One-Sixteenth

You wrote:

>…gaining a conceptual understanding falls under my category of "reading and playing," and you don't need any kind of formal program to do it.

>But at the elementary level, I can't waste time on formal science if "formal science" means dumbed-down information, coloring pages, cutsey crafts, and combining vinegar and baking soda AGAIN ... nor if it means "read and outline/fill in the blank."
>I bet we're really on the same page here, Dave.

Yes, I think so.

The American public-school, grade-school science programs are actually worse than you described.

Much worse.

For example, a few years ago, I spent a few minutes flipping through my niece’s fifth-grade science book: it was one of the most widely used in the country (Harcourt). I only had time to read a few pages, but in that time I was able to find out that, surprisingly, the speed of sound is proportional to its frequency! Of course, the speed of sound is pretty much independent of frequency – that’s why it is called *the* speed of sound. Anyone working on producing that book who let a whopper like this through should never have been allowed to pass a high-school physics class (maybe they didn’t).

The situation is not much better for US middle-school and high-school science texts.

Anyone interested in the subject should check out the Textbook League (http://www.textbookleague.org/ ), which has reviewed a number of US science texts from a scientific/secularist perspective.

As a rule of thumb, I do not use *any* textbook in any subject that is generally used in the US public schools. They are almost all disasters.

I’m willing to make exceptions, of course. The Textbook League does recommend the BSCS Biology “Blue” book, which I have looked at and which is OK. I also have a copy of PSSC Physics, which is fairly nice (and now out of print).

Perhaps your and my difference is simply terminological. I think that I might classify all of science, through Nobel-prize-winning work (maybe especially Nobel-prize-winning work!), as, in your words, "reading and playing." If you’re good enough, when you get older, you get to play with tensor analysis or mass spectrometers or DNA polymerase, but if you do not view it as, in some sense, play, you probably will not get it.

Also, if you fully and easily understand a science book that you are reading, you are not challenging yourself enough – read something harder. The textbook myth that science is a complete, easily wrapped-up finished product is false: it does not look that way to real research scientists (ask me about superstring theory someday --- aaaaarghhhh!).

It *might* make sense at the high-school level to choose one text for physics, etc. to work through in order to “cover all the bases,” but only if the student is also reading other books, back issues of Scientific American, etc. to learn what science really is – i.e., playing with nature and with our own ideas and concepts trying to better understand nature.

I do want to reiterate that, in a sense, the concepts are everything. “Plugging and grinding” to calculate an answer is a colossal waste of time unless it is the final stage of a process of conceptual understanding. The famous physicist John Wheeler once said that you should never do a calculation in physics unless you already know the answer. What he meant, of course, is that the calculation can check your conceptual understanding and work out the last decimal place – but it is never a substitute for conceptual understanding.

Attaining conceptual understanding, even at a grade-school level is hard work, incidentally. Newton’s Third Law can be stated without calculus or even algebra. But few people aside from physicists (and I have some doubt about some of my colleagues in physics) really get it and can apply it consistently.

The same thing is true in math. Someone who can do complicated integrals galore but who does not understand intuitively why the fundamental theorem of calculus is true has wasted all of his time. Few scientists (and fewer engineers) spend much of their time actually working out integrals. But they need a clear intuitive grasp of the concepts of integral, derivative, etc. to understand what they are doing.

Dave