Me three. The key is the false dichotomy implied by contrasting constructivist teaching, in which students discover their own algorithms, with "blindly teaching algorithms". It is possible to sightedly teach algorithms :-) As a professional mathematician I have to develop ways to solve problems nobody yet knows how to solve, but if I insisted on solving for myself problems that do have known solutions, I'd never get to the new stuff. I've banged on before about how important it is for children to wrestle with mathematical problems that are hard for them, and doubtless I will again, so I appreciate the motivation behind constructivism, but I don't like the dogma.

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