Is Calculus the ultimate goal of mathematical education? Arthur Benjamin has a slightly subversive suggestion in this TED presentation.
I would however change the emphasis away from Gaussians to Poisson.
PS: Apparently I can’t embed videos here. Anyway, his thesis is that mathematical education over the past century has concentrated entirely on taking students to the pinnacle of being able to do Calculus and leave them there high and dry. Instead, he suggests that the ultimate goal of mathematical education should be statistics, which is of more practical use to more people. I don’t think he means to suggest that Calculus should not be taught — I couldn’t even understand propagation of errors without Calculus — but rather that the emphasis must shift to a more practical goal. I was brought up to believe that all the world is a partial differential equation, but even I can see that this is a sensible suggestion.