The sole direct
path to enduring improvement in the methods of instruction and
learning consists in centering upon the conditions which exact,
promote, and test thinking. Thinking is the method of
intelligent learning, of learning that employs and rewards mind.
We speak, legitimately enough, about the method of thinking, but
the important thing to bear in mind about method is that
thinking is method, the method of intelligent experience in the
course which it takes.
I. The initial stage of that developing experience which is
called thinking is experience. This remark may sound like a
silly truism. It ought to be one; but unfortunately it is not.
On the contrary, thinking is often regarded both in philosophic
theory and in educational practice as something cut off from
experience, and capable of being cultivated in isolation. In
fact, the inherent limitations of experience are often urged as
the sufficient ground for attention to thinking. Experience is
then thought to be confined to the senses and appetites; to a
mere material world, while thinking proceeds from a higher
faculty (of reason), and is occupied with spiritual or at least
literary things. So, oftentimes, a sharp distinction is made
between pure mathematics as a peculiarly fit subject matter of
thought (since it has nothing to do with physical existences) and
applied mathematics, which has utilitarian but not mental value.
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