As I have said, algebra should be subordinated to geometry. Algebra
has as its distinctive method the principle of substitution, whereby
symbols of equal and, for the most part, absolute generality are
substituted for one another, and the results stand for one fact as
well as for another, in disregard of the worth of the particular in
the scheme of nature. For the same reason, deductive logic is not a
good discipline for these students; empirical psychology, or political
economy, is a better introduction to the moral sciences for them when
they reach the high school. This explains what was meant above in the
remark as to the method of teaching grammar. As to language study
generally, I think the value of it, at this period, and later, is
extraordinarily overrated. The proportion of time given to language
study in our secondary schools is nothing short of a public crime in
its effect upon students of this type--and indeed of any type. This,
however, is a matter to which we return below. The average student
comes to college with his sense of exploration, his inductive
capacity, stifled at its birth. He stands appalled when confronted
with the unassimilated details of any science which does not give him
a "key" in the shape of general formulas made up beforehand. Were it
not that his enlarging experience of life is all the while running
counter to the trend of his so-called education, he would probably
graduate ready for the social position in which authority takes the
place of evidence, and imitation is the method of life.
Second, the teacher should be on the lookout for a tendency which is
very characteristic of a student of this type, the tendency, i. e., to
fall into elaborate guessing at results. Take a little child of about
seven or eight years of age, especially one who has the marks of motor
heredity, and observe the method of his acquisition of new words in
reading. First he speaks the word which his habit dictates, and, that
being wrong, he rolls his eyes away from the text and makes a guess of
the first word that comes into his mind; this he keeps up as long as
the teacher persists in asking him to try again. Here is the same
tendency that carries him later on in his education to a general
conclusion by a short cut. He has not learned to interpret the data of
a deliberate judgment, and his attention does not dwell on the
necessary details. So with him all through his training; he is always
ready with a guess. Here, again, the teacher can do him good only by
patiently employing the inductive method. Lead him back to the
simplest elements of the problem in hand, and help him gradually to
build up a result step by step.
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