us see
whether we can lead them to "develop" the rule instead of learning it
out of the text; that is, we will proceed inductively. First draw a
rectangle 4 by 6 on the board.

Q. What do we call this figure?

A. A rectangle.

Q. How shall we find its area?

A. Multiply its base 4 by its altitude 6; the area is 24.

Q. Now I draw a line diagonally across the rectangle; how
many figures are there?

A. Two. (Teacher here gives new word "triangle" and explains
it.)

Q. How do the base and altitude of the triangles compare
with the base and altitude of the rectangle?

A. They are the same.

Q. How do the two triangles compare in area?

A. They are equal; each is half of the rectangle.

Q. Then, if each is half of the rectangle, what must be the
area of one of the triangles?

A. The area of each triangle is 12, for the area of the
rectangle is 24, and the area of each triangle is half that
of the rectangle.

Q. Then, how may we find the area of a triangle?

A. Multiply the base by the altitude and take one half the
product.

Of course the teacher may have to supplement questions like the above
by others to assist the child in arriving at the desired answer, but
the method is the same in any case. The inductive method is the
child's natural way of learning, and should be applied to nearly all
school branches. Too many teachers have children learn rules and
definitions which mean little or nothing to them. This is not only
discouraging to the child and a serious waste of time, but it develops
bad habits of study by making the pupil think he is learning something
when he is not. Only when the fact or process learned is _understood_
is it true knowledge. The inductive method begins with what the child
already knows and, step by step, leads him to understand the new
truths. It comes last to the rule or definition after the meaning is
clearly seen.

_b. Dangers of the question-and-answer method._--No matter how good a
method may be, there are always some dangers connected with its use,
some points at which a teacher needs to be on guard to see that the
method is not misused or over-used. The question-and-answer method is
no exception to this rule.

One of the greatest dangers in the use of this method is that pupils
will come to depend on the questions as a crutch to help them along
mentally when they