I have always been an avid supporter of teaching processes for solving problems in school rather than teaching facts that can be recited when called upon. It probably has something to do with how I was taught early in elementary school to "discover" the ways in which a problem could be solved. I remember figuring out key algebraic equations using blocks that represented an "x" quantity and a "y" quantity. However, I quickly found that it is useful to be able to quickly recall some core bits of knowledge if I was to move forward in learning concepts, or what Papert calls, "Big Ideas." Consequently, I struggled in high school to exercise my "memorization" muscle in order to concentrate on the next steps of the problem solving process.
However-- the fault I find in teaching processes is that with the way that children are taught to learn and to test, children will apply the process of memorization to the processes they have learned. The main fault being that while they may have "discovered" the process in the first place, and therefore gained syntonic knowledge over alienated or dissociated knowledge, they still are not generating new processes. Assuming that tests remain the best way to assess a child's learning (which I don't believe they are), a child will have to learn to assimilate the process he discovered using the memorization technique he used to apply to facts. Thus, in teaching processes have we, as educators, in fact escaped the problem of memorization?
To extrapolate this idea to programming computers--I can understand how LOGO would be a great way to teach logic as a line of command will always result in the same outcome. One can rely on its stability as a concept. The big idea being that a child is able to discover the meaning of "zero" in a hands-on way. Yet, is the straight forward input-output model the best way to approach learning seeing as this model does not reflect problem-solving in the real world. There are times when certain actions (inputs) do not lead to the same results (outputs). This is where the role of the teacher is paramount. The teacher accommodates for the fact that a child may think differently and therefore may come up with multiple different ways of solving an equation. It is this teacher who allows the child to write in an answer and explain his reasoning in a multiple choice test if none of the a,b, c, or d answers appeal to him--of course, the answer being within reason. In this way, a child can learn facts, processes, but also ways of imagining new approaches and new processes to solve problems. That is what our education system needs to aim to accomplish: a step away from memorization and a way of valuing the answers that fall in between the lines of a five paragraph essay rather than the ones that fit into age-old models. The question remains; at what point does an educator allow the child this freedom, when does she remove the scaffolding to see whether he can stand on his own.