conditions, but
the rapidity of the changes in our country may be inferred from the
fact that in the first half of the nineteenth century Harvard placed
in comparatively short succession three mathematical subjects on its
list of entrance requirements; viz., arithmetic in 1802, algebra in
1820, and geometry in 1844. Although Harvard had not established any
mathematical admission requirements for more than a century and a half
after its opening, she initiated three such requirements within half a
century. It is interesting to note that for at least ninety years from
the opening of Harvard, arithmetic was taught during the senior year
as one of the finishing subjects of a college education.[7]

The passage of some of the subjects of elementary mathematics from the
colleges to the secondary schools raised two very fundamental
questions. The first of these concerned mostly the secondary schools,
since it involved an adaptation to the needs of younger students of
the more or less crystallized textbook material which came to them
from the colleges. The second of these questions affected the colleges
only, since it involved the selection of proper material to base upon
the foundations laid by the secondary schools. It is natural that the
influence of the colleges should have been somewhat harmful with
respect to the secondary schools, since the interests of the former
seemed to be best met by restricting most of the energies of the
secondary teachers of mathematics to the thorough drilling of their
students in dexterous formal manipulations of algebraic symbols and
the demonstration of fundamental abstract theorems of geometry.

=Relation of mathematics in secondary schools and college=

Students who come to college with a solid and broad foundation but
without any knowledge of the superstructure can readily be inspired
and enthused by the erection of a beautiful superstructure on a
foundation laid mostly underground, with little direct evidence of its
value or importance. The injustice and shortsightedness of the
tendency to restrict the secondary schools to such foundation work
would not have been so apparent if the majority of the secondary
school students would have entered college. As a matter of fact it
tended to bring secondary mathematics into disrepute and thus to
threaten college mathematics at its very foundation. It is only in
recent years that strong efforts have been made to correct this very
serious mathemati