-relation between the two processes
of reasoning. We have already noted on page 322 that, in such inductive
lessons as teaching the definition of a noun or the rule for the
addition of fractions, both the preparatory step and the application
involve deduction. It is to be noted further, however, that even in the
development of an inductive lesson there is a continual interplay
between induction and deduction. This will be readily seen in the case
of a pupil seeking to discover the rule for determining the number of
repeaters in the addition of recurring decimals. When he notes that
adding three numbers with one, one, and two repeaters respectively,
gives him two repeaters in his answer, he is more than likely to infer
that the rule is to have in the answer the highest number found among
the addenda. So far as he makes this inference, he undoubtedly will
apply it in interpreting the next problem, and if the next numbers have
one, one, and three repeaters respectively, he will likely be quite
convinced that his former inference is correct. When, however, he meets
a question with one, two, and three repeaters respectively, he finds his
former inference is incorrect, and may, thereupon, draw a new inference,
which he will now proceed to apply to further examples. The general fact
to be noted here, however, is that, so far as the mind during the
examination of the particular examples reaches any conclusion in an
inductive lesson, it evidently applies this conclusion to some degree in
the study of the further examples, or thinks deductively, even during
the inductive process.

=Development of Reasoning Power.=--Since reasoning is essentially a
purposive form of thinking, it is evident that any reasoning process
will depend largely upon the presence of some problem which shall
stimulate the mind to seek out relations necessary to its solution.
Power to reason, therefore, is conditioned by the ability to attend
voluntarily to the problem and discover the necessary relations. It is
further evident that the accuracy of any reasoning process must be
dependent upon the accuracy of the judgments upon which the conclusions
are based. But these judgments in turn depend for their accuracy upon
the accuracy of the concepts involved. Correct reasoning, therefore,
must depend largely upon the accuracy of our concepts, or, in other
words, upon the old knowledge at our command. On the other hand,
however, it has been seen that both deductiv