A friend of mine sent me a link (to a link) last week. The second link is an essay on the teaching of mathematics. It breaks my heart, both for its truth and its beauty.
I think the author is dead on about what’s wrong in the teaching of mathematics — and not just in K-12. He is also absolutely on the mark when he describes what mathematics means to me.
It is very well written, and I think it is very worthwhile reading.
There was an interesting question and answer out on the sci.math newsgroup (and probably sci.physics). The question was posed in John Baez’ June 20 “This Week’s Finds in Mathematical Physics (Week 276)” and answered in the very next post in the thread, by Phillip Helbig.
Here is the question. What would happen to the earth if Betelgeuse went supernova?
We can get a quick answer far more easily than I thought — and apparently, more easily than the original poster realized. We don’t have to compute the energy released; all we need is absolute and apparent stellar magnitudes, at least for starters. (Eventually we might want to know more, but the first answer gives us a good idea of what would be going on.)
In the end, I am reminded of just how large interstellar distances are.
Now, I am not going to work out the answer for you. But my reason may not be what you expect. It isn’t that someone else worked it out, and it isn’t even that “you should do this yourself”. In fact, when I worked it out I got a slightly different answer from the one on the newsgroup.
No. I think this qualifies as a great pedagogical question.
This is an absolutely wonderful question to have in mind when you go look up stellar magnitudes. Whether you are cracking open an old astronomy textbook to look at something now forgotten, or whether stellar magnitudes are completely new to you — the question of how bright a supernova would be in our sky could go a long way in organizing the material as you reread or read it.
So I’m not going to work out the answer, because I don’t want to deprive you of the experience of reading about stellar magnitudes with that question in mind.
I do not know very many questions like that. I latch on to them when I find them, but in my experience they are few and far between.
The very first such question that I remember is about human blood types. Somewhere, sometime, someone showed me an introduction to the ABO human blood groups — specifically an introduction which said that when you had finished the chapter you would know three of these, four of those, three of something else, and so on.
I think that is ridiculous, to enumerate the number of alternatives or examples of something one would learn.
If you want to go read about the ABO blood groups, then let me ask you a question.
Can your mother donate blood to you?
If anyone were guaranteed to be able to donate blood to you, you would think your mother could.
To answer that question, you need to understand certain things. The question itself provides a wonderful guide to study.
I would welcome additional questions like those two.
Now let me find out what mathematics my inner child wants to do, before I get back to wavelets, and the minor mathematical distractions I’m using for now when the wavelets get confusing or discouraging.