Mind-opening thoughts about early education of math and science by Alan Kay:
Scientists escape to a large extent from simple belief by having done enough real experimentation, modeling building using mathematics that suggests new experiments, etc., to realize that science is more like map-making for real navigators than bible-making: IOW, the maps need to be as accurate as possible with annotations for errors and kinds of measurements, done by competent map-makers rather than story tellers, and they are always subject to improvement and rediscovery: they never completely represent the territory they are trying to map, etc.
Many of us who having been learning how to help children become scientists (that is to be able to think and act as scientists some of the time) have gathered evidence which shows that helping children actually do real science at the earliest possible ages is the best known way to help them move from simple beliefs in dogma to the more skeptical, empirically derived models of science.[…]
There is abundant evidence that helping children move from human built-in heuristics and the commonsense of their local culture to the “uncommonsense” and heuristic thinking of science, math, etc., is best done at the earliest possible ages. This presents many difficulties ranging from understanding how young children think to the very real problem that “the younger the children, the more adept need to be their mentors (and the opposite is more often the case)”.[…]
So, for young and youngish children (say from 4 to 12) we still have a whole world of design problems. For one thing, this is not an homogenous group. Cognitively and kinesthetically it is at least two groups (and three groupings is an even better fit). So, we really think of three specially designed and constructed environments here, where each should have graceful ramps into the next one.
The current thresholds exclude many designs, but more than one kind of design could serve. If several designs could be found that serve, then we have a chance to see if the thresholds can be raised. This is why we encourage others to try their own comprehensive environments for children. Most of the historical progress in this area has come from a number of groups using each other’s ideas to make better attempts (this is a lot like the way any science is supposed to work). One of the difficulties today is that many of the attempts over the last 15 or so years have been done with too low a sense of threshold and thus start to clog and confuse the real issues.
I think one of the trickiest issues in this kind of design is an analogy to the learning of science itself, and that is “how much should the learners/users have to do by themselves vs. how much should the curriculum/system do for them?” Most computer users have been mostly exposed to “productivity tools” in which as many things as possible have been done for them. The kinds of educational environments we are talking about here are at their best when the learner does the important parts by themselves, and any black or translucent boxes serve only on the side and not at the center of the learning. What is the center and what is the side will shift as the learning progresses, and this has to be accommodated.
OTOH, the extreme build it from scratch approach is not the best way for most minds, especially young ones. The best way seems to be to pick the areas that need to be from scratch and do the best job possible to make all difficulties be important ones whose overcoming is the whole point of the educational process (this is in direct analogy to how sports and music are taught – the desire is to facilitate a real change for the better, and this can be honestly difficult for the learner).