How do I know that we really need to rethink the math curriculum again? I was just talking with a colleague. And we both check the routine questions on our tests using Wolframalpha. If experts in the field know that appropriately used technology does the work as well as they do then perhaps novices should check their work in the same way.
I think a lot more emphasis needs to go into letting students know when to use each tool they have available. For instance, if I had to find the expansion of a binomial to the fourth power, I might use Pascal’s Triangle as a tool to get the coefficients of the expansion and perform the arithmetic needed mentally. If I had to find the expansion of a binomial to the 8th power, or even needed to know a certain term (maybe to answer a question in probability) I am certainly going to use technology and not the binomial theorem. “expand (p + q)^8” doesn’t take long to type.