Abstract thought in applications

Sitting here in Para Coffee grading my students' first exam of the semester. It's not going so well, or at least not as well as I'd hoped. I feel like the last time I taught this course my students were a little more prepared for calculus. I guess what I have to remember is that this is spring term--a chance for those who really hate math to get this class out of the way. Oh boy.

As I grade, I'm realizing how silly it is when we break things down into "abstract" and "concrete." In math, solving concrete problems takes abstract thought--that's the whole point of even learning this stuff. You need to build something with a given amount of material and optimize the amount of space it contains. You need to maximize the speed of your vehicle. Whatever. The point is that if you just attacked the problem with no abstract thought whatsoever, you'd be stuck. If you can't imagine the problem as anything other than what it looks like on the surface, you can't solve it.

The real distinction, in my opinion, is between abstract and habitual. Students hate word problems. Why? Because they don't always look the same as every other problem they've ever done. They actually have to approach the problem on its own terms. That's frustrating, and students commonly express the opinion that their teacher "never gave us anything like this before." Students can do habitual assignments pretty well. It's much harder to get them to actually solve a problem. That's why they'd prefer to just take a bunch of meaningless limits and crank out a number or a "DNE" (does not exist) than solve real problems that someone in real life might actually ask. I worry about the implications for their future occupations. Will they be stuck just doing the same task over and over again, simply because that's easier? I suppose there's nothing wrong with that. It's just that you'd think a UVA student might imagine something more. I don't know.

The problem is that students have a hard time seeing the heart of a problem. They don't want to sit down and think about principles. It's so easy to treat everything mechanically. Yet it's so much easier to actually solve a problem by first figuring out what in the world they're looking for. And yes, that means abstractly. For instance, if you're looking for area, write down area = length times width. This is a thoroughly abstract statement, but it gives you a guide to solving the problem. You can't approach a concrete problem and solve it without identifying the abstract principles governing it. Indeed, one's knowledge of the abstract is tested best in application questions.

That's it for now--just a short rant on the difficulties of teaching math. I admit I can't help like feeling that my students' failure is my failure, even though that's absurd. I'm just some grad student the school throws up in front of these kids for less than three hours a week. Most of what these students need to know, there's no way I can teach them in three weeks before their first exam.

What is "intelligent"? What is "design"?

If you read my posts on a regular basis (I really have to wonder how many of you there are) you may have noticed that I keep coming back to two seemingly abstract subjects: epistemology, and the philosophy of mind. These seem to creep up on me as an unavoidable subtext to just about every debate I care about: between Christianity and atheism, concerning the origins of life and the material world, and even on bioethics. Nowhere has this been more true than in the debate concerning evolution that seems to go on relentlessly. I've been part of a reading group on Francis Collins' book, The Language of God, in which he lays out a case for Christianity with a special emphasis on harmony between faith and science. The reading group involves Christians and atheists/agnostics of various backgrounds, and I've appreciated the chance to clarify some of the key issues. The key issues are, in my opinion, all matters of epistemology.

Materialism and the Mind

Christianity has historically embraced a dualist interpretation of the mind/body problem inherited largely from the Greeks (Plato, Aristotle, etc.). There are two main reasons for this embrace: the first is explanatory, and the second is ontological. The explanatory power of dualism is intuitive to many (if not most) people. Thought does not appear to be physical, and reason appears to ascertain truths far more abstract than any material substance. It seems intuitively plausible that reason itself must be the product of a non-material substance. Along these lines an even more compelling case can be made for the non-physical existence of the will, which, if separated from the mind, constitutes perhaps yet a third "substance" in addition to the mind and the body. The ontology of dualism (or trio-ism?) is probably even more important to the Christian than this explanatory power. It typically helps explain the image of God in man, the ability for human beings to spiritual, and the significance of human life over and against plant and animal life.

Did we really expect anything different?

Planned Parenthood is an organization whose moral compass is so totally backward that its employees can look directly at the bloody corpse of an aborted fetus and not repent. Is it really any wonder that its employees would see nothing wrong with an underage sex ring?

Data, the comedian

He's probably funnier than most of the scientists who know how he works.

Two bioethics issues with one story

A helpful article from LifeNews.com: "Babies Can Be Treated With Adult Stem Cells, Even in the Womb." As the title suggests, this report outlines a few ways in which scientists are using adult (not embryonic) stem cells to treat children of a young age, even unborn children.

Two things: First, the more the public realizes the advantages of adult stem cell research, hopefully the less we will support the destructive kind of embryonic stem cell research. They really are two very different things.

Second, I wonder how long we can live with the moral tension created by the ability to both save and destroy life in the womb. In a world where it's possible to cure defects in children still in the womb, how much longer will we really believe it's okay to kill these same children?

A Church sign worth reading

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