Immagini della pagina
PDF
ePub

Simplified Spelling

SUPT. R. K. BUEHRLE, LANCASTER, PA.

OW that the agitation for simplified

Now

speling is going on, and is likely to claim considerabl attention becaus of the great probability of its accomplishing material results, it may not be out of place to call attention to the great waste of time and material incurd by the retention and insertion of silent letters. On examination of the editorial colum of one of our local papers, it is found by actual count that about 9% of all the letters used ar silent, or in other words, useles. This would show that the quantity of paper requird in the printing of books and papers, etc., is increast by about one-tenth, and hence the cost of the paper alone is increast by that amount. Of cours, the labor requird to print is in the same proportion, and it would therfor seem that with the adoption of simplified speling the cost of all printed matter would be one-tenth les. Naturally ther would be a saving in its carriage by mail.

It will easily be seen that in a cuntry wher ther is so much printed matter as in ours, the saving would run into the millions. In the matter of time consumed in the writing of silent letters in the schools, we have another tremendous item of waste and on careful examination it was found that in the third year cours of our schools pupils can write on an average only twenty silent letters per minute, in the fourth year thirty-one, in the fifth year forty-four, and in the sixth year forty-eight. Now assuming that the proportion of silent letters is the same in the exercises in the schools as it has been found to be in the editorial of the paper referred to, the waste of time for the eighteen millions of pupils in the schools in the cuntry is simply appalling. What

[ocr errors]

might not be accomplisht if this time devoted to the writing and pronunciation of ofen misleading letters were givn to the acquisition of some other language, or some other practically useful study? In this respect, the American pupil, as well as his English cousin, is at a very great disadvantage. While the forener who is desirous of acquiring a knowledge of English at a mature age when his logical faculty is supposed to be developt and should be of some service to him, is simply confounded when told the pronunciation of a very large number of our words which set all logic at defiance, such as for instance: tough, dough, slough, through, thorough, and bade, have, give and live.

The argument ofen herd that everybody would be expected to lern the new speling, is entirely fallacious, becaus, while, of cours, the children would be expected to lern only the new way of speling, it is very reasonabl to suppose that those who have lernt the old way of speling would keep on writing their way if they preferd that, while the proof-readers would simply do what their office would tel them to do with regard to the speling of words in print. This, to some extent, they do now. If a speling reformer sends his copy to the printing office they politely inform him that it cannot be printed that way, and that he must submit to the rules of the office as regards the speling of his production, or els hav it rejected. The task therfor would be imposed only on the proof-readers. It would simply be an extension of the practis now followd in the case of the thousands of words which are spelt in two ways by recognized authorities. Indeed I suppose that in a very short time this would ceas, becaus

if it is once establisht as a practis to conform the speling as far as possibl to the pronunciation, everybody wil be anxious to reduce the number of letters requird to properly spel a word, to the smallest possibl number. This is the fundamental law in all language. Changes in pronunciation are going on constantly in the direction of economy of effort, abbreviating words by rejecting sounds that ar difficult or require special effort. The aim of the advocates of simplifying our speling means simply that we should make changes in speling to correspond with the changes in pronunciation, for many, if not all our silent letters wer once sonant. The final e in have, the gh in through, the t in nestle and often, wer all once sounded. Occasionally entire syllabls ar dropt as in drawing-room for withdrawing-room, 'phone for telephone and auto for automobile. All this is in the direction of laborsaving; why should it not be extended to speling? Why should anybody prefer to write programme for program?

Controlling the Gang

HAVE you in your school a boy who is a member of a "gang?" If you have you know that he considers whatever the gang approves is right, and may be performed; and if this happens to be wrong, the best you can do, by your discipline, is to hold him in check temporarily. If you cannot get control of the gang and influence it as a whole, you cannot accomplish much in the way of reforming any individual member thereof. Your point of attack must always be the ringleader of the group; you must strive to turn his sentiment your way. In order to accomplish this, you must exert a strong influence outside of the school-room; you must possess ability to adapt yourself to the impulses and interests of boys in a group. You must be able to become as one of them for the time, and work from the inside. You can never accomplish much good as an out

sider, fighting the sentiment of the gang. I have never known any teacher to win out permanently in discipline, who set himself against the sentiment of his school. On the other hand, if you are adopted by the "crowd" as a "brother," a "good fellow," you can, if you are capable and judicious achieve anything you wish. I have constantly to inspect the work of teachers who, although they know much, alike of matter and method, are nevertheless failures because they do not understand the psychology of the gang; they do not feel easy with boys; they become self-conscious and formal as soon as they get into a group of young people. So the boys draw away from the teacher, more or less unconsciously; antagonisms slowly spring up, and ultimately he is looked upon as an enemy, and a proper target for the gang's aggression and ridicule. Make it your first object in entering any school to show that you have sympathy with the group, and that you can, on the playground as well as in the school-room, be a leader, and you will never have any serious trouble with discipline. The greatest word in discipline is leadership in and out of the school.Popular Educator.

WHERE GO THE BOATS?

Robert Louis Stevenson Dark brown is the river,

Golden is the sand.

It flows along forever,

With trees on either hand.
Green leaves a-floating,

Castles of the foam,
Beats of mine a-boating-
Where will all come home?

On goes the river

And out past the mill, Away down the valley, Away down the hill.

Away down the river,

A hundred miles or more, Other little children

Shall bring my boats ashore.

Multiplication and Division of Decimals

WILLIAM F. WHITE, PH.D., MATHEMATICS, STATE NORMAL SCHOOL, NEW PALTZ, N. Y.

FOR the multiplication of whole numbers

the Italians invented many methods.

Pacioli (1494) gives eight.

Of these, only one was in common use, and it alone has survived in commerce and the schools. Shown in I below. It was called bericuocolo (honey cake or ginger bread) by the Florentines, and scacchiera (chess or checker board) by the Venetians. The little squares in the partial products fell into disuse (and with them the names which they made appropriate) leaving the familiar form II below. The Treviso arithmetic (1478) the first arithmetic printed, contains a long example in multiplication, which appears about as it would appear on the blackboard of an American school today.

In 1585 appeared Simon Stevin's immortal La Disme, only seven pages, but the first publication to expound decimal fractions, though the same author had used them in an interest table published the year before. III (below) is from La Disme, and shows Stevin's notation (tenths the first order of decimals, etc). IV is the same example with the decimals expressed by the notation now prevalent in America. Let us call this arrangement of work Stevin's method.

A quarter of a century later, an arrangement was used by Adrian Romain in which all decimal points are in a vertical column. (See V below.) It may have been used earlier. I shall be glad to have attention called to an earlier use. In the meantime I shall, for the sake of a name, call this arrangement Romain's method.

For the historical facts I am indebted mainly to the two leading American authorities on the history of mathematics

-Professor Cajori, of Colorado College, and Professor David Eugene Smith, of Teachers College, Columbia University.

Romain's method is advocated in a few of the best recent advanced arithmetics, but Stevin's is still vastly the more common; and these two are the only methods in use. Romain's has four slight advantages: (1) A person setting down an example from dictation can begin to write the multiplier as soon as the place of its decimal point is seen, while in Stevin's method he waits to hear the entire multiplier before he writes any of it, in order to have its last (right hand) figure stand beneath the last figure of the multiplicand (though this position may be regarded as a nonessential feature in Stevin's arrangement). (2) Romain's method fits more naturally with the "Austrian" method of division (decimal point of quotient over that of divisor). (3) After the partial products are added, it is not necessary to count and point off in the product as many decimal places as there are in the multiplicand and multiplier together, since the decimal point in the product is directly beneath that in the multiplicand.

(4) Romain's method is more readily adapted to abridged multiplication where only approximate results are required. On the other hand Stevin's method has one very decided advantage: the first figure written in each partial product is directly beneath its figure in the multiplier, so that it is not necessary, as it is in Romain's, to determine the place of the decimal point in a partial product. important is this last, that Stevin's alone. has been generally taught to children,

So

notwithstanding the numerous points in favor of Romain's.

It occurred to the writer recently to try to combine in one method the advantages of both of the Flemish methods, and he hit upon the following simple rule: Write the units figure of the multiplier under the last (right hand) figure of the multiplicand, begin each partial product under the figure by which you are multiplying, and all decimal points in products will then be directly beneath that in the multiplicand. Decimal points in partial products may be written or not as desired. The reason underlying the rule is apparent. VI shows the arrangement of work.

In this arrangement the placing of the partial products is automatic, as in Stevin's method, and the pointing off in the product is automatic, as in Romain's. It is available for use by the child in his first multiplication of decimals and by the skilled computer in his abridged work.

To assist in keeping like decimal orders in the same column it is recommended that a vertical line as shown in VII and VIII be drawn before the partial products are written. This is analogous to the line separating cents from dollars in ledgers, billheads, etc. The first use of a vertical line as decimal separatrix is probably in an example in Napier's Rabdologia (1617). He draws it through the partial and complete products. This is also the first example of abridged multiplication. A circumference is computed whose diameter is 635.

VII illustrates the application of the method here advocated to multiplication in which only an approximation is sought. The diameter of a circle is found by measurement to be 74.28 cm. This is correct to 0.01 cm. No computation can give the circumference to any higher degree of accuracy. Partial products are kept to three places in order to determine the correct figure for the second decimal place in the complete product. The

arrangement of work shows what figures to omit.

It should be remarked that all three methods of multiplication of decimals are alike and like the multiplication of whole numbers in that one may multiply first by the digit of lowest order in the multiplier or by the digit of highest order first. The method of multiplying by the highest order first was described by the Italian arithmeticians as a dietro. Though it may seem to be working backwards, it is not so in fact; for it puts the more important before the less, and has practical advantage in abridged multiplication, like that shown. in VII. But that question is distinct from the one under consideration.

Stevin writes the last figure of the multiplier under the last figure of the multiplicand; Romain writes units under units; the method here proposed writes units under last. In whole numbers, units figure is the last.

Applied to the ordinary multiplication of decimals, as in VI or VIII, the method here proposed seems to be well adapted to schoolroom use, possessing all the simplicity of Stevin's. Methods classes in this normal school to whom the method was presented, immediately preferred it, and a grade in the training school used it readily. Of course this proves nothing, for every method is a success in the hands of its advocates.

The analogous method for division of decimals would possess analogous advantages. It would avoid the necessity of multiplying the divisor and dividend by such a power of 10 as will make the divisor integral, as in the method now perhaps most in favor, and the necessity of counting to point off in the quotient a number of decimal places equal to the number in the dividend minus that in the divisor, as in the older method still common. Like the latter, it begins the division at once; and like the former, its pointing off is automatic. IX shows the arrangement. The figure

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]
« IndietroContinua »