Teaching, why its important.

I feel like crap so there is little point in working and if I am going to waste time I might as well do something I enjoy:-)

I suppose I am biased but taking 4 classes (Ok, I am auditing one of them...) has got me thinking about teaching. Specifically, is there a right and wrong way to do it?

A seminar on the future of man and machine brought an interesting perspective. He was mainly concerned with the prospect of computers replacing humans at many jobs. The answer is no because while computers are far better at tasks that are either very simple and repetitive or highly complex with lots of rules they are very poor at the middle ground. Luckily, humans are freaking Vikings at the middle ground. That, though, is not what was interesting. To prove his point he made several conjectures: all learning is done by experience, and language is an imperfect way of conveying experience. I will focus on the second point and its importance in science education later but today is all about experience.

It is mind boggling to me that Boyle of the infamous Boyles Law spent years playing with gases and his special vacuum pump before he was willing to publish the fact that pressure is inversely proportional to volume. Think about when a student learns about this though... I think I had to have been taught this in middle school at least. In essence though before I could drive I learned one of the most important physical discoveries of the scientific revolution. If you think about it the average college graduate in science or engineering knows more then most of history's geniuses.

*I will grant that my appreciation of Boyles Law in middle school was not great. But at age 24 I think I understand it and an amazing amount of other physical truisms. My point is more that had you gone back in time and told 14 year old Boyle that pressure is inversely proportional to volume for damn near any gas so long as temperature is held constant he would have a much more difficult time swallowing this little bit of chemistry lore.*

The reason that is not so much that knowledge is necessarily compressed so much as it is experienced in a different way. The key is that while he had to stumble somewhat blindly around till he had accumulated the experience necessary to learn his own law we are taught it with foresight. Before we are taught Boyles Law we are shown the molecular nature of the matter as well as a host of other little tidbits that make these laws seem obvious. The fact that solids and liquids have a pressure vs. volume relationship that is dependent upon composition doesn't conflict at all with the universality of PV=constant for gases.

Boyles law is an extreme case but the lesson to be learned from this is that the quality of the experience can vastly accelerate learning. This is what teaching is all about! Teachers spend time finding and isolating the experiences that will best help you learn that particular truth. Since students are rarely able to see physical phenomena in action or, if you are partial to the liberal arts, witness the truth of the human spirit, teachers have the added task of constructing these experiences in the mind of the student.

So what lessons or Laws of Teaching can be drawn from this?

The basics are all important. If a teacher is to construct an experience within a students mind they can't start from scratch. A teacher must set up a situation in the mind of the student and then that situation is experienced, if you will, virtually. When conveying Boyles law to me in high school I already understood that air was mostly empty space so I could see in my mind the air molecules getting closer together and hitting the wall more often. Just think about the number of concepts inherent in what I just said. Pressure, momentum, molecular nature of matter, and ext... are needed to construct that mental image. I could certainly memorize PV=constant but I couldn't appreciate it without the basics.

A.k.a. you can't teach calculus to a six year old.

More importantly this gives us a point of attack to address teaching plans. The first thing to do is to quantify the "mental tools" that the students have. No matter what, you must present the material in terms of these building blocks. This is the cardinal sin of college professors. They present material given the concepts they have internalized, not their students. I have had some incredable professors, Prof. Prahl and Prof. Alexander immediatly come to mind, yet the students hated them! These professors presented amazing material and in a coherent manor if you already had your batchelors degree. TAing for both of them was so much fun for just that reason, I finally got it. On the other hand, TAing was a challenge because I had to put alot of effort into teaching in terms of what my students had a base level understanding of.

This helps explain why I was able to give up on students. For some I would just give them the answers or formulas they needed because it was pretty clear that no matter what language I used they just didn't get it. These students didn't spend the effort or were not capable of building the basis of knowledge necessary to understand what was being said. Neither of us had time to start from scratch so we were resigned to just memorize and hope for the best.

It also explains why proofs and derivations are often a poor way to teach a concept. Few people have mastered the concept of proofs and derivations so much effort is spent simply grapling with the presentation of the concept. If this approach is to be taken it might be best to spend some time at the begining of the class going over the derivation process and familiarizing students with it so that when the time comes they have that tool.

I could go on but (I'm feeling more sick...) the main take home message is that teaching takes effort. If you are not willing to put in that effort then perhaps the best option is to teach from the book as so many professors do. At least then you are more likely to teach in terms of concepts they understand. Ultimately there is no substitution for getting to know your students and what they know.