divert the child's
attention from the acquiring and organising of the system of language
forms to the premature acquirement of the content of language. What
results is obvious: the main interest being in the content, the
interest in the mechanical construction of the form suffers, and as a
consequence the child never attains a full mastery over the instrumental
art.

In the latter case we attempt to do two things at the same time in our
teaching of arithmetic. In every concrete application of arithmetic
there are two interests involved: in the first place, there is the
number interest--the interest in the analysing and recombining of a
group, undertaken for the sake of the reconstruction itself; in the
second place, there is the business or real interest, which the number
interest indeed subserves, but the two interests are in no case
identical. If we attempt to teach the two together, we as a rule teach
both badly. The pupil will have but a hazy idea of the business
relation, and will run the risk of imperfectly organising the pure
number system. Hence all kinds of impossible problems may be given to
the child without raising any suspicion of error in his mind, and such
cases furnish certain evidence that the business relation does not
really concern him, but that his whole attention is engaged with the
purely constructive aspect of number. Another example of the same error
of confounding two separate things is the "blind mixture we make of
arithmetic and measuring." Because arithmetic is involved in all
measuring we assume that when the child can add together feet and
inches, therefore he has a complete knowledge of these spatial
magnitudes. But manifestly, if spatial magnitude is to be taught
intelligently, it must at first be taught independently of the number
relation, which is a general system instrumental in the realisation of
many concrete interests.

From these considerations, certain general results follow. On the one
hand, the earlier conception of the aim of the Primary School as being
mainly concerned with the acquirement and organisation of the three
elementary arts as ends in themselves must be condemned. Language and
number systems are means to the realisation of certain concrete ends of
after-life, and the school during the later stages of education must
endeavour to lead the child to perceive how these systems may be
utilised in the furtherance of these real concrete interests. On the
other hand, t