Tuesday, March 14, 2006

One day before the Ides of March

Q: What is 11.00101?
A: It is the binary expansion of Pi to 5 places.

Which is my way of introducing that today is Pi Day (3.14). And with that it is a way to note that there are certainly many ways to view an idea (in this case there are many ways to represent the number Pi) but often particular representations (in this case the decimal expansion of Pi) take root in the collective consciousness as a way to identify an idea and perhaps as the way to view it.

With that, I want to take a fresh look at the 3 R’s and in particular at their interplay. There is a common notion that these are learned separately or if there is a tie between them, then it is between Reading and Writing. Surely those are related, but I want to focus on how knowing the third R (Arithmetic) can benefit the execution of the second R (Writing). And, of course, I don’t really mean Arithmetic; I mean Math, more broadly considered. I’ve long held that knowing math well can help make one a good writer and indeed that it is a good gateway area of knowledge into becoming a good writer. At the least, that has been the case for me. So here I’d like to explain what I mean.

When I was in eleventh grade I was fortunate enough to take a class on Number Theory. We used this book, but I think a lot of what we did we just derived in class. I learned about Perfect Numbers, Factorials, Euclid’s Prime Postulate, and a bunch of other stuff that was fun, if useless. Indeed, the really great part of the class was in the lesson that ideas in themselves are something to delight in. Ideas can provide much amusement and questions about those ideas can lead to interesting paths of investigation. Sometimes the University is critiqued as having too much “theory for theory’s sake” and not enough relevance for what is going on in the real world. And I’m sympathetic with that critique. But on the other side of the coin, ideas are important for themselves, not simply as representations of reality. Learning Math is a great way to reach that understanding. And to me, it was the fundamental way to get that lesson. Everything else had an air of contingency to it, of being situated in the specifics. Only math had that purity of idea where that preceded the application.

Studying math is also an excellent way to learn about making good argument. A significant part of that comes from learning how to do proofs. What needs to shown? What steps along the way are sufficient for that? This is not a mechanical thing and I believe some people might get turned off from math too early because they think it is mechanical (and boring). Part of learning to do proofs is learning how to make your own “Aha moments” by finding the interconnection between one part of the argument and the other. And it creates a strong sense of where to look when search for the source of an idea. This is a critical skill in maturing as a thinker.

Math also is a great way of communicating a sense of taste. Arguments can be made in an elegant way. Or they can be done sloppily. Why is elegance to be preferred? That is not an arbitrary thing. Elegance in the argument creates joy in the one who hears the argument and that in turn creates joy in the other one who creates the argument.
Learning taste is a key, if overlooked, aspect of an education, any education. And in this sense by learning it in Math, the lesson can transfer to other areas.

Now let me change directions. I didn’t stumble onto this topic. My honor students are working on their projects that are due this week. In the process of coaching them I’ve gotten a good sense of their writing. While a couple of them have a mature style, which shows up even in their initial drafts, too many of them write in a fuzzy, imprecise way that conveys a sense of being unsure about the topic. Of course they are unsure; they are beginners on the economics. But when one sentence contradicts its predecessor, or there is excessive repetition of an idea, or the sentences appear disjoint it shows they are unsure about how to present argument itself.

I’ve made the claim (following many others) that students don’t write enough and certainly to the extent that practice makes perfect, that is one explanation of what I’m seeing right there. But I also wonder whether these kids got as good a math education while in high school as I did 30 years earlier. Remember that these are kids in the Campus Honors program, meaning they are among the best and the brightest here, and the vast majority are engineering students. So they more than likely had a “rigorous” program in math. But I fear they didn’t learn math as a form of argument and so didn’t develop a taste for argument. And I believe I'm seeing that in the writing. Their first instinct is to find "what I as the teacher am looking for" rather than to make a coherent argument based on their own current understanding of the topic. And, indeed, I believe that learning math would positively dispose the students to making arguments on their own.

In critiquing their work I use an approach based on my own personal modifications of what I learned in a Writing Across the Curriculum Seminar I attended many years ago. To me argument and dialog go hand in hand and so my critique as much as possible is written as response to what they say so that I'm pushing them to make argument even if they haven't viewed that as the initial purpose of the assignment. Of course, I critique the economics too and if they make an implausible conjecture I will try to point out why that is not right and how to consider something that is more appropriate. This is hard work for me but it is the part of the course where I feel the most that I'm teaching and where it is clear to me that they are receptive to the critique because they have a stake in the paper they are writing and because they have a chance to modify the document as a consequence of what I have suggested. All of this is part of the ABC's of the WAC approach and I must say that I've found WAC to be a good basis for considering how to teach the entire course, even the piece with no writing intensive component.

What does Internet technology do in this vein? The obvious key thing is to lessen the lags between submission, response, and revision. This promotes engagement and that is clearly good. It also makes teaching feel like running a sprint - it wears you out quickly. But I wonder if having a few quick bursts like this during the semester is better for the students than having a sustained but more reserved critique of the writing throughout.

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