Annie Murphy Paul, describing systems that attempt to adapt to what you know and don't know about math:
Tyler breezed through the first part of his homework, but 10 questions in he hit a rough patch. “Write the equation in function form: 3x-y=5,” read the problem on the screen. Tyler worked the problem out in pencil first and then typed “5-3x” into the box. The response was instantaneous: “Sorry, wrong answer.” Tyler’s shoulders slumped. He tried again, his pencil scratching the paper. Another answer — “5/3x” — yielded another error message, but a third try, with “3x-5,” worked better. “Correct!” the computer proclaimed.
S.H. Erlwanger [pdf] forty years ago:
Through using IPI, learning mathematics has become a "wild goose chase" in which [Benny] is chasing particular answers. Mathematics is not a rational and logical subject in which he can verify his answers by an independent process.
See if this describes your adaptive learning startup:
A basic assumption in [your startup's name here] is that pupils can make progress in individualized learning most effectively if they proceed through sequences of objectives that are arranged in a hierarchical order so that what a student studies in any given lesson is based on prerequisite abilities that he has mastered in preceding lessons.
I don't have anything against personalization per se. But the technology that enables that personalization defines and constrains the math we can personalize. Currently it defines that math very, very narrowly.
Individualization in [your startup's name here] implies permitting him to cover the prescribed mathematics curriculum at his own rate. But since the objectives in mathematics must be defined in precise behavioral terms, important educational outcomes, such as learning how to think mathematically, appreciating the power and beauty of mathematics, and developing mathematical intuition are excluded.
Look, if you're building one of these systems, you have to read and understand Benny's Conception of Rules and Answers in IPI Mathematics. Ask questions here. Let's figure this out. We'd all love for you to make some interesting new mistakes. Right now you're just repeating mistakes that are forty years old.
BTW. In Education's Digital Future last night, I said I felt the next Kasparov v. Deep Blue competition would be between a grandmaster teacher and an adaptive learning engine. Give them both some written student work. Which one can accurately identify what the student knows and doesn't know and what to do next?
I said this in a small group and a couple of technologists razzed me. One said that he doesn't even get that kind of feedback in the lecture halls at Stanford, which is totally fair, though that isn't the model I'm defending.
Another said, "Actually, computers are already better." He told me that adaptive systems can tell you the best time of the day for you to study, how much time you spend on problems, the answer you choose most often when you're stuck, and a bunch of other metrics that are simple enough to parse from a student's clickstream. Of course, not one of them addresses the student's most pressing question, "Why am I getting this answer wrong?" So, like Benny, the student clicks a different answer and the wild goose chase begins again.