The basic tenet of constructivism - a trend in the theory of education and pedagogical practice - is that children learn by actively constructing their own knowledge as opposed to being seen as empty vessels to be filled with pre-existent information. There are of course legitimate doubts whether every child is capable of rediscovering all (or even some of) the requisite facts and theories that took centuries to be formulated by the best professional minds.
I always thought that, for example, letting the kids discover the value of π by tabulating measurements of several round objects is not only futile but actually counterproductive because the obsession with the value 3.14159... per se overlooks a fact of greater importance which is the mere existence of π. Finding a certain number (even if seen as an approximation to an abstract value) does not explain the reason for the proximity of multiple measurements.
I have just come across an argument that alerts to another negative aspect of constructivism. In A Cultural History of Physics Károly Simonyi writes (pp 1-2)
There is much talk in the contemporary pedagogical literature about education for independent, "critical," thinking. In scientific education attempts are often made to achieve this goal by presenting students with the laws of nature not as established fact or the opinion of experts, but providing them with the experimental setup used by the discoverer of the law, so that with the help of the experiments, the students can rediscover the laws for themselves. Yet in reality, such attempts are frequently good only for giving the student a completely false impression of the degree of difficulty in discovereing new laws, with the result that they are unable to appreciate adequately the contributions of the great thinkers. ...
As an example, we might mention here the inclined plane, a typical means by which students rediscover the laws of motion under constant acceleration, allowing them to reproduce the intellectual leap of Galileo (1564-1642). But if we give the students an inclined plane ans some smooth spheres to roll down, we have removed the only significant new element of discovery and originality. All that remains is mechanical work, which from the point of view of an experimental psychologist would not be much different from studying the behavior of a laboratory rat traversing a maze.
Galileo's great achievement was to have found an experimental approach that does not use materials found in nature. In this case, the description of the experimental setup is the crucial step ...
Children learn much by themselves while interacting, playing, and observing. However, reducing the process of education to mechanical work is bound to leave essential gaps in kids' knowledge. There won't be much progress in the educational system unless the adherents of the spectrum of the contemporary pedagogical theories agree that none of the latter is universally the best.