ill be unchanged.)

What have we done with the numerator and denominator in every case? How
has the fraction been affected? What rule may we infer from these
examples? (Multiplying the numerator and denominator by the same number
does not alter the value of the fraction.)

THE FORMAL STEPS

In describing the process of acquiring either a general notion or a
general truth, the psychologist and logician usually divide it into four
parts as follows:

1. The person is said to analyse a number of particular cases. In the
above examples this would mean, in the conceptual lesson, noting the
various characteristics of the several words, John, Toronto, desk, etc.;
and in the second lesson, noting the facts involved in the several cases
of shading.

2. The mind is said to compare the characteristics of the several
particular cases, noting any likenesses and unlikenesses.

3. The mind is said to pick out, or abstract, any quality or quantities
common to all the particular cases.

4. Finally the mind is supposed to synthesise these common
characteristics into a general notion, or concept, in the conceptual
process, and into a general truth if the process is inductive.

Thus the conceptual and inductive processes are both said to involve the
same four steps of:

1. _Analysis._--Interpreting a number of individual cases.

2. _Comparison._--Noting likenesses and differences between the several
individual examples.

3. _Abstraction._--Selecting the common characteristics.

4. _Generalization._--Synthesis of common characteristics into a general
truth or a general notion, as the case may be.

=Criticism.=--Here again it will be found, however, that the steps of
the logician do not fully represent what takes place in the pupil's mind
as he goes through the learning process in a conceptual or inductive
lesson. It is to be noted first that the above outline does not signify
the presence of any problem to cause the child to proceed with the
analysis of the several particular cases. Assuming the existence of the
problem, unless this problem involves all the particular examples, the
question arises whether the learner will suspend coming to any
conclusion until he has analysed and compared all the particular cases
before him. It is here that the actual learning process is found to vary
somewhat from the outline of the psychologist and logician. As will be
seen below, the child really finds his problem in the first particular