An article in the NY Times complains that math skills aren’t prized in our society and as a result, we’re missing out on a lot of talent. Girls in particular, but boys also are discouraged from doing anything that labels them as smart, and thus nerdy.
No surprise. I was good in math, but my problem with math is how it is taught divorced from real life situations. As an adult, I look around me and realize that complex math is what professionals are using to design houses and build bridges and manufacture just about everything. And these skills are only taught in specialized, advanced math classes that are labeled as something different. Astronomy, for instance, or Engineering, or Architecture, or Production.
What I find infuriating is that math is not taught at the introductory level as it ought to be taught, not stripped of all relevance to the complex work of the world, but specifically tied to it. I spent an entire year learning trigonometry, and I did well in the class, but even then, I had only a vague notion of what use trigonometry had in the real world. Yes, I knew that harmonic curves are related to sine curves. But I had no school work that tied the two together. Thus there was no need to learn trigonometry beyond what I had to in order to pass the course. And no need or opportunity to retain the knowledge and use it again in a trig course that connected the dots. Imagine how much more interesting and useful it would have been to have been taught about sine curves in conjunction with music theory. Or with any other area of relevance to trig.
Similarly, my friend who sent me the article (yes, you, James) mentioned logorithms. I remember doing quite well with them. (As I said, I was good in math.) But even then, I didn’t know what real-world purpose logorithms served. There were tables of them, but why? I’m sure they told us, but the information did not stay in my head because it never got used outside of math class. And we talk about algorithms all the time, but how are they related to logorithms?
Calculus, which I took in college and which was taught so poorly that basically my entire section failed, was another mystery. What it was for, I could not grasp, and thus it was hard to remember any calculus function long enough to pass an exam. And yet it turned out that calculus was a prerequisite for astronomy, a subject about which I and many other people are interested. But the general public knows very little about the complex math of astronomy. It’s as if the scientists speak a secret language to each other, and we’re just left to admire the bright side of the moon.
Why must we all learn math stripped of its color and life? I grant that some people have a sheer love of numbers, and that those people may be determining math curriculums. But it’s crazy to deliberately make a field of study theoretical only, when you can sell it to people so much more readily if you make it real world. Although choosing which real world application to teach might be an issue of economy, and that’s why it gets taught at the theoretical level instead.
(At this point, I must mention that I trotted out this theory at a party recently and the calculus teacher there refused to comment on it, claiming he did not want to offend. Actually, he refused to say anything more on any topic, period. So even though he may have had insightful, valid objections to my theory, since he obviously considered himself above his company and couldn’t be bothered to voice them, I haven’t a clue what they might be. Other than that math classes actually are taught today with direct links to the real world uses, and I’m just a blowhard with amnesia. )
Even simple math functions need more humanizing. Students may leave school knowing how to add, subtract, multiply and divide, but if they don’t know when to do it, they know nothing. People make wild guesses during essential mathematical transactions, and merchants and marketers constantly take advantage of this. We need to know whether a bottle with 200 ibuprofen at $4 is cheaper per pill than a bottle of 500 at $7.22. (I can’t do the math in my head, and the prices are deliberately uneven in order to make it hard for me.) Shelf talkers often don’t compare by the same terms. We need to know just how many variables we must take into consideration—mathematically—when we decide on many other essential purchases and conditions of our lives. But mostly, we guess.
Why is adding and subtracting not taught using ATM withdrawals and fees? Is Drive Thru banking taught including the cost of idling the car versus parking and walking inside and then re-starting the car? What about the value of a bulk buy at a grocery store versus the rate at which we consume the item? Whether to take the cash back or the interest break on a car deal?
Maybe some teachers do use these real world calculations. Then I guess the question becomes why didn’t they stick? Why are we constantly making very wild guesses at the true cost of things we buy? We could all be carrying graphing calculators hanging from our belts or handbags, and making complex calculations based on many variables. Or computers that talk to our home computers. Which would mean that no one would ever buy a chair again that doesn’t fit through the door to their home. But we don’t. We go along, deliberately vague, letting our wild guesses arbite our buying decisions. It’s crazy. Which costs less, a used or a new car? Used, flat out. Which costs more, a new car or a leased car? A leased car. Which costs more, a loan from a bank or from the finance company the car dealership uses? The dealership loan. Which saves you more money, a lower interest rate or cash back at purchase? I don’t remember, and I don’t know the calculation that would give me the true savings in interest. (Ah, there are more variables in this: How many years you expect to own the car, how you expect to use it, etc.)
These are all decisions ordinary people have to make. Why isn’t the math we learn infused with these situations? I don’t care how long it takes Johnny to get to a mythical city at 30 miles per hour versus at 60 miles per hour. I want to know what advanced mathematical calculation explains why it takes him two hours to drive 25 miles at 7:30 AM, and only one hour at 10 AM, and what that extra commuting time is going to do to his personal time, his family life, his sleep habits, and his chances of getting a promotion because he’s always exhausted at work. Real life. Real math. Real money.