It would be interesting to understand how "school mathematics" displaced "actual mathematics" in our educational system.
I suspect that part of explanation has to do with computers. The word "computer" was originally a job title (see, for example the Harvard Computers: http://en.wikipedia.org/wiki/Harvard_Computers). It changed meaning in the middle of the twentieth century when mechanical (and later electronic) computers displaced human computers.
It seems like much of "school mathematics" is vocational training to work as a computer. Unfortunately, we don't employ people to do computation anymore because the cheapest and worst computer you can but will be thousands of times more productive at computation than a human being.
If our mathematics curriculum was designed to train people to be computers, and that profession no longer exists, it's no wonder that school mathematics seems pointless and disjointed.
I think "actual mathematics" was used to refer to abstract and/or high level mathematics, the sort a math major might take in college. While "school mathematics" was used to refer to arithmetic and algebra.
I suspect that part of explanation has to do with computers. The word "computer" was originally a job title (see, for example the Harvard Computers: http://en.wikipedia.org/wiki/Harvard_Computers). It changed meaning in the middle of the twentieth century when mechanical (and later electronic) computers displaced human computers.
It seems like much of "school mathematics" is vocational training to work as a computer. Unfortunately, we don't employ people to do computation anymore because the cheapest and worst computer you can but will be thousands of times more productive at computation than a human being.
If our mathematics curriculum was designed to train people to be computers, and that profession no longer exists, it's no wonder that school mathematics seems pointless and disjointed.