[SpaceBar]

Algebra is not “advanced math.”

Dr. Israel Herstein would disagree but I digress. There are really two distinct tiers of what people call algebra. There is the method of symbolic substitution in what would otherwise just be arithmetic, and amounts to almost a rote memorization of a collection of "tricks" of manipulation to isolate the sought quantity. But there is another variety which focuses on abstract structure that is independent of the pedestrian notion of numerical value. The latter is what is taught at the college level for math majors, and is one of the most beautiful disciplines of pure analysis that exists.

[thecodont]

But there is another variety [of algebra] which focuses on abstract structure that is independent of the pedestrian notion of numerical value. The latter is what is taught at the college level for math majors, and is one of the most beautiful disciplines of pure analysis that exists.

What would such a course (or courses) typically be called? Thanks.

[thecodont]

But there is another variety [of algebra] which focuses on abstract structure that is independent of the pedestrian notion of numerical value. The latter is what is taught at the college level for math majors, and is one of the most beautiful disciplines of pure analysis that exists.

What would such a course (or courses) typically be called? Thanks.

[thecodont]

But there is another variety [of algebra] which focuses on abstract structure that is independent of the pedestrian notion of numerical value. The latter is what is taught at the college level for math majors, and is one of the most beautiful disciplines of pure analysis that exists.

What would such a course (or courses) typically be called? Thanks.

[NVDave]

They’re not teaching the latter form in any high school - as you point out, the abstract stuff is for math majors.

The high school variant, as you also point out, can be learned by rote.

And therein lies the issue: The modern teaching methods movement decries “drill and kill,” but want to know something? There are some things where “drills” work just fine. I don’t have to even think about how to multiply numbers up to 15, because we memorized them. If I had to think about how to do multiplication, I would have never made it through all the math involved in electrical engineering.

Here’s the teaching method that would solve most all of today’s problems in education:

http://www.southparkstudios.com/clips/103440/drug-free-treatment

[dr_lew]

... The latter is what is taught at the college level for math majors, and is one of the most beautiful disciplines of pure analysis that exists.

I feel a song coming on.