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The time is long past when we could teach our students all they will need to know. The principal function of education—higher education in particular—must be to help individuals to their own intellectual feet: to give them conceptual starting points and an awareness of what it means to learn and understand something so that they can continue to read, study, and learn as need and opportunity arise, without perpetual formal instruction.
To continue genuine learning on one's own (not just accumulating facts) requires the capacity to judge when understanding has been achieved and to draw conclusions and make inferences from acquired knowledge. Inferring, in turn, entails testing one's own thinking, and the results of such thinking, for correctness or at least for internal coherence and consistency. This is, of course, a very sophisticated level of intellectual activity, and students must first be made aware of the process and its importance. Then they need practice and help.
In science courses, they should be required to test and verify results and conclusions by checking that the results make sense in extreme or special cases that can be reasoned out simply and directly. They should be led to solve a problem in alternative ways when that is possible. Such thinking should be conducted in both quantitative and qualitative situations. In the humanities and social sciences, the checks for internal consistency are more subtle, but they are equally important and should be cultivated explicitly. Students should be helped to sense when they can be confident of the soundness, consistency, or plausibility of their own reasoning so that they can consciously dispense with the teacher and cease relying on someone else for the "right answer".
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