# Down with Algebra II!

That’s the title of this Slate article. The first few lines chill my mathematical soul:

My personal feeling is that this is heresy. But, of course, I loved Algebra II. I actually went to summer school to take it early, so I could eventually take Calculus in high school.

But I realize that not everyone shares me feeling. Pepper Mill, is a mathphobe, and her experience taking higher math in college was horrifying to her. She barely escaped – and that is no exaggeration. Our daughter MilliCal has not had as hard a time of it (apparently the result of mixing those genes), but she doesn’t love math. She celebrated when she finished the required math courses at college, saying she was glad that she never had to take another math course again.
I discussed all this many times with some of our high-tech friends (we run in geeky circles), and was astonished to learn that one couple, despite working in engineering, virtually never use higher math at all. This blew me away – I use it all the time. I figure it’s part of the job. But apparently even a lot of techies don’t require anything much beyond Algebra I in their daily lives (while I’m doing derivatives and performing mathematical transforms of various types, and doing integrals)
I realize that most people don’t need a lot of this, and shouldn’t be penalized for their intellectual makeup. But on the other hand, I’m worried about plans to replace this with “Consumer math” and statistics not merely being an alternative to higher algebra and calculus, but supplanting it. We definitely need to have Algebra II around as a springboard for scientists and engineers. Even if they don’t use it in later life.

Thoughts?

Sorry, what’s included in Algebra II?

I rarely use derivatives, limits or integrals in day-to-day life; or trig, for that matter. But stats, at a level which you can’t really understand without the integrals, oh yes. One of my pet peeves* is the amount of misused stats I run into at least once a month, and I’m not even talking about political analysis: I mean by engineers and scientists.

• Is it still called a “pet peeve” when you can feel your blood pressure climbing from “way too low” all the way to “way too high”? It seems like too mild a name.

At least one aspect of Calculus.

Focusing on the theory, how to set up an intergral properly, what they mean, the limitations and gotchas, practicallities and all that jazz.

Probably a good idea. “wasting” a bunch of time learning a hundred different ways to actually solve a particular integral? Not so much IMO.

I agree with him. It is fine to offer advanced Algebra to those that want to take it but also foolhardy to think it should be nearly universally required for high school students in the U.S. In my experience, it is taught in a very abstract way and little attempt is ever made to demonstrate what you can actually do with that knowledge even if you master it.

Statistics is vastly more useful in real life and even most professions that advanced Algebra or Calculus. With limited slots available for required classes, advanced Algebra should step aside in favor of Stats.

I am 100% convinced that I only graduated from high school because my Algebra II teacher liked me and threw me a bone (read: passing grade) because he liked me and/or noticed it was my only failing grade.

I cannot get math for the life of me and do think it’s partly unfair that I had to be forced to take it, fail on a regular basis, and was made to feel worse about myself because of it for something that I have never used in my life.

Am I smart enough to think of a viable replacement/solution? Not even a little. But I do understand where the guy is coming from

I agree with him. I’ve been a professional scientist for 35 years, but have never had to use higher math.

My high school didn’t offer calculus, and I flunked my first course in it in college. It was the only class I ever flunked at any level. Since it was a requirement for my major, I retook an easier course and did well, but got overconfident and got a D in the next course I took.

Certainly, there are people in my field (Ecology) that use calculus and other mathematical techniques, but the career doesn’t require them.

I think it would be far, far more useful to require a basic course in statistics and probability - or just in critical thinking and the scientific method. I lot of the problem with public understanding of science, in particular global climate change, stems from the fact that most people don’t have a clue about estimating probabilities.

This is pretty much Pepper Mill’s experience. Her Calculus Professor gave her a passing grade, but made her swear not to take math again. That suited her fine – she didn’t know why she needed calculus for a Business curriculum. To tel the truth, neither do I.

And MilliCal’s last required course was – Shagnasty take note — Statistics. I heartily agree that a knowledge of statistics is probably a lot more useful than calculus. Nonetheless, as I helped her with her homework, I couldn’t help but notice the many workarounds used to avoid explicit calculus, and longed to simply take some derivatives or perform some integrals to get the answers in a straightforward way.

I like the idea of a basic statistics course; probably more useful to the vast run of Americans than say… physics, algebra II or trigonometry.

Just teaching people that a 180% increase in something doesn’t mean anything in and of itself would be a triumph. I’m so tired of people getting all torqued because they saw on the news that something causes an 180% more likely to get some kind of cancer! And in fact, what happened is that the chance of getting of said cancer is like 1/1,000,000, and now it’s 1.8/1,000,000 if you eat bacon, or whatever. So you went from a one in a million chance to a 2 in a million chance. Still nothing to worry about, but the breathless headlines want to make you think otherwise.

I’m a math-lover and an engineer (it says so on my card!), but professionally I never use calculus.

I agree that for the vast majority of people, a basic understanding of statistics would be far more valuable (both professionally and personally) than calculus.

Some mathematicians might not like trying to teach stats to high schoolers, since you need calculus to derive lots of statistics equations and results, but I think at a High School level, it’s OK to skip over those derivations.

Miscellaneous thoughts, from a (non-STEM) college professor’s point of view:

1. High school and college course requirements are two different issues. The purpose of high school is to prepare students who haven’t necessarily got any idea what they want to do with their lives for as many possibilities as possible; at the college level, it’s expected that students will narrow down those possibilities and specialize. Thus, I have absolutely no problem with allowing college students in a major that doesn’t have more specific requirements to choose whether they fulfill their math requirement by taking College Algebra or Statistics, but I’m a bit more wary about shunting ninth-graders into a non-algebra track that will require them to spend years catching up if they decide later on that they want to become scientists or engineers.

2. Hacker is probably correct that statistics would be more practical. (I got as far as calculus in high school, but I don’t ever use it, so I don’t remember most of it; on the other hand, I’ve never had a statistics course, but I sometimes wish I had, since I do encounter spreadsheets of survey results and standardized test scores fairly often in my everyday life, and I have to rely on the social science folks to tell me what they mean. If nothing else, I would get more out of reading FiveThirtyEight.com.) On the other hand, algebra and calculus stretched my mind in some interesting ways, and I’m glad to have been exposed to that way of thinking. (I don’t know whether taking statistics has the same effect, though, and for all I know it might.)

3. I do see a lot of students who have real, serious difficulty getting through college because of the math requirement. (Sometimes they are very capable students in other respects; often not.) Currently, they are required to take College Algebra – the equivalent of what would be Algebra II in high school; there has been some talk of allowing them to substitute a statistics course in order to graduate a few more people in a timely manner. I have no problem with this, but I’m also skeptical about whether it will actually work, especially if the underlying problem is math-phobia and/or lack of study skills.

Speaking from my own experience, I found Algebra II baffling and difficult. To this day I don’t think I’ve ever needed it. However, somehow I rocked calculus. Though I’ve forgotten much of it, when I read random wikipedia or science articles, it’s nice that my brain doesn’t immediately freeze up when it sees an integral sign.

On the one hand, I sympathize with arguments about resource allocation, and that learning Algebra II might not be the most efficient use of time for many students. On the other hand, I really don’t like this very modern idea that the sole purpose of schooling is to train people for job skills.

How many people have jobs where they have to analyze the meter of a poem, or know why the Battle of Hastings was important, or speak a second language? Most people don’t, and yet these discussions about reforming curricula always seem to focus on math rather than history or English or foreign languages. For some reason, the study of those are widely recognized as valuable, whether one “needs” them or not, and they should be. Because we don’t study history or poetry to get a job. The purpose of a liberal education is not to churn out people with a particular set of skills, it’s to teach people how to think and how to be well-rounded, reasonable people. Mathematical and logical reasoning is part of that, even if you never need to do math at your job.

Whether the ideals of liberal education would be better served by substituting Algebra II for stats, I have no idea. I will note that I’m while I also found Algebra II and Trig to be somewhat difficult, I breezed through AP Calc easily. (Though the mistakes that I did make in calculus were all algebra mistakes.)

So obviously my point of view is not the same as someone who failed algebra after multiple attempts, or had shitty teachers (I was mostly lucky in that department) or a phobia of math. But I do wonder why it always seems to be math topics in particular that are the focus of articles like this.

Keith Devlin delivers a smackdown to Andrew Hacker and his book in this blog post, noting that the book is full of strawmen and Hacker doesn’t even know that pi is demonstrably irrational (see the last three paragraphs).

Was it specifically a Business Calculus course? Because IME the calculus class required for Business majors at most schools is different from the version taken by STEM majors.

In any case, I can easily understand why it might behoove a businessperson at least to be familiar with concepts like marginals and rates of change and optimization that are studied in calculus classes, even if they don’t regularly work with the mathematical details.

College Algebra is not currently part of the Illinois General Education Core Curriculum; college students are supposed to take some other math course instead to satisfy a general math requirement. Here’s the reasoning:

Definitely not a Business Calculus course. The very title would have sent Pepper Mill screaming from the room, like the protagonist at the end of an H.P. Lovecraft story. I wouldn’t be able to take that – my life has enough italics in it already!
No, it was what appeared to be a normal Business Math course, at the end of which Calculus lay stealthily in wait, ready to grasp the unwary victim with its epsilon proofs and pinching theorems.

Right, the stats I took in 9th grade (before calculus or trig) were discontinuous functions. The stats in 12th grade and in college were for continuous functions (Gaussian only for 12th; that plus Student’s t, X[sup]2[/sup], F, J… in college Applied Stats), those involved integrals. In Applied Stats there were some parts which if you isolated them from everything else did not require calculus, but if you isolated them that much they were useless; I suspect one of the reasons so many people who have officially been trained in Design of Experiments are so horrible at it is that they were taught the material in isolation.

Now, one thing that’s very important: so long as students reach college unable to recognize that something represented by a symbol other than x can be a variable, and so long as they don’t know that you can take any variable and call it x, they’re so far down in Algebra 0 that anything built on it will be a Damn Big Problem. About 90% of the questions I got when tutoring Chemistry in the US were actually about that inability to recognize [CaCO[sub]3[/sub][sup]-[/sup]] or [H[sup]+[/sup]] as being a variable. “But it’s not X!” “So, call it X.” “Uh?”

I was a journalism major in college and basically am allergic to math, although I’m not actually that bad at it. I took all the higher math in high school, but only did well in Geometry and Trig. I have actually used Algebra 1, geom and trig in my daily life (a little knowledge of Trig is helpful when playing pool).

And I agree that statistics would be much more useful – I took statistics in college.

But you know what else would be really useful? Economics and personal finance. (I think that would be microeconomics.) Even better would be if high schools offered both higher math like Alg II and Physics as well as statistics, and econ/finance. So you’d have, you know, choices.

I have two high schoolers and a state that requires passing of Algebra II (or two tries at Algebra II).

My daughter will take B/C Calc as a Junior. She isn’t planning on a STEM field and in fact has the problem that a lot of the high achieving high schoolers have - colleges want four years of math, she’ll exhaust high school math courses before she gets in four years (she’ll take Stats her Senior year). She’ll have to leave campus if she wants four years of math - and will have more math than she needs for her field of study.

My son finished Alg II as a Sophomore - and won’t take more math because he got through it by the skin of his teeth and isn’t college bound. He does want to go to trade school - and is far more likely to make use of Algebra in his work life than his sister, but applied Algebra is different.

A lot of kids aren’t graduating from high school. They don’t graduate because they need to pass higher level math - or Chemistry - or read Shakespeare. And none of those things are necessary for the majority of people in their lives.

If you don’t like math well enough to take math in high school, your chances of waking up one day and deciding to be an Engineer are pretty slim. But if you don’t like math enough to pass math and graduate high school, your chances of being able to support yourself are also really slim - and the consequences are much worse.

The same argument can be extended to my son needing to write college level English essays to pass eleventh grade English - he isn’t going to be writing a lot of compare and contrast essays as a pipefitter - and why would you need to write at a college level to get a C in eleventh grade? Its setting him up to fail early when he is sixteen or seventeen years old. Fortunately, he’s got two parents who will work him through an essay until it will get a C.

This was my experience also. A while back I returned to school just to stretch my brain a bit. As an adult I was able to whizz through College Algebra and got A’s in Calc 1,2 & 3, but in high school? Fugetaboutit.
I haven’t used complex algebra or Calculus since.