"school is _life_." Is this difference in the
concept of the school a vital one?

7. How may this difference of concept affect the work of the teacher?
the attitude of the pupil?

8. What definition of education will best harmonize with the ideals of
this chapter?

CHAPTER II

THE TEACHER

=Teachers contrasted.=--The vitalized school is an expression of the
vitalized teacher. In the hands of the teacher of another sort, the
vitalized school is impossible. Unless she can see in the multiplication
table the power that throws the bridge across the river, that builds
pyramids, that constructs railways, that sends ships across the ocean,
that tunnels mountains and navigates the air, this table becomes a
stupid thing, a dead thing, and an incubus upon the spirits of her
pupils. To such a teacher mathematics is a lifeless thing, without hope
or potency, the school is a mere convenience for the earning of a
livelihood, the work is the drudgery of bondage, and the children are
little less than an impertinence. The vitalized teacher is different. To
her the multiplication table pulsates with life. It stretches forth its
beneficent hand to give employment to a million workers, and food to a
million homes. It pervades every mart of trade; it loads trains and
ships with the commerce of nations; and it helps to amplify and ennoble
civilization.

=Vitalized mathematics.=--In this table she sees a prophecy of great
achievements in engineering, architecture, transportation, and the
myriad applications of science. In brief, mathematics to her is vibrant
with life both in its present uses and in its possibilities. She knows
that it is a part of the texture of the daily life of every home as well
as of national life. She knows that it pertains to individual,
community, and national well-being. Knowing this, she feels that it is
quite worth while for herself and her pupils, both for the present and
for the future. She feels that, if she would know life, she must know
mathematics, because it is a part of life; that, if she would teach life
to her pupils, she must teach them mathematics as an integral part of
life; and that she must teach it in such a way that it will be as much a
part of themselves as their bodily organs. She wants them to know the
mathematics as they know that the rain is falling or that the sun is
shining, because the rain, the sunshine, and the mathematics are all
elements of life. Her great aim is to hav