The concept of inflexible knowledge has made the rounds on the edu-circuit for years now. In short, math education isn’t working, because if it were, then people would be able to apply prior knowledge to solve problems in new situations. That is, knowledge would just transfer like a hot knife through butter.
Robert Craigen, math professor at U. of Manitoba has this take on the idea of “inflexible knowledge”:
It isn’t knowledge that is inflexible — it is people. One should learn the knowledge, and then have practice and exposure applying it in flexible ways. The error of progressive ed is the notion that if one doesn’t acquire knowledge in particular ways then it isn’t flexible.
traditional math 