Who to Teach?

When I first got interested in teaching, one of the reasons I wanted to do it is because a lot of people don't see how math is relevant to their lives, and I think that makes their lives a lot worse. People who can use math fluently can adapt to their surroundings better, can manipulate their environment, are less likely to get cheated by deals they don't understand, etc. I really think it not only makes your life better, but it makes your life better by a huge amount.

Now there's a lot of people who don't see how math is relevant, but they're still good at it. They probably won't ever credit math with their successes in life, but I honestly don't worry about them that much. They'll be able to figure things out when they need to. But there are a lot of people who really can't handle math related things. There are people who fundamentally don't understand credit cards and end up poor the rest of their life because of it. There are people who get suckered in to signing up for premium packages even though they utilize about a tenth of the resources. There are people who think they'll be in the top 10% of the nation, when they don't even have a chance, or understand what that means. In fact, most people think they're above average. People who aren't capable of sitting down and reasoning through their situations are at a severe disadvantage. If everything goes well in their life and difficult decisions never come up, then it's not such a big issue. It is feasible that you could get by without math in an ideal situation. However most people will be faced with difficult choices. Do I chose place X for $500 a month, or place Y for $700 a month? Each of those choices has many repercussions on the rest of your life. Do I get a car loan, or do I take the bus? A friend of my mom's bought an SUV a few years ago. She liked the idea of being able to spontaneously go into the mountains. Not my kind of thing really, since I'm so indoorsy, but I can see that being a nice thing to have. So we know the benefits. What are the costs? And how do you best compare them to weigh your options? Do you compare the money spent on renting a car vs paying off one you own? How about factoring in flexibility (you have to pay for the car you own- you don't have to rent a car if you can't afford it)? And how do you account for environmental concerns? And even if those aren't important to you, what about other lasting factors? How will your credit score be affected if you're pushing yourself to pay for a car? What if you, like my mom's friend, pay only the minimum balance on the car every month? My mom's friend didn't even realize she had bad credit until she applied for a loan to buy a house. That must have hurt to find out that paying the minimum balance every month was making it harder and harder to own a home. She thought she was paying what she owed and so should have great credit. She didn't realize that she was never touching the principle and that when applying to get a loan, it appeared that she already had a large debt.

Are all of these concerns math related? Not directly. Some of it is just misinformation leading to misfortune. But what caused that level of misinformation? When you sign a contract for a credit card, all the rules are spread out and described. Of course, if you can't understand percentages or compound interest, it might not mean much to you. If your grasp over mathematics is so poor that you can't understand contracts that you sign yourself into, then maybe you'll have trouble figuring out how to work within the system. Maybe you'll have a harder time calculating the costs and benefits of something you wish to purchase. Maybe you won't save up the money you need for retirement and will have to keep working until eventually your company fires your for being unfit to work and you've destroyed your health just trying to make ends meet. Most people do not have enough money for retirement. Would it have been any different if they had sat down and calculated their earnings at an earlier stage of life? Would they have still decided to buy the fancier car or the larger house or get the hundreds of DVDs for their collection? Why do people buy things that they cannot afford? Is it because they don't see the consequences? Or is it because they don't understand them? It is a difficult mathematical calculation to even decide what it is that you can and cannot afford. It takes further understanding to realize what the repercussions are for going over the limit, or even for not going positive enough. I want to help people use math so their lives are better. Even if people don't see these as mathematical calculations, if someone is good at math, they'll be able to figure things out on their own. It grants them a certain independence and makes me confident that they'll go on to do fine. It's the students who struggle with even simple computations who worry me. What decisions will they make when the stakes are higher? Where instead of getting grades, they get debt? I worry for them a lot. And that why I want to teach. I figure that's the best way to help these people and the best way to target ignorance.

However certain signs indicate to me that that might not be the path I take when teaching. Several people in my program have commented to me that I would really excel at teaching the higher level calculus classes, especially when I comment about having difficulties with my lower achieving class. I keep thinking to myself, "But those kids are fine! They'll get by just fine without me. They'll go to college and make some realizations and maybe they'll get burned at times, but they'll learn from it and figure out a way to come back." It's the other kids who I worry might not bounce back so easily. I want to help them so that they won't be at such a disadvantage. But I don't know sometimes. Was I really a help to my last class? I don't really think so. It's true that I don't know where they would have been without me, but I have to say I wasn't happy with where they ended up. Most of them quit trying, or were unhappy about trying when everyone else just copied from them. I didn't get across any of the idea that were really important to me, some of the ideas that took several paragraphs up above. But I've been thinking about it recently- those ideas aren't simple. It's true that the struggling students don't understand a lot of what I just wrote about, but I'm not so sure the advanced students do either. None of them have credit cards- why should they understand credit debt? But they might be in a better position to understand some of those things. I just assumed that they'd figure it out as they went though life, but who's to say that they would? I know a lot of bright people who got turned off to math and then never touched it again. Will I be able to do more good helping remedial kids (against nearly overwhelming odds, I might add), or helping the already gifted who have a better chance of actually showing some improvement because of me? Is this a case of helping the wealthy (in knowledge) get wealthier? Will I really enact any change this way? I would like to help the most needy, but of course, those are the hardest to help. I don't know what to do.

Truthfully, I'm just going to have to try different things and see what feels most rewarding to me. It's not like I have to choose one or the other. I think I can try both, even at the same time. It's just hard for me to consider changing my original reason for getting into teaching, to shift my target group from the students of early math to the students who have already mastered (or gotten past at least) the basics. It's a tough decision and even after writing for a while, I don't feel like I have any answers.