After graduation, there’s that lurking temptation to do the unthinkable: to sell your soul and jump into finance. Now I’m not hating on any of you who did this. Business is an important, even necessary part of society. So we need people to do it. The work is hard; the hours are long; but I hear the pay is pretty good. And actually, I think that my job is from a social health perspective far worse. You see, I’m in the education field.

People who go into the high-paced financial markets, well, they really can do very limited damage. Right out of school, few of us are in a position to ruin countries economically or otherwise. They keep the harm to themselves. High levels of stress combined with few hours to sleep leave the worker mentally and physically drained. Then, in those few hours they do have to themselves, many seek refuge in drugs or alcohol. Not all do, of course. But even those who do don’t really leave a lasting gash on society. Ah, but then there are those like me. The quiet, horrible types who try to help out others.

At least in business, there isn’t any real pretension to altruism. In education, that’s all we claim to do. Invest in the children today to save the world of tomorrow, and the like. However, it’s seldom that easy. Oftentimes, people deign to do charitable acts which tend more to harm than to help. Remember that obnoxious girl who tried to order her food at Boca Grande in Spanish? It took her fourteen times as long as everyone else and made everyone in the restaurant (except, possibly, the girl—she didn’t stop, after all) feel uncomfortable. That sort of thing happens a lot in education, but the effects are more permanent. Try as we might, people like to simplify complicated processes because, well, that’s human nature.

I freelance for a publishing company in the math textbook division. Right now I write tests for an accompanying middle school textbook series. And let me tell you, while it’s hard to write a good math textbook problem, it’s very easy to write a bad one. Many states, and indeed the country at large, have pushed for more so-called real-world math. These over-contextualized problems do wonders to confuse and hinder understanding. The research shows how bad they are, but people seem to love them. Or, rather, they love to make their children do them. No one actually loves to do them. That’s why many parents won’t help their children do their math homework. (And whoa, what a message that sends the kids: math is unimportant; it’s okay not to be good at math; do it now and soon it’ll be over. Why don’t we accept a similar level of ignorance in other fields? It’s embarrassing not to be a “reading person” but perfectly fine not to be a “math person.”)

Motivated by the enthusiasm and reward real-world problems brought Agatha Christie (to be honest: I don’t know anything about Agatha Christie aside from this quotation, which pops-up in math education reading from time to time. In fact, up until recently I thought she was Angela Lansbury), I rely on her words. They float around in my head and guide my writing:

I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours I found it quite enthralling.

And so I try to sneak in problems that use only thinly veiled real-world examples, but are secretly robust, real math problems. I’d include some examples, but I’ve signed a non-disclosure contract.

Some of my problems don’t have numbers at all, and even ask students to draw and label their answers. Of course, for every problem I come up with that I think is mathematically constructive, I submit six or seven others that I think are damaging. And here’s the problem: I actively hurt children. I help to spread and reinforce American mathphobia, one problem at a time. Because of me (and those like me), children learn to believe that math is boring, calculation according to some magic set of standards that devious, smart, and totally absent people make up. Still, it’s nice to know that I’m fighting back the cancer of classically construed middle school math, albeit not by much.

And the textbook series that I’m writing for isn’t extremely terrible. The authors sprinkle in short and extended response questions among the rote drill calculations. Some of the questions are open-ended. And they’re big on listing the standards each problem uses. Yet the text introduces the meat of each standard through by example, leaving the student to abstract and generalize rules on his own. (This is quite generally a dangerous practice.) Obvious over-contextualization aside, these margin notes do encourage basic metacognitive reasoning. In a small, roundabout way, they ask the studenst to think about what they’re thinking about. More practically, the kids (and their parents) know up-front what material they’re accountable for. And they get to see that these problems weren’t made up completely at random. Someone thought about them. So the cost of the materials is justified, right? Yes, I think it’s a political ploy. A good one, though.

And this is the most frustrating part about it. The standards trick people into thinking that there is some golden set of content and skills that a person should have in order to be considered mathematically competent or numerically literate or whatever fashionable buzzword you can come up with. The fact of the matter is, there isn’t. Math isn’t about what you know, it’s about how to organize what you know. I don’t know much graph theory; does that mean I’m innumerate? No way. I can do more geometry than plenty of professional graphy theory mathematicians, I’m sure. They know what they like; I know what I like. The crazy thing is, I know how to reason the same way as the graph theorists. The take home: the mathematical content of a textbook is really a vehicle for the abstract reasoning behind it all. For this reason, curricula can really be a lot more flexible than they are. Now don’t get me wrong. I’m not going to say that kids shouldn’t learn arithmetic. I will argue that maybe they should learn it another way. Even when we publish fancy standards in our books but forget to change the way we approach those standards, we really haven’t done anything. Kids have been learning how to add in just about the same way for over a century. Meanwhile there’s been lots of ground-breaking research done on how people learn, think, and understand over the course of the last one hundred years. Why do we so willingly ignore it?

But I do have a curriculum, and I use it. Meanwhile, I can only do so much to take into account the kids who’ll be using my books. We’re never going to meet. I don’t know anything about them, except, possibly their average age and vague geographic location. It’s important to have a good sense of what they know, how they understand it, and how they learned it. Projecting two years into the future about strangers is hard stuff. I have to write blind to my reader.

Whatever its impact, I’m very lucky to have the opportunity to work on textbooks. With some careful thought and hard work, maybe I can make a small contribution for the better in middle school education (before running back into academia to play for the rest of my life).

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You say:

Even when we publish fancy standards in our books but forget to change the way we approach those standards, we really haven’t done anything. Kids have been learning how to add in just about the same way for over a century. Meanwhile there’s been lots of ground-breaking research done on how people learn, think, and understand over the course of the last one hundred years. Why do we so willingly ignore it?

My wife is a math teacher in the SF Bay Area.

We have many discussions about math teaching and the students she gets.

You sound a bit like all those people who push new-fangled ideas about teaching math.

We may have spent a hundred years investigating how people learn, but the best way to learn to ride a bike is to get on one and try, and to pick yourself up when you fall off and try again. Having a parent run along behind to hold the bike up is good at first, as are trainer wheels, but eventually, you have to spend time riding the damn bike.

It seems to us that many (perhaps most) students today have been given the idea that they have no responsibility to learn and that teachers have all the responsibility for their failure to master the material. They believe in instant tratification and will not put in the time with the homework and the exercises. That is, they will not ride the bike and expect to become BMX celebrities simply by being told about angular momentum and bearings and friction.

Another sad aspect of modern teaching is the notion that all students will grow to be 6 foot tall. Given that there is an approximately normal distribution of abilities, not all students are going to be able to deal with Calculus.

Until the whole education profession understands these issues, I don’t think we can expect any change.

Loki, thanks for taking this so seriously. I really appreciate reader feedback; it’s the only way I’ll get better at straightening these things out. Even still, I think you’ve read me wrong. We agree perhaps more than you realize. However, I think that an adequate response really needs more room than will usefully fit into this comment box. Look for a proper, full entry addressing your comment very soon.

Thanks …

We were discussing this issue again last night.

I suggested that we have learned in the last few years that fear is one of the more potent ways to make people learn, and she pointed out that she gets better success when she forces students to come up to the board and work through problems. Sometimes the students need a little help in the form of reminders or hints, but it seems they often can do the job in the end. I suspect that the fear factor is working here, as the student is in danger of looking stupid in front of his/her peers, and it becomes very potent when the teacher helps the student achieve success.

In the olde days, students were more afraid of teachers than they are today, which perhaps motivated more of them to master the material.

Fear towards teacher works sometimes but now a days the law indeed supporting kids incase of punishments towards kids.Mya be kids even develop their skills through online math games which gives a way to learn it in entertaining way.