As I might have mentioned here in passing before, I’ve been supporting myself through tutoring lately. I figure, I can’t get a job as an engineer, I might as well put all that overpriced math and science education to use. Luckily for me, there are lots of people in this area who are more than willing to drop $30 an hour for me to help their kids with math. (This boggles my mind. I have one student who meets with me for several hours a day. In one day she might easily pay me over $100. I can’t remember the last time I spent that much on anything, other than airfare and the Xbox I bought as a graduation gift to myself.)
Anyway, it has been an interesting experience so far. I have effectively learned two things:
1. I am actually really good at math.
2. I have managed to become really good at math despite the best efforts of my education.
This has been a pretty liberating revelation.
One thing that MIT does quite effectively is destroy your self-esteem. Part of that is by nature, and part of it is by design. Going to school with only some of the smartest technical minds you will ever meet is a good way to convince yourself that you’re bad at math. But rather than just let that process run its course, MIT also goes out of its way to break your spirit so they can rebuild you in their image as the engineer they think you should be. I’m not complaining about this last bit- I mean, it sucks, but it’s part of the territory. If you decide to study at MIT you agree to take that as part of the package. I’m just saying it leaves you a tad vulnerable on the other side.
But even controlling for that, I think math education in general is quite effective at destroying self-esteem. The last good math teacher I remember having was in 7th grade. I don’t remember exactly what it is you’re taught in 7th grade math, but I remember Mrs. Stobel standing in front of the class, talking and making sense.
After middle school I spent 8 years getting educated at two of the best technical schools the country has to offer (my STEM magnet high school is nationally ranked). I had to go through a rigorous application process to even get into either of those schools, so why did I leave each of them feeling like I was worse and worse at math?
Even at MIT (especially at MIT?), math instructors are awful. MIT provides a lot of course content online for free through OpenCourseWare, and now a lot of the video lectures are also on YouTube as well. I’ve been watching some old calc lectures, to refresh my memory of some of the finer points of things like implicit differentiation, and I discovered- those lectures are awful! One of the lectures I watched was about the number e, and after a few minutes I had to stop taking notes because I figured it was just making me more confused. I scrolled down to read some of the posted comments, and someone had written, “I understood what e was before I watched this…” I completely understand the sentiment.
Textbooks are equally horrid. My one student is using the textbook Applied Calculus, and I’ve been reading most of it as we make our way through her various homework assignments. It’s horrendous.
Normally, when you’re reading a math book, it’s because you haven’t yet learned the subject. So when you get really confused, the tendency is to blame the subject, or yourself. “Math is really hard,” or, “I’m really stupid.” But stick at something long enough, do it enough times, and eventually it will start to make some kind of sense to your brain. Then when you go back to teach it to someone else, you’re in the new position of reading a math textbook on a subject you already understand. Now, when you read through it, and it doesn’t make any sense, you know it’s not because math is hard or you’re stupid. It’s because the textbook sucks. This textbook particularly annoys me because I can tell it thinks it’s being clever. After they give the quadratic equation, which allows you to solve for the roots of a parabola, they mention that a similar equation exists for cubic equations. This is followed by a footnote, which says, “We would like to show you this equation, but unfortunately it doesn’t fit in this footnote.”
Seriously? That’s obnoxious. Your job is not to chuckle at your own cheekiness. Your job is to explain mathematical concepts in a way that makes sense to students who are trying to learn the material. Imagine reading your textbook, looking for that equation, and that’s what you find. Are you likely to find that amusing? Or are you likely to drop your textbook in disgust, and dread math class as a place of nothing but frustration and aggravation?
Word problems introduce made-up units with accompanying made-up symbols that serve no other purpose than to overwhelm the poor student whose brain is already struggling to keep straight x, y, a, h, mx+b, ax^2 + bx +c….and the solutions manual is riddled with errors.
And that’s just the problems with this particular book. The rest of it is filled with what is considered standard fare for textbooks- dry, boring, confusing lines of equations taking up whole pages as way of “proof” that I guarantee you my student (who is extremely diligent otherwise, and puts in more hours studying than I ever have) will never read- and neither will 75% of her class. Obviously some equations are necessary, but whatever happened to explaining things in words? How can a student of math, who by definition is still learning all the terminology and notation, be expected to understand self referential pages of symbology? Instant immersion may work for learning Chinese, but not calculus.
Danica McKeller wrote a book to encourage middle school girls to excel in math, called Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail
This is something that I have not seen in any math textbooks, or heard in any math classes since the aforementioned Mrs. Stobel in the 7th grade.
And why? I see no reason for it. Now that I understand calculus, I can look at calculus textbooks and know for certain that there’s no reason to explain the concepts in such convoluted and stuffy ways.
So I resolve to like math again, like I did when I was a kid. I resolve to make sense of all the calculus I’ve forgotten, and the differential equations I’ve never learned, and I resolve to like it. And if I had any idea how to go about doing so, I’d even resolve to writing a math textbook. And not one like Math Doesn’t Suck, that is wonderful but limited only to people who like pink and whose parents go out of their way to find extra help, but the kind that would actually be used in a classroom.
In the meantime, I’ll keep tutoring my half a dozen students, and hopefully will convince some of them that math isn’t as stuffy as it seems.
