Like anything else, constructivism can be over-applied, though it certainly does have a lot of strengths. I read your blog post. I don't think it's accurate to make the sweeping statement, "Once a child learns an algorithm it is as if mathematical thinking stops". In addition I think the "fastest and most efficient way for [a] specific brain to work" will be more and more often a pre-defined algorithm as a child starts learning advanced math, since not all children will unerringly find the most efficient solution to a problem left to their own devices.
Lucounu - Well said; your description matches our personal experience. Unfortunately, the people we've spoken to in our school district seem a bit dogmatic when it comes to constructivism and math, and don't seem to think this way...
DH would go as far as suggesting some kids might get frustrated with the expectation that they rediscover the algorithms on their own, knowing that the grown ups were holding back known, efficient ones.
