Myrtle
02-21-2008, 02:59 PM
Here's an interesting blog entry on a topic that I don't come across very often. A literature professor questions the role of math in the quadrivium a la classical education and respondents to the blog entry include two mathematicians as well as somebody else you might recognize:
Saving Mathematics (http://www.geneveith.com/saving-mathematics/_346/)
The discussion boils down to if the study of math should center around its applications to solving the problems of the physical world or if it should be studied for its own sake--The age old rigor vs relevance argument.
Although that is confusing for me because in the algebra program we are using the applications are studied, they are just treated rigorously rather than heuristically.
As an aside, the proofy algebra has been going okay. I busted out Euclid and started having my son model his proofs in algebra based on how Euclid did it rather than how purely how Frank Allen does it. This amounts to beginning the proof with "the enunciation" or stating in prose what concept he wishes to prove. The second part is declaring the variables to be used, the third is restating the concept symbolically, the fourth is the actually proof written as a series of implications (if, then statements) and finally the conclusion.
The kid is not doing these entirely from scratch but certainly can do anything that amounts to a derivation from scratch. He'll see something like, "Show that -(a - b) = b - a and will recognize, according to him, that "this is just a special case of the general case that we just proved" however, actually proving that the additive inverse of a number or expression is equivalent to the product of that number or expression and negative one takes a bit of Socratic prompting.
Saving Mathematics (http://www.geneveith.com/saving-mathematics/_346/)
The discussion boils down to if the study of math should center around its applications to solving the problems of the physical world or if it should be studied for its own sake--The age old rigor vs relevance argument.
Although that is confusing for me because in the algebra program we are using the applications are studied, they are just treated rigorously rather than heuristically.
As an aside, the proofy algebra has been going okay. I busted out Euclid and started having my son model his proofs in algebra based on how Euclid did it rather than how purely how Frank Allen does it. This amounts to beginning the proof with "the enunciation" or stating in prose what concept he wishes to prove. The second part is declaring the variables to be used, the third is restating the concept symbolically, the fourth is the actually proof written as a series of implications (if, then statements) and finally the conclusion.
The kid is not doing these entirely from scratch but certainly can do anything that amounts to a derivation from scratch. He'll see something like, "Show that -(a - b) = b - a and will recognize, according to him, that "this is just a special case of the general case that we just proved" however, actually proving that the additive inverse of a number or expression is equivalent to the product of that number or expression and negative one takes a bit of Socratic prompting.