’ve come up with much easier and better ways to think about it. The abstraction level is just not that high. We’re not talking about quantum mechanics or something. Students in other cultures don’t seem to struggle in the same way, and I don’t think we’re inherently dumber or anything.

Depending on where you look, 30%-50% of students fail algebra II. Let’s say it is closer to 30 because a large number of this statistic does not take into account that there are lazy/rebellious/apatethic/whatever students who can easily handle the abstraction, but just don’t put any work in and fail for that reason. I’d imagine the number of people who try really hard and still fail is pretty low (maybe 20% or less? I’m just making stuff up at this point, but probably way less if you count people who never pass it).

Is it too insensitive and politically incorrect for me to say that someone who can’t handle this level of abstraction probably isn’t cut out for college in any subject? Is college for everyone? I can’t remember what the proper response is to this anymore. What if the number who never pass is around 5%? Is saying this 5% isn’t cut out for college still too much? Sure, give them a high school diploma if they can’t do it, but college may not be the best fit. It seems a good litmus test.

What major won’t require abstraction at least at the level of algebra II? STEM is out. English? Definitely out, unless you somehow avoid all literary theory. Business? Most business degrees require some form of calculus. Music? I hope you can somehow get out of your post-tonal theory classes. History? There has been a recent surge of Bayesian methods in historical methods.

I guess the point is that 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.

Again, if a high school diploma isn’t meant to indicate readiness for college, then who cares what you do?

*Cringes and waits for backlash*

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Author: hilbertthm90

I am a mathematics graduate student fascinated in how all my interests fit together.

6 thoughts on “Thoughts on Nicholson Baker’s Case Against Algebra II

  1. No backlash. Some really excellent points. I think the real problem with algebra right now is that it’s not being taught in a way that could make it more exciting and relevant to high school and even elementary school students. I think we need to throw in some basic programming and boolean logic and things that would help students better develop the computational thinking they will probably need whether they go to university or not. It’s like they’re stuck in some Victorian, Bertrand Russell world of fixed variables and rigid set theory, when they should really be learning to have fun with paradoxes and iteration.

  2. The purpose of high school is to destroy all traces of individuality, so that we can learn how, as adults, to please the group. That and learning to cope with pain through daily beatings.

  3. I should have phrased this more clearly. I shouldn’t ask “what is the purpose of high school,” but “what ought to be the purpose of high school?”

  4. Excellent points and questions! Best yet response to N Baker’s excellent piece. I happened to “love” algebra as a fun puzzle of sorts in high school but have never used it in “reality” except to calculate the “original” price of an item if a sales tax = 7%. haha. Why aren’t student’s taught “stories” of reality in high school (i.e. recipe calcs, room and carpentry calculations of space and angle etc.) where algebra can relate to future living? I never could figure that out. It could be FUN and PRACTICAL! Yes, what is purpose of high school? Not EVERYONE is cut out for college. Vocational training is great for a many people! Our purpose is to work and make a living.

  5. I pretty much agree with you but I’d argue against seeing that algebra is the exemplar of abstract thinking. In fact we do abstract thinking all the time – what kind of thinking is not abstract? Mathematics is a particular kind of thinking that is is useful (and aesthetic) in itself, and for the quantitative sciences.

    It is fairly obvious that a lot of kids do not like mathematics and do not enjoy studying it. Why put them through that mill? Plus, it means when they grow up and bump into a real mathematician they may be actually curious as to what they do as opposed to associating him/her with all the bad memories that force-fed mathematics brings up.

  6. I can’t help but quote from John Scalzi’s famous “Being Poor” essay: “Being poor is having to live with choices you didn’t know you made when you were 14 years old.” Punting math because it takes some work can have serious consequences later in life.

    Still, the most serious problem with the line argument being bandied about is that it can be applied to any field of learning. If there is no point in learning anything, why even bother with high school?

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