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.
Good math courses will explore the development or construction of specific algorithms in depth, and give plenty of chances for development of problem-solving skills, but to reinvent the wheel by forcing a child to come up with every algorithm would be pointless, and slow down the learning process to a huge degree.
Developing one's own approach to a problem is a valuable skill that needs practice. There are plenty of other ones, including the ability to take in highly structured information and understand it quickly, then apply it.
As an example, I taught my son how to do conversions from Roman numerals to base ten, up through 100, in under a minute, after which he was flawless. This is often taught as a math skill, although one could certainly develop a wonderful math talent without ever learning about Roman numerals; it's more of an encoding/decoding and linguistic skill. But in any event, he learned it quickly, which gave him practice in learning rules and applying them quickly.
Taking the constructivist approach, I might have given him some samples of Roman numerals and base 10 numbers, then let him figure out the rules himself. That would have given him practice in problem solving, and he might have had fun, since he likes puzzles. In the end I think he gets plenty of practice in such things, though, so in a sense it would have just represented a delay of something else.
I believe that a strength of constructivism, for early education in math as you've explained it, is simply a focus on what's going on, instead of the notation being used. For example a child certainly could learn long division by rote practice of shuffling numbers and lines around, and do little to increase their math understanding. However I also think a focus on understanding processes involved can be part of teaching; one doesn't have to depend on a student finding the understanding themselves.
Another strength of educational constructivism as you've explained it is the discouragement of passivity. I think, again, that this is helpful and necessary, but it's not true that simply explaining an algorithm will shut a child's mind off. The devil is in the details of the teaching and the balance of active thinking activities in which a child engages.
There's simply no reason that a correct understanding of a mental model can only be approached through self-led exploration. Nor can it be true that a child will always learn the best model on their own. When a child's own model is wrong, it gets replaced by the correct one that needs to be taught by the teacher anyway-- or it's not, leading to later confusion.
ETA: A few links:
http://en.wikipedia.org/wiki/Constructivism_(learning_theory) http://en.wikipedia.org/wiki/Math_Warshttp://en.wikipedia.org/wiki/Worked-example_effecthttp://en.wikipedia.org/wiki/Expertise_reversal_effect
