who teaches the subject, and the one who
teaches the child. The number of the first type is still very large in
spite of all the books that inveigh against this conception. It were
easy to find a teacher whose practice indicates that she thinks that all
the arithmetic there is or ought to be is to be found in the book that
lies on her desk. It seems not to occur to her that a score of books
might be written that would be equal in merit to the one she is using,
some of which might be far better adapted to the children in her
particular school. If she were asked to teach arithmetic without the aid
of a book, she would shed copious tears, if, indeed, she did not resign.

=The first type.=--To such a teacher the book is the Ultima Thule of all
her endeavors, and when the pupils can pass the examination she feels
that her work is a success. If the problem in the book does not fit the
child, so much the worse for the child, and she proceeds to try to make
him fit the problem. It does not occur to her to construct problems that
will fit the child. When she comes to the solution of the right
triangle, the baseball diamond does not come to her mind. She has the
boy learn a rule and try to apply it instead of having him find the
distance from first base to third in a direct line. In her thinking such
a proceeding would be banal because it would violate the sanctity of the
book. She must adhere to the book though the heavens fall, and the boy
with them.

=The book supreme.=--She seems quite unable to draw upon the farm, the
grocery, the store, or the playground for suitable problems. These
things seem to be obscured by her supreme devotion to the book. She
lacks fertility of resources, nor does she realize this lack, because
her eyes are fastened upon the book rather than upon the child. Were she
as intent upon the child as she is upon the book, his interests would
direct attention to the things toward which his inclinations yearn and
toward which his aptitudes lure him. In such a case, her ingenuity and
resourcefulness would roam over wide fields in quest of the objects of
his native interests and she would return to him laden with material
that would fit the needs of the child far better than the material of
the book.

=The child supreme.=--The teacher whose primary consideration is the
child and who sees in the child the object and focus of all her
activities, never makes a fetish of the book. It has its use, to be
sure, bu