The advantage of a knowledge of arithmetic has never been
disputed.
Its universal application to the business of life renders it an
important acquisition to all ranks and conditions of men. The
practicability of imparting the rudiments of arithmetic to very young
children has been satisfactorily shewn by the Infant-school System;
and it has been found, likewise, that it is the readiest and surest
way of developing the thinking faculties of the infant mind. Since the
most complicated and difficult questions of arithmetic, as well as
the most simple, are all solvable by the same rules, and on the same
principles, it is of the utmost importance to give children a clear
insight into the primary principles of number. For this purpose we
take care to shew them, by visible objects, that all numbers are
combinations of unity; and that all changes of number must arise
either from adding to or taking from a certain stated number. After
this, or rather, perhaps I should say, in conjunction with this
instruction, we exhibit to the children the _signs_ of number, and
make them acquainted with their various combinations; and lastly, we
bring them to the abstract consideration of number; or what may be
termed _mental arithmetic_. If you reverse this, which has generally
been the system of instruction pursued--if you set a child to learn
its multiplication, pence, and other tables, before you have shewn it
by _realities_, the combinations of unity which these tables express
in words--you are rendering the whole abstruse, difficult, and
uninteresting; and, in short, are giving it knowledge which it is
unable to apply.
As far as regards the general principles of numerical tuition, it may
be sufficient to state, that we should begin with unity, and proceed
very gradually, by slow and sure steps, through the simplest forms of
combinations to the more comprehensive. Trace and retrace your first
steps--the children can never be too thoroughly familiar with the
first principles or facts of number.
We have various ways of teaching arithmetic, in use in the schools;
I shall speak of them all, beginning with a description of the
arithmeticon, which is of great utility.
I have thought it necessary in this edition to give the original
woodcut of the arithmeticon, which it will be seen contains twelve
wires, with one ball on the first wire, two on the second, and so
progressing up to twelve. The improvement is, that each wire should
contain twelve balls, so that the whole of the multiplication table
may be done by it, up to 12 times 12 are 144. The next step was having
the balls painted black and white alternately, to assist the sense of
seeing, it being certain that an uneducated eye cannot distinguish
the combinations of colour, any more than an uneducated ear can
distinguish the combinations of sounds. So far the thing succeeded
with respect to the sense of seeing; but there was yet another thing
to be legislated for, and that was to prevent the children's attention
being drawn off from the objects to which it was to be directed, viz.
the smaller number of balls as separated from the greater. This object
could only be attained by inventing a board to slide in and hide the
greater number from their view, and so far we succeeded in gaining
their undivided attention to the balls we thought necessary to move
out. Time and experience only could shew that there was another thing
wanting, and that was a tablet, as represented in the second woodcut,
which had a tendency to teach the children the difference between real
numbers and representative characters, therefore the necessity of
brass figures, as represented on the tablet; hence the children would
call figure seven No. 1, it being but one object, and each figure they
would only count as one, thus making 937, which are the representative
characters, only three, which is the real fact, there being only three
objects. It was therefore found necessary to teach the children
that the figure seven would represent 7 ones, 7 tens, 7 hundreds, 7
thousands, or 7 millions, according to where it might be placed in
connection with the other figures; and as this has already been
described, I feel it unnecessary to enlarge upon the subject.
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