rt, straight line as part of a large curve. Thereupon he forms the
idea of a curve composed of a number of short, straight lines, and on
this principle is able to express himself in such forms as are shown
here.

[Illustration]

[Illustration]

In this simple process of adjustment there are clearly involved the four
stages referred to above, as follows:

1. _The Problem._--The forming of a curved letter by means of straight
sticks.

2. _A Selecting Process._--Selecting of the ideas straight and curved
and the fixing of attention upon them.

3. _A Relating Process._--An organization of the selected ideas into a
new experience in which the curve is viewed as made up of a number of
short, straight lines.

4. _Expression._--Working out the physical expression of the new
experience in the actual forming of capitals involving curved lines.

=Example from Arithmetic.=--An analysis of the process by which a child
learns that there are four twos in eight, shows also the following
factors:

1. _The Problem._--To find out how many twos are contained in the
vaguely known eight.

2. _A Selecting Process._--To meet this problem the pupil is led from
his present knowledge of the number two, to proceed to divide eight
objects into groups of two; and, from his previous knowledge of the
number four, to measure the number of these groups of two.

3. _A Relating Process._--Next the three ideas two, four, and eight are
translated into a new experience, constituting a mental solution of the
present problem.

4. _Expression._--This new experience expresses itself in various ways
in the child's dealings with the number problems connected with his
environment.

=Example from Geometry.=--Taking as another example the process by which
a student may learn that the exterior angle of a triangle is equal to
the two interior and opposite angles, there appear also the same stages,
thus:

1. _The Problem._--The conception of a difficulty or problem in the
geometrical environment which calls for solution, or adjustment--the
relation of the angle _a_ to the angles _b_ and _c_ in Figure 1.

[Illustration: Fig. 1]

[Illustration: Fig. 2]

[Illustration: Fig. 3]

2. _A Selecting Process._--With this problem as a motive there follows,
as suggested by Figure 2, the selecting of a series of ideas from the
previous experiences of the pupil which seem relative to, or are
considered valuable for solving the problem in hand.

3. _A Relat