phrase a
tutor can use; but even these words will convey no meaning until they
have been associated with the pupil's perceptions. When he has once
perceived the combination of the numbers with real objects, it will
then be easy to teach him that the words _are called_, _are_, and
_make_, in the foregoing proposition, are synonymous terms.

We have chosen the first simple instance we could recollect, to show
how difficult the words we generally use in teaching arithmetic, must
be to our young pupils. It would be an unprofitable task to enumerate
all the puzzling technical terms which, in their earliest lessons,
children are obliged to hear, without being able to understand.

It is not from want of capacity that so many children are deficient in
arithmetical skill; and it is absurd to say, "such a child has no
genius for arithmetic. Such a child cannot be made to comprehend any
thing about numbers." These assertions prove nothing, but that the
persons who make them, are ignorant of the art of teaching. A child's
seeming stupidity in learning arithmetic, may, perhaps, be a proof of
intelligence and good sense. It is easy to make a boy, who does not
reason, repeat by rote any technical rules which a common
writing-master, with magisterial solemnity, may lay down for him; but
a child who reasons, will not be thus easily managed; he stops,
frowns, hesitates, questions his master, is wretched and refractory,
until he can discover why he is to proceed in such and such a manner;
he is not content with seeing his preceptor make figures and lines
upon a slate, and perform wondrous operations with the self-complacent
dexterity of a conjurer. A sensible boy is not satisfied with merely
seeing the total of a given sum, or the answer to a given question,
_come out right_; he insists upon knowing why it is right. He is not
content to be led to the treasures of science blindfold; he would tear
the bandage from his eyes, that he might know the way to them again.

That many children, who have been thought to be slow in learning
arithmetic, have, after their escape from the hands of pedagogues,
become remarkable for their quickness, is a fact sufficiently proved
by experience. We shall only mention one instance, which we happened
to meet with whilst we were writing this chapter. John Ludwig, a Saxon
peasant, was dismissed from school when he was a child, after four
years ineffectual struggle to learn the common rules of arithmetic. He
h