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One alternative that is used by many undergraduate and high school computer science curricula is the language Scheme. This is a modified version of Lisp, but with a focus on simplicity. This language allows students to easily program complex abstractions with a small set of primitives.
There is a good application, free to download, which lets you simply type in Scheme statements and see the output -- Dr. Scheme (http://www.drscheme.org) -- and there's a good community for all levels of Scheme programming (http://www.schemers.org).
I think Scheme is a good alternative to the problems the author addresses with the lack of BASIC availability. It is easy to learn, easy to program, and a very powerful tool for teaching more complex programming problems.
While I think the problems in this article are all valid, it seems like the author has not really explored all the alternatives. I'm sure Scheme is not the only alternative out there, but to me it seems an obvious choice for trying out math problems and seeing how computers think.
