Kindergarten and elementary schools emphasize fundamental skill development and nurture the growth of perceptual skills by which young minds may comprehend the world around them. In junior and senior high school education the complexity of the universe is revealed in broad and simplistic terms. The undergraduate phase of university education hones the capacity for reasoning through exposure to increasingly specialized and complex areas of learning. Throughout these phases of education the student learns to move from the concrete to the abstract, from the general to the specific, from the literal to the figurative. Similarly, the teacher is asked to direct the process of education by exposing students to increasingly deeper levels of knowledge, and to reveal the subtle inter-dependencies among the various branches of learning.
Graduate education is the final stage in the development of intellectual independence.
It is different from undergraduate education in that the student is encouraged to establish premises, to hypothesize, and to defend both the procedures and the conclusion of independent investigation. The burden of proof for the verifiability of knowledge rests on the student, not on the faculty member. It is a curious fact of life that, while moving from the general to the specific, and from the elementary to advanced by probing deeper and deeper into the chosen field of specialization, the mind reveals its maturation by ultimately returning to a position of generality. It is as if the real reason for formal education were to reduce our complex universe to a set of simple propositions. The previous statements represent ideals.