The example that really stuck with me was synthetic division, a more concise but less intuitive way of performing polynomial long division. Both of these topics are pretty much useless in daily life but polynomial long division does, at least, give the student some insight into the relationship between polynomials and familiar base-ten numbers. Synthetic division has no such value; it's just a faster but less interesting way of doing something you'll never have to do.
I started asking hardcore math people -- mathematicians, statisticians, physicists, rocket scientists*-- if they'd ever used synthetic division. By an overwhelming margin, the answer I got was "what's synthetic division?" Not only did they not need it; it made so little impression that they forgot ever learning it.
Which bring us to this passage from a recent Dana Goldstein post (discussed earlier):
The problem, according to [David] Coleman, is that American curriculum standards have traditionally been written by committees whose members advocate for their pet pedagogical theories, such as traditional vs. reform math.Except, of course, that's not what happened here. As was the case with so many topics in mathematics, synthetic division remained in the curriculum because no one who knew what was going on had bothered to look that closely. Coleman has a clever narrative, but it doesn't fit the facts all that well.
Now I have a request for all the math geeks in the audience. Since we need to pare down the curriculum, what you choose to cut? Specifically, what mathematical topics that you learned in school can future generations do without?
* Literal rocket scientists -- JPL's just down the road.
Also posted in a slightly different form at Observational Epidemiology.