Many children who have trouble understanding mathematics also have a hopelessly deficient model of what mathematical understanding is like. Particularly bad are models which expect understanding to come in a flash, all at once, ready made. This binary model is expressed by the fact that the child will admit the existence of only two states of knowledge often expressed by “I get it” and “I don’t get it.” They lack—and even resist—a model of understanding something through a process of additions, refinements, debugging and so on. These children’s way of thinking about learning is clearly disastrously antithetical to learning any concept that cannot be acquired in one bite.
(Papert, S. (1971) Teaching Children Thinking. In Contemporary Issues in Technology and Teacher Education, 5(3/4), 353-365.)
And on the higher education end of the spectrum, all of the things that really matter are those things that take patience, time, and persistence to acquire. But these are the very things excluded by this binary notion of understanding in which many children are immersed and to which most college freshmen are completely habituated.
This also makes a good argument for insisting that students — particularly those in the STEM disciplines, but I would argue anybody — should learn computer programming as part of their studies. You cannot learn to program without engaging in the non-binary notion of understanding Papert is describing. Papert knows a thing or two about that subject.
(By the way, I must give Gary Stager many thanks for running The Daily Papert. It is a great resource. The month of March is ridiculously busy for me but once it’s over I am going on a massive Papert reading spree.)