Arthur Benjamin thinks that the current model of the mathematics curriculum — leading from arithmetic to algebra and ultimately to calculus — is flawed and needs to be changed. Watch this 3-minute TED talk for what he thinks ought to be the real summit of the mathematics curriculum:
I am in a great deal of agreement with Prof. Benjamin here. The secondary school math curriculum does indeed seem poised to point students towards calculus. While that is appropriate for some, it is not appropriate for all; while on the other hand, a better knowledge of discrete math, especially probability and statistics, would be appropriate for everybody.
Moreover, Prof. Benjamin did not stress one of the most important selling points for refocusing on discrete math: The mathematical background requirements are a lot lower than they are for calculus. Students currently have to take two years of algebra, at least a semester of trigonometry, and often an entire course in Precalculus on top of all that just to have a fighting change in calculus. And even then it doesn’t always work. Probability and statistics, on the other hand, gets to good ideas, deep ones at that, without nearly so much training.
On the other hand, what about those students who do end up going into science, math, engineering, economics, or other fields requiring calculus? If probability and statistics becomes the summit of the secondary curriculum, then at what point do those kids get the precalculus training they need in order to complete calculus (which I interpret to mean a year of calculus) by the end of their freshman year in college? Would they be having to double up on math courses — statistics on the one hand and precalculus on the other? Would they need to decide that they wanted a STEM-related career early on in high school, and if so, is that good for them?