[dboreham]

Careful there: long arithmetic probably isn't a great example, since it has no purpose to someone with a calculator -- it would be better to spend the time teaching number theory, no? And, I believe it's important to convey that "this method really only makes sense if you have a computer". Nothing turns students off like mechanical wrote method learning.

[Ericson2314]

Everyone should know how to hand-substitute lambdas and do arithmetic slowly. We should skip all the rote crap to make people faster.