A lot of people made the assumption about math that you are making now back during our transition to block scheduling, and as someone from a campus which has taught math both ways, I can unequivocally state that the data show you are absolutely wrong. A math professor (my husband) who taught three courses on the semester system in the fall, and then the same three on the block in the spring, was scrambling to add new material to those courses in the spring. Because the students were focused on ONE THING, as their brains were designed to do, they did not have to be retaught the same concepts over and over, which is what happens on the semester. Hence, a lot more time for new material.

Now, if you really know about current college math courses, you might counter that most of them are not about real thinking, which is true. But although the first set of courses my husband taught were 100-level gen eds for freshmen, the same result holds true for the upper-level courses such as geometry with proofs. The reason it took so long for stuff to “sink in” in your experience is that your brain was distracted by too much other stuff – i.e. your other courses. Imagine spending eight hours a day thinking only about math. (You might think you’d get burned out, but then again, it’s only for three and a half weeks.) It’s called immersion, and for some reason everyone seems to think that’s a good way to learn a language, but not anything else. They’re wrong.

One of the ways this becomes obvious is if a professor says on Monday, “Here is a problem. You have no idea how to even approach it now, but on Friday you will turn in the solution.” Imagine the thrill students get when it turns out to be true. Part of what helps them succeed is that they get immediate feedback that they are actually *learning* something. The value of this may not seem obvious to you and I who were academic geeks from the start, but to a first generation college student ranch kid who assumes that she “can’t do math” because “it’s too hard,” it’s incalculable. The students gain confidence, and they work harder. And they spend way bigger blocks of time *thinking*, which god knows is rare enough at every educational level these days.

Anyway, thanks for proving the whole point of this essay by your response.

As for health care – simply adding a public option to what we already have, and allowing everyone the choice of what they want, is about as baby-step as you can get, given that a majority of us out here (that is, a majority before the massive right-wing misinformation campaign) would prefer to see for-profit insurance companies eliminated entirely and conversion to single-payer, AND, that many countries have better, cheaper health care through reforms they have already made in that direction. You speak as if the wheel is being invented here, that we have no idea of the implications of government insurance. That’s laughable given we have a lot of government insurance already (if the problem is creation of incentives that lead us in the wrong direction, those can be fixed – god knows that’s pretty much the no. 1 problem the president’s trying to deal with).

I dare say that if you are happy with your for-profit, private, insurance company, you either have a lot of money (and thus a much better plan than the masses), or you have never had a serious illness. Get back to me when you’ve had an HMO in charge of the actual treatment of your cancer, heart problems, etc. I have. Personally, I’ll worry about things like incentives when I actually get the coverage that they told me I paid for, without ridiculous piles of paperwork (see here) …which in England, where I lived for a time (and whose system of course is not perfect), simply doesn’t exist.

A public option is simply a radical change. Life’s experiences say take things step-by-step. Whatever form of cognition you chose to attach to that method, I would say that is a much more compelling argument than any you make here.

To be crude about it, we can put out house fires by explodiing the houses that are burning. It will often prevent spread to other houses. But the method is too radical (not in the political sense of the word).

I dare say, you haven’t the foggiest notion of the complexity of incentives that a public option will create. Did you know for example that certain Medicare pricing rules actually create an opportunity for collusion by healthcare providers? it took economists a while to figure this out; a subtle fact, which of course businessmen figured out pretty quickly.

The system is more complex than simple phrases like “public option” indicate. Too many moving parts. Acknowledge that. Any good scientist tries to eliminate variables in trying to draw inferences about phenomena; and introducing complexity into experiments just results in almost hopelessly bad experiments from which no good conclusions can be drawn.

The process of trying to isolate variables for testing, is just anohter way of saying, KISS, take baby steps. Humans are very bad at conceptualizing any more than the simplest, most well-defined of problems, and the inter-workings of our vast health care system is anything but simple, even if someone can slap a label on some complex plan and call it siimply “public option.” There must be a phrase in academia for attaching a misleading shorthand to a problem, and using that shorthand rather than the problem itself, to try to think out a solution.

As a former mathematician who retains connections to the math department, and having thought about math a great deal in my life, I have always thought that a semester system is best for learning it. We always used to say that you learn a subject in math at one level in an undergrad, another in the grad course, better yet when you teach it as a TA to undergrads, and finally best when you (if you reach that level) become a professor. It becomes simpler as your scope expands.

Put differently, math takes time to sink in.

I recently encountered this phenomenon myself. I was discussing something with the Chair of the Math Dept at Michigan, who is world class. He is an Algebrist, and mentioned that some problem (for a finite field, F, its multiplicative group is cyclic) is tricky to prove. This made me wonder whether I could still do it after 25+ years away from the subject. I did. It took me about a week to get it correct, but my instinct on how to start the problem was pretty much close to dead-on. Something only brute force would have gotten me in college.

I could, I suppose, be persuaded that some computational math courses might be taught in a month; but once you start injecting proofs (epsilon-delta proofs, for example, for continuity), it seems students get quite mystified, and it takes a while for them to realize it isn’t so mystifying.

I don’t know enough about chemistry or physics to know whether they are similar, though I could imagine it.

I know slow-going in math is quite helpful. It also allows a prof to give tough problems, with a week to solve them. It is the rigor of solving those tough problems that trains the really good mathematicians, or gets those who will pursue other careers to think in detailed and logical ways – to strive for excellence.