On Oct 27, 2012, at 2:15 PM, Paul Tanner <firstname.lastname@example.org> wrote:
> Why not? I say this because some other countries treat their > elementary school kids as able to handle these "big words" and "big > concepts" of algebra (like "inverse" and the properties or laws like > "commutative" and "distributive") earlier than you seem to think > American kids are capable. > > The idea of inverse operations is how Korean elementary school kids > are taught subtraction and division - they actually introduce > subtraction *as soon as* they introduce addition by teaching > subtraction to be the operation that is the inverse of addition, and > they actually introduce division *as soon as* they introduce > multiplication by teaching division to be the operation that is the > inverse of multiplication. > > And we these "big words" and "big concepts" in Liping Ma's book being > used by Chinese elementary school teachers when explaining things to > their kids - they start this even in the 1st grade.
I teach subtraction before addition is complete and by the time I teach multiplication, division occurs simultaneously. This is a natural and automatic sense. Like knowing that hot is the opposite of cold, happy the opposite of sad. What it isn't, and what you pretended it to be, is an algebraic truth to be used to solve problems.
I have studied the exams and test results of all of these countries, and their curriculums when available. I have found no evidence of teaching algebra to elementary kids. If they were teaching algebra to 4th graders as you suggest then the 8th grade exams would be off the charts. They owe their success to a very simple notion. They take arithmetic in practice very seriously. Naturally then, when they take an exam of that is essentially arithmetic in practice, they do very well.