## Mathochism: Thrown to the wolves

**One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?
**

When I started taking math classes at the college, I was usually one of the older students, but not necessarily the oldest. This semester, pretty much every student is young enough to be my child. I think the professor is about my age, but she may actually be a few years younger.

Considering the obvious age difference, and the fact that I am not their peer, I’ve been flattered by how several young students, both men and women, have been friendly and welcoming.

I’ve built a particular rapport with one young man named Phil. Phil is not only taking Calc, but also Physics and Philosophy. He has already taken Calc I and Calc II, and passed both classes, but because of the vagaries of the academic bureaucracy, and switching schools, he is being forced to take Calc I again. (He’s also had the Calc Dementor for a class, and we bonded over CD’s less than congenial mien.)

Even with his background in Calculus and his taking Physics, which reinforces concepts like differentiation, Phil is not acing this class. He was able to solve that implicit differentiation/linear approximation problem I complained bitterly about on Wednesday, but he told me he did so using methods he had learned in Physics class.

He asked me yesterday how I did on the test, and I shrugged. I told him I was sure I failed again, but that I was resigned to learning from the failures and sticking with the class because, ironically, I am actually understanding the material, even if I am unable to convey that on the test.

I also mentioned that an F was not technically an issue, since I wasn’t concerned about GPAs.

“So you’re just brushing up, huh?”

I considered his question, and then thought, “What the hell.” I told him that I am a journalist, and about the Mathochism project (though not about this blog, or the project’s name), that I had gone back to school to try to prove I could learn math and learn to love it. I told him I am writing a book about the issues involved in trying to learn math. I added that this was not some exposé on our college, but a more general view of the obstacles students face when pursuing STEM.

I then told him about starting from pre-algebra, and working my way up the sequence, and how I had been getting As and high Bs the entire time.

Until now. I told him that I was getting increasingly frustrated by my performance on tests, even though I understood lectures and aced the homework.

This led to a discussion of what we both thought were the obstacles in this class. We agreed that, while our teacher was a great lecturer and engaged with her students, she often rushes through lectures and never has a lot of time to address student questions in class. We remembered one instance when the professor helped a student with a question at the beginning of class, then was unable to finish the lecture. We also talked about how, because of the time crunch, there was never much time to really have an in-depth discussion of the material, which is quite complicated.

I shared my discussion with the professor where she mentioned the department’s desire to make us “independent,” and added that, while I didn’t mind being independent, that it shouldn’t mean having to scour other calculus books and the Internet for practice problems that would actually prepare me for an exam. Why not provide students with supplemental problem sheets that really challenged them? Or better yet, find a book that did this?

“That’s because this is a weed-out course,” he said. “They don’t want everyone to pass calculus. That’s why we’re thrown to the wolves.”

Huh. Yeah, I know that sounds inflammatory. But I do find it interesting that a big reason he is not struggling like I am is because he has already learned this material. When the best way to pass a course is to have already taken it, sometimes several times, what does that say about the way the academic institution who offers it has decided to structure it?

Since we were having this conversation in the classroom, we were not hard to overhear. Though Phil and I were the ones talking, his neighbor, a young man named Juan, also got involved. Juan has been friendly with Phil and reserved with me, which is fine. I am not going to force rapport. But I do know he is struggling even harder than I am, and like me, he has also gone through the sequence.

He opened up about that, which drew in the young man sitting behind me. That young man — let’s call him Matt, though I don’t actually know his name — chimed in, saying he thought it was weird that the college’s own program had failed to properly prepare me and Juan for the rigors of Calculus. So yes — he too felt that the way the course was structured was more aimed at weeding out than helping students learn.

Moreover Matt, like Phil, has taken Calculus before. I already knew that, since the way he asks questions in class often makes the professor admonish him that “we haven’t gotten there yet!” Because of that, I don’t believe he struggles like Juan and I do. Or the number of others struggling, too. Our class has quite a few students dismayed by their sudden math illiteracy. I know this because I can’t help overhearing them as I stand in the hall before class.

And I know this because the professor told me during that conversation we had about independence.

Which leads me back to the question, if the only way I can pass this class is by taking it before, so that the obstacles — the time crunch, the inadequate problem sets — don’t matter, then what does that say about the institution offering it? And if their ultimate goal is indeed to weed us out, how does that jibe with the lofty goals of academics and politicians who bemoan the shrinking number of STEM students in this country?

Phil has told me he wants to become a physicist. He is acing his Physics class, but even a C in Calculus will hobble his chances of transferring to a good school. Is it right to weed him out? Or does he deserve better?

Math instructors who read this, what do you think about Phil’s comment? Is he right? Are we being set up to fail? Are they throwing us to the wolves?

And if he is, is my college alone in doing this, or is this a universal tactic? Do universities across the country set their students up to fail?

And if we sincerely want our population to be more numerate, is this the best way to go about it? When I had these issues last semester, I thought it was just the professor. But now the professor is not the obstacle. This is an institutional obstacle. And I’m not struggling with it alone.

*All text copyrighted by A.K. Whitney, and cannot be used without permission.
*

Yes, your friend is right and yes, this is a universal thing in American colleges. My school doesn’t have a weed-out math class but it does have weed-out engineering classes which serve the same purpose. Weed-out classes aren’t anything new. My mom, who went to school in the 70s, says that calculus 2 was the weed-out math at her liberal arts college.

The reason that calculus 1 is a weed-out at your school is because the demand for calculus classes much higher than what the school can provide. The fairest way to limit enrollment in calculus 2 and 3 is to make calculus 1 very hard.

The reason that weed-out classes exist in general is because professors want get rid of the students who can’t handle the work of more advanced classes. It’s better for almost everybody if those who can’t make it leave the program earlier rather then later.

No, this is not the best way to make our population more numerate. A terrific response to your question can be found in an essay called “Lockhart’s Lament”. It’s long but it’s very engaging. I highly encourage you to read it when you get a chance: http://www.maa.org/devlin/LockhartsLament.pdf

Thanks for the link. As to “fairness” and “best for” — well, I see the logic, but find it utterly depressing.

Honestly, part of the issue is that the paradigm shift brought about by the information age hasn’t reflected back to the classroom. I don’t need to know how to differentiate a function – I can log on to Wolfram and have the program differentiate it for me. It might, however be good for me to know the techniques behind it, broadly. This is different from even 30 years ago.

Back then, there were strange self-fulfilling prophecies in mathematics. There is sort of this concept of the “Privileged Mathematical Elite” who got through 4 semesters of calculus to apply it to actual, real world problems. This is a bottom-up mathematical approach – you need arithmetic to figure out algebra, which you need for linear algebra (useful in some applications of Discrete Math), combinatorics (for statistics, other portions of discrete math), or calculus. Calculus teaches you differentiation and integration, first with one variable, then through trig for engineering applications (Fourier Transformations, anyone) then with multiple variables, so that you can solve differential equations, which are real problems. Meanwhile you’re studying statistics for more statistics, discrete for more discrete (and other applications, such as cryptography), but by this time most people have gotten lost. There’s a conflict here – before we have machines to perform these calculations, we have to do them by hand. As a result, we needed extreme degrees of accuracy.

I think I could sit down with you and explain how a Fourier transformation works, (you can stack various shifted sine and cosine curves together to approximate a function you found in nature, which is really cool), and you would have an idea about how to use one. However, without a strong calculus background, you probably couldn’t perform one. I could also sit down with you and explain the concept of a differential equation (the net goal of calculus in the first place), and we could look at one. We might even be able to use your calculus knowledge to do something useful, but only because we live in an information age paradigm – I can model stuff on the computer, there are programs to perform hard functions for me, etc.

As regards your “Weeding out” concern, I think there are some varied issues that are being brought up here. The first problem is institutional – There are a lot of courses that require subsets of mathematics (it would make sense to see these techniques taught in a single course), so you get into class overload – we have to teach 5 million things at once (physics students need x, econ students need y, engineering students need z, and they need them by certain points in their own courses). I really don’t know how to de-couple mathematics from these requirements effectively except possibly splitting calculus up further and making everyone take an elementary calculus course.

However, calculus has a secondary need as well, and that is to prepare you for higher levels of calculus. Higher level mathematics gets substantially harder (you’ll be working more heavily with those special cases on tests that you hate), and not everyone has the aptitude for it. It strikes me that (and it’s tough to tell from your study here), that calculus homework is being given to prepare non-math students for the calc they’ll need, and the tests are being given to determine your aptitude to pursue the discipline. So there is sort of a weeding out process here – is it more “Wrong” for someone to discover they can never really do well enough to be a math major during their first year of college than their fourth? You could argue that you could increase the difficulty of the homework, but that might be counterproductive to the students who don’t need the advanced calc understanding.

So there’s this strange balancing act – I’m a CS major, and I WILL NEVER USE any calculus I’ve learned (at least not for the rest of my foreseeable academic and professional career). If calculus is made “hard enough” for math students, it might be “too hard” for non-math students. We could try to split math courses up further, but then this defeats the purposes of centralizing math. It’s tough all around.

I’m not sure I have anything to add to the comments already given about weeder classes. Certainly this concept was all over the STEM curriculum when I did undergrad, in math and physics and chemistry and engineering. Sometimes I think it just because the material is damn hard.

I have a comment about a C in calculus holding Phil back from his goal of being a physicist. Calculus, and mathematics, is absolutely essentially to physics and if he really wants to understand physics, then he will need to be completely fluent in calculus. (After all, Newton invented calculus to help him describe the problems in physics.) The more advanced the classes in physics he takes are, the more he will have to depend on his understanding of calculus and so it is absolutely essential that he understands it.

That being said, I also have a friend who got a C in differential equations her freshman year, and is now a grad student in math with a prestigious national fellowship. So if you can show that you have learned more and gone beyond that level, it won’t hold one back.