MBlume comments on Being a teacher - Less Wrong
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Learned to program at five. If someone has the programming gear, five is a perfectly good time to teach them to program. Just show them some Python code (I was reading BASIC, bleah) and see if they can deduce the rules and try writing their own. If someone is meant to be a programmer then a programmer they shall be.
You mention reading BASIC -- did you by any chance have those math textbooks with BASIC programs printed in the appendices?