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If math is about measurement, then Mathletics may have your child's number. Much like games that post the best scores of players, the Mathletics SOAP API makes student scores accessible to programs as well as its website.
Wolfram Alpha, the up-and-coming "answer engine" that we reported on back in May, has just released an API that developers have been awaiting since this spring. The new RESTful API provides access to the vast stores of data and computational knowledge available through the Wolfram Alpha project (technical details at our Wolfram Alpha API profile).