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I used to program in MS-DOS basic when I was a kid. I googled for "FreeDOS basic" and there seem to free solutions available now.
Even if you want Commodore 64 or Sinclair, their are emulators available for free download. You can have all the retroness you need to run old math book examples.
I've read some of Brin's books, but like this article, its something that sounds interesting that goes nowhere.
P.S. get your kid to program in Java, and skip the BASIC.