=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 Relating Process._--These relative ideas pass into the formation
of a new experience, as illustrated in Figure 3, constituting the
solution of the problem.

4. _Expression._--A further applying of this experience may be made in
adjusting the pupil to other problems connected with his geometric
environment; as, for example, to discover the sum of the interior angles
of a triangle.