[ghshephard]

Isn't it the case that 99% of the population just needs to know it exists, and, in the very, very, very rare case they ever need it again, they would simply look it up?

I'd rather spend our children's time letting them know that these formulas exist, making sure they can perform them as needed, and then have them move onto something new. No need to drill / memorize trivial (as opposed to fundamental and foundation) stuff that is 2 seconds a way with google.

The worst kind of math education was that endless dribble associated with memorizing useless patterns that could easily be looked up in a book. At one point I had (painfully, oh my god, so painfully) memorized about 20 different patterns so I could chunk up integrals into products of u(x)v(x)only to spit them back on exam day, and never again look back on any kind of calculus. That was not a pleasant day week in high school. Would have been much better spent learning Geometry, Prob/Stats, Discrete Math, Linear Algebra, or any other host of mathematically oriented topics.

[SoftwareMaven]

Kids forget. If you just introduce a concept, spend a day or even a week on it, then move on to a different concept, most kids (if not almost all) will forget it by the beginning of the next school year.

Personally, it think the time for manipulation of symbols has passed. Math should be only about concepts and hardware or software should do he manipulation. But then you run into systemic issues like "how do I test all students". The factory-styled learning environment needs to die.