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.

Speaking generally, the fundamental fallacy in methods of instruction
lies in supposing that experience on the part of pupils may be assumed.
What is here insisted upon is the necessity of an actual empirical
situation as the initiating phase of thought. Experience is here taken
as previously defined: trying to do something and having the thing
perceptibly do something to one in return. The fallacy consists
in supposing that we can begin with ready-made subject matter of
arithmetic, or geography, or whatever, irrespective of some direct
personal experience of a situation. Even the kindergarten and Montessori
techniques are so anxious to get at intellectual distinctions, without
"waste of time," that they tend to ignore--or reduce--the immediate
crude handling of the familiar material of experience, and to introduce
pupils at once to material which expresses the intellectual distinctions
which adults have made. But the first stage of contact with any new
material, at whatever age of maturity, must inevitably be of the trial
and error sort. An individual must actually try, in play or work, to do
something with material in carrying out his own impulsive activity,
and then note the interaction of his energy and that of the material
employed. This is what happens when a child at first begins to build
with blocks, and it is equally what happens when a scientific man in his
laboratory begins to experiment with unfamiliar objects.

Hence the first approach to any subject in school, if thought is to be
aroused and not word