Let me clarify my connection to curriculum. I am primarily a software designer (although I have experience as a high school teacher) my role is to build interactive software based on, and in support of, these ideas. I will PM you a link to the project page (I will be happy to post it publically with a moderator's permission).
So with the caveat that these ideas are my pretty well-informed interpretations of the ideas expressed by educational researchers, I will continue...
This is not "new math". Many educational researchers are developing these ideas based research on what kids are learning, and how they learn better. The fact that we don't do a very good job teaching algebra is pretty universally accepted and backed up by a whole lot of research. The researchers are figuring out how to do better (and have the research to back it up).
But I was trying to present the idea that teaching the mechanical "do the same thing to both sides" is inferior to teaching the much more logical and fundamental "don't change the solution set" on its own merits.
Why shouldn't we teach students math based on "why it works" instead of teaching mechanical rules that sometimes don't work?
How do you prove women are evil?
Well
Women = Time * Money (known fact)
but
Time = Money
So
Women = Money ^ 2
Know we also know money is the root of all evil, so substitute that in:
Money = sqrt(evil)
Giving us
Women = sqrt(evil) ^ 2 = evil
Ta da!
No
Women = time and4(+) money
Time=money
Women =money+money=2*money
money is the root of all evil
evil=money^2
money=sqrt(evil)
so
Women= 2*sqrt(evil)
Not as neat, but still not a good thing
Rap
