I enjoyed your post Twoballcane but I do, respectfully, have to disagree with you. However, before I get into it, I think it’s important to differentiate the direction both of us are coming at this from.
Your point seems to be focused on developing those with an interest and aptitude in science/math to their full potential. My point was far more general; it was gauged towards increasing the scientific understanding/critical thinking capacity of the populous. I come from this more general viewpoint because it relates very closely to what I feel is the crux of many societal issues but that is another, much longer, story.
When it comes to training someone to mastering any skill, repetitive training or intensive exposure is important; I don’t disagree with you here. However, there is a disconnect between repetitive training of mental math problems and a good engineer, just as there is between shooting 1000 free throws a day and being an NBA all-star. Mathematical proficiency is a tool that good engineers need but a good engineer needs other tools as well as the capacity to bring them all together in an effective manner.
The problem that I have with promoting proficiency through repetition is that it yields prescriptive problem solvers. They are great for handing a difficult, yet formulaic, problem to and having them grind through it. However, they require a prescribed problem to solve; they rarely have the imagination and creativity to ask what problem should be solved and why. This, to me, is crucial to an innovative society, which is crucial to a successful society.
Now, I don’t actually think that you are saying if we get engineering students to do 1000 math problems a day, and only that, they will be better engineers. However, you do seem to, rather flippantly, dismiss the concept of promoting scientific awe in the classroom as fluff. I think you do this partly because you extrapolate my comments to mean that I want all fluff and no hard, chalk-to-board, pencil-to-paper style math and science. This is not what I’m saying. I think subjects should be structured as such:
1) Introduction to the topic
2) History of the topic, going through past mistakes and developments which lead to the current understanding
3) Why the topic is important and interesting
4) pencil-to-paper style problem solving
Currently, we skip steps 2 and 3. So when you say “math and science is a dry subject”, I understand why you say that. Step 4 may not be “fun” however it’s downright painful without steps 2 and 3. Beyond being painful, it’s also futile. Napoleon said “The more I study the world, the more I am convinced of the inability of brute force to create anything durable”.
Sure, I could get a good grade in the subject, but I can do so by doing enough problems to develop a formulaic way of solving the problem without understanding any of the content. F=ma can be solved without really understanding what “F” is.
Not teaching kids why the subject is important and beautiful is to withhold the single greatest factor in them being interested and successful in that subject. I can’t begin to guess at the number of brilliant students we’ve pushed out of math and science (and into finance…) because of our “brute force” method of teaching (as well as an ill-placed notion that monetary wealth is the ultimate form of success…but that’s another topic).
Having said all this, I think we are actually closer to agreeing with each other than it appears. We both want an educated, scientific literate society (at least enough so to make an informed vote), we both want qualified, passionate teachers educating our youth (and should agree that teachers should make more money and have more prestige) and we both see scientific development as intrinsically linked to a prospering society. Where we appear to differ is the method. I enjoy differing opinions on this subject because it gets me thinking about it and I feel it is one of the most important topics to discuss.