less_ number is placed _before_ one representing a _greater_, its value
is to be _subtracted_; thus, IV. represents _four_; IX., _nine_; XL.,
_forty_, etc. When the child understands what is here presented, he has
the key to the whole matter. He is acquainted with the principle upon
which the tables are constructed, and a little practice will enable him
to apply it, as well to what is _not_ in the table as to what _is_ in
it. I have known scholars study that table faithfully _four months_, and
then have but an imperfect knowledge of what was _in the book_. I have
known others who, with _one hour's_ study, after _five minutes'_
instruction in the principles here laid down, understood the table
perfectly, and could recite it, without making a single mistake, even
before they had studied the whole of it _once over_.

_Third._ The manner in which _reading_ is generally taught is hardly
superior to the modes of instruction already considered. In many
instances, commendable effort is made to secure correct pronunciation,
and a proper observance of the inflections and pauses. But there is a
great lack in _understanding_ what is read. When visiting schools, with
the permission of the teacher, I usually interrogate reading classes
with reference to the meaning of what they have read. Occasionally I
receive answers that give satisfactory evidences of correct instruction.
Generally, however, the scholars have no distinct idea concerning the
author's meaning. They, astonished, sometimes say, "I didn't know as the
_meaning_ has any thing to do with reading; I try to pronounce the words
right, and mind the stops." Teachers sometimes say their scholars are
poor readers, and it takes all their attention to pronounce their words
correctly. They therefore do not wish to have them _try_ to _understand_
what they read, thinking it would be a hinderance to them. They
occasionally justify themselves in the course they pursue, saying, "I
don't have time to question my classes on their reading, nor hardly time
to look over and correct mistakes." At the same time they will read
three or four times around, twice a day or oftener. The idea prevails
extensively, judging from the practice of teachers, that the value of
their services depends upon the extent of the various exercises of the
school. If the classes can read several times around, twice a day, and
spell two or three pages, teachers frequently think they have done well,
even though one hal