The charge may be justly made, that, in many of our schools, precise and correct expression of thought is often grossly neglected. Many causes conspire to induce, on the part both of teacher and pupil, the habit of using sentences which are, in some cases, incomplete and ungrammatical, and in other cases, utterly devoid, in themselves, of any meaning whatever.

We propose, at present, to refer to only one of these causes, namely, the loose and unscholarlike language of many of our popular text books. For the sake of illustration, we will first examine a little more than one page of the University Edition of an Algebra, which holds, we presume deservedly, a high rank among the many valuable mathematical treatises now used in our common schools. We select the tenth page, and three lines on the eleventh page, for examination; and will make quotations with remarks and queries.

1. "Two quantities, one above another, as numerator and denom

inator, thus

a

وہ

indicates that a is divided by b."

REMARK.-If this be true, then the expression

that a is divided by b.

m

indicates

n

2. "Double horizontal lines, thus, =, represent equality." QUERY. Of how many double lines does the symbol in question consist? Does not the author mean two horizontal lines or one double horizontal line?

3. "Points between terms, thus, a:b:: c: d, represent proportion, and are read, as a is to b so is c to d."

REMARKS. The points are, certainly, not read as the author asserts. The letters and points, taken together, are so read, however. Moreover, in the first quotation, the text reads, "quantities indicates," and why should it not, in the third quotation, read "points represents"?

3

4. "The following sign represents root, ✔. attached, thus, 3√, ‘√, 3√, etc., indicates the etc., root."

With small figures third, fourth, fifth,

QUERY. What is the subject of the word indicates, in this quotation?

5. "This symbol, a>b, signifies that a is greater than b." REMARK.The symbol is not a>b, but it is the character between a and b.

6. Simple quantities consist of a single term."

QUERY. How many simple quantities consist of the single term a? The author means that a simple quantity consists of a single term.

7. "The measure of a quantity is some exact factor of that quantity."

QUERY. Is it quite obvious what an exact factor of a quantity

a

is? The product of 6, 7,

factor, or a measure of ab?

6

and is ab; and is 6, then, an exact 3

8. "The root of a quantity is some equal factor of that quantity.” QUERY. "Equal" to what? How can one quantity, standing alone, be called equal?

9. "The square root is one of two equal factors."

REMARK. If this be true, then 2 is the square root of 12; for the factors of 12 are 2, 3, and 2; and 2 is one of the equal factors 2 and 2.

But, leaving the tenth and eleventh pages, I quote from other parts of the work.

10." The perpendicular cross, thus +, called plus, denotes addition." 66 Quantities affected by like signs, when multiplied together,

give plus."

REMARK. The pupil is left to infer that the product of a and b is a perpendicular cross; for we find in the work, no definition of plus, except that given in the quotation above.

11. "To reduce improper fractions to mixed quantities, divide the numerator etc."

Had the author used the singular number, and said "to reduce an improper fraction, etc," the sense would have been obvious. 12. To reduce fractions to a common denominator."

QUERY. How can fractions be reduced to a denominator? They may be as easily reduced to a numerator, or a triangle, or a metaphor.

But we need quote no more. Teachers can scarcely do a greater service to their pupils, than to demand, in recitations, even of the simplest character, a precise and accurate use of language. Such a demand would induce accurate habits of thought, and would secure more directly than almost any other means, the great practical object of the teacher's profession, the cultivation of the intellectual powers.

We scarcely need to add that no text-book should be introduced into a school in which thought is not expressed with perspicuity, precision, and good taste, and that no teacher should allow in himself the habit of using language which will not stand the test of a rigid criticism.

The errors which we have criticised above, appear more important when we consider that they are mostly found in the author's definitions of mathematical terms. Teachers are sometimes not aware how much of the obscurity of mind manifested by their pupils in regard to comprehending the subjects of their study, arises from their ignorance of the definition of the terms employed in treating these subjects. One of our own pupils, on one occasion, was found unable to understand the application of a rule for the quantity, or accent, of the penult of a Latin word. The rule seemed a plain one, and we saw no reason for the provoking obtuseness of the boy, till a friend, who sat by us, solved the diffi

culty by showing that the boy did not know the meaning of the word penult. Let the teacher who reads this, ask his pupils in the study of arithmetic to write the definition of the word common, in the phrase "common denominator," and he, perhaps, will be surprised to find how few of them really comprehend the meaning of the word. Let him try a similar experiment in regard to the words "reduce," "multiple," "factor," "prime," "integral," etc. Moreover, it does not follow, that, because the pupil can repeat the definition of a term, he necessarily understands the definition. One of Webster's definitions of "network" is, "reticulated or decussated work." Now, this definition needs to be defined. So, too, when the mathematical term "measure is defined to be "an exact factor," it is difficult to see what light the definition affords, until the word "exact" has been defined. The word "factor," also, in almost all works on arithmetic, is imperfectly defined.

.

"A factor of any number is a name given to one of two or more numbers, which, being multiplied together, produce that number."

Now, the popular work from which we take the above definition, calls quantities, like 24, numbers, (that is, mixed numbers). But would any one allow that 2 and 2 are the factors of 5, and that 5 is a composite number?

A better era in regard to the subject under discussion, is, we trust, approaching. Still, however, inaccurate, and even senseless expressions hold their place in the "latest editions, improved and revised."

We have opened, for illustration, a popular arithmetic, now very extensively used in the schools of the country. On page 134, we read that "a prime number is a number which can be divided only by itself or a unit; as 1, 3, 5, 7." And yet the author shows, on page 162, that one of these very numbers, namely 5, can be divided by Again, we read of "reducing fractions to a common denominator," an expression which, as already suggested, is, in itself, devoid of meaning. But we confess that in this work we find but few points worthy of severe criticism. The glaring defects of older works on arithmetic but seldom appear in more recent treatises. Mr. Greenleaf's Introduction to the National Arithmetic, shows a great improvement, in accuracy, upon his

original work. Mr. Eaton's Arithmetic is written with such regard to accuracy of expression as to deserve the popularity which it has acquired.

In conclusion, allow us to suggest that, while the community is generously coming forward to the work of perfecting all the external arrangements of our school-houses and our schools, we are bound, as a profession, to strive to secure the highest point of excellence in all the best methods of instruction, and that the subject of this article affords to us one of the most useful and inviting fields of study and improvement.

WRITTEN EXCUSES.

MR. EDITOR :- Will you allow me a little space in your paper, for a few remarks relative to an article in the November number of the Teacher, under the caption of "Written Excuses?"

The author, "A. P. S." takes notice, at some length, of a previous article in the March number, and endeavors to prove, that the injustice complained of, is simply an instance of neglect, or want of care, or possibly, of misunderstanding, and that, too, not on the part of the teacher, but of the parent. I have a personal interest in this matter, I am the mother referred to.

If "A. P. S." will read over the article in the March number, in the light of his own rule, as found in his "Hints to Beginners," he may, perhaps, see the affair in a different aspect. The rule is as follows: "Do not be jealous of your authority. Insist upon obedience, and a compliance with all the requirements of the school, if occasion demands, but make allowance for the peculiar circumstances of your pupils, and avoid an imperious bearing, that will be repulsive to their better nature."

"A. P. S." says, "the statement of the case presupposes the existence of a rule which had not been set aside, although the mother had requested that in her case it might be done." In reply to this, let me say, that I sent a note to the teacher, stating the