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What makes for good science and mathematics education?

Abdul Alhazred

Philosopher
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"The fear of the Lord is the beginning of knowledge."

Check. That friggin' Yahweh scares the bejesus out of me.
 
What makes for good science and mathematics education?
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a deep appreciation that good maths is perfect,
and that the best science is not.

illustrated with enthusiasm, challenging but (just) doable tasks, and a sense of the excitement in the real thing.
 
lenny said:


a deep appreciation that good maths is perfect,
and that the best science is not.

illustrated with enthusiasm, challenging but (just) doable tasks, and a sense of the excitement in the real thing.
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When math and reality disagree, you go with reality. Mathematics is basically metaphysics...
 
Perpetual Student said:
The above comment clearly indicates a profound ignorance of mathematics.
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I assume (if math is anything other than metaphyics) that you have some sort of a story in which you can purchase a three or a seven, or a tree from which you can pick a nine....
 
In broad terms, metaphysics is to do with the nature of reality ("being as such" and so on) and, nowadays, things like free will and the nature of mental phenomena.

Mathematics, on the other hand, is to do with the relationships between abstract concepts like sets and integers. It may be applied in forming useful models of parts of reality, but (unless you are Max Tegmark? ;)) mathematics is decidedly not metaphysics.

http://plato.stanford.edu/entries/metaphysics/
 
By being taught how to memorize better, first. But this could be said for other subjectmatter as well, perhaps even more so for history and foreign language.
 
icebear said:
When math and reality disagree, you go with reality. ...
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Maths has a nasty habit of catching up and expanding so as to agree in the end. Or at least not to disagree.

Physicists make up mathematics now and then. They often get the details wrong, which are corrected later, but with the help of reality they sometimes open up area of mathematics that were (literally) inconceivable.
 
icebear said:
I assume (if math is anything other than metaphyics) that you have some sort of a story in which you can purchase a three or a seven, or a tree from which you can pick a nine....
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Why would you assume that?

Now, I don't speak for Perpetual Student and our notions of what mathematics is about might ultimately disagree, but to me it seems completely straightforward that mathematics has nothing to do with metaphysics. Mathematics per se does not make any claims of reality or that it describes what reality is ultimately like... which directly implies that mathematics is not metaphysics.

Of course, some individual mathematicians may be of a Platonist bent or whatever, but that's clearly a case of particular metaphysical views claiming things about mathematics rather than mathematics claiming anything about metaphysics.

You seem to be ignorant not only of mathematics, but what metaphysics is about as well (or at least tries to be about; I don't care to go into argument about whether or not it's any good at it).
 
icebear said:
When math and reality disagree, you go with reality. Mathematics is basically metaphysics...
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No, math is "the language of Nature." (Galileo)

Physics creates math: Geo-metry (literally, land measurement) would have been impossible without Egyptians' attempts at getting corners of the tillage to be right angles. Calculus and differential equations came about through the investigation of motion.

Abstract math - the creation of human mind - becomes the right language for new physics: Dirac's incorporation of infinite-dimensional spaces (Hilbert spaces) into quantum theory, Einsteins incorporation of differential geometry in general relativity, and the incorporation of the utterly and purely abstract fiber bundle theory in the standard model.
 
Vorpal said:
Mathematics per se does not make any claims of reality or that it describes what reality is ultimately like...
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agreed.

Sam H said:
No, math is "the language of Nature." (Galileo)
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i believe that Galileo believed that, and perhaps it was important for the initialization of western science that people carried a religious belief (no evidence) that the world could be understood perfectly via mathematics.

it now seems maths is perhaps richer than Nature. and there is no evidence that it can describe Nature with mathematical precision, once one moves beyond the integers.

a good maths and science education repeatedly illustrates those points.
 
Corsair 115 said:
KHAAAAAANNNNNN!!!!

Oh, wait, you don't mean Khan Noonien Singh? I was wondering how a genetically engineered fictional despot had a YouTube series.
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One of his many skills. He also has a cleaning business I understand - he specializes in polishing knobs. Kirk, on the Enterprise, had him do it for most of the crew!
 
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