or rather totally ignores it, as not involved in the number process. The text-books in arithmetic before mentioned, following as they do The Psychology of Number, avoid both extremes. They begin (especially, of course, in the primary) with the "How many" as applied to some total; and keeping together things which psychologically cannot be separated, proceed from the vague how many and the vague how much to the definite so many and the definite so much. There is thus gradually yet surely evolved the concept of ratio—a concept which is indispensable in practical life, and without which there can be no science of arithmetic.

As already said the "how much" and the "how many" are correlative; i. e., number and magnitude have a mutually defining relation; making definite the one depends on making definite the other. Yet there are persons who know so little of Dr. Dewey's power of analysis as to suppose (or assert) that he actually teaches that the numerical definition of a quantity has nothing to do with number-with units and with the how many of them which make up the quantity.

The mental movements of such critics are about as effective against the position of Dewey, the philosopher, as were the movements of the unwieldy Spanish hulks against that other Dewey, the naval hero.

This one sample of the critic's "understanding" and "fairness" must suffice: ex uno disce omnia. J. A. MCLELLAN.

PRESIDENT, ONTARIO NORMAL.

NOTES.

Miss Harriett Powell will teach mathematics in the Rockport High School next year.

The Anderson High School is fortunate in securing the services of Mr. E. C. Welborn as teach. er of mathematics. He is a superior teacher and a well-trained mathematician.

Professor S. C. Davison has been granted a scholarship at Harvard and will go there next year for graduate study.

The American Book Co. is now issuing the Cornell Mathematical Series under the general editorship of Professor Waite. Murray's Integral Calculus has already appeared, and an Analytic Geometry and a Differential Calculus are in press.

The international Lobachérski prize of five hundred roubles for the best work in geometry, preferably non-Euclidean, has just been awarded to Sophus Lie of Leipzig. Lie is one of the two or three greatest mathematicians of the world.

Scott, Foresman & Co. of Chicago have just issued the Rational Elementary Arithmetic by Dr. H. H. Belfield, director of the Chicago Manual Train

ing School. Comparison is the basis of the work. For this purpose colored lines, squares, spheres and rectangles are used. In this way drill in color and number is combined. From comparison the way is led by easy stages to concrete problems of every-day experience. Drill in the abstract combinations of numbers is made a prominent feature. The book is made up entirely of problems and exercises. The matter treated in the problems covers a wide range of interesting and valuable knowledge. The book will certainly interest the pupils and assist them in easily mastering elementary arithmetic.

There has recently been issued from the press of Longmans, Green & Co. a little book on Elementary and Constructional Geometry by E. H. Nichols of the Brown & Nichols School, Cambridge, Massachusetts. It is intended for pupils beginning geometry at the age of ten or twelve, and is to be a guide to the teacher rather than a class text-book. The main purpose of the book is to make the pupil expert in the construction of geometrical figures and to familiarize him with the language and concepts of geometry. The exercises are interesting and well arranged. In our western schools the book will prove useful by furnishing useful and desirable supplementary work for the seventh and eighth grades.

In the preface of the Primary Public School Arithmetic the following very round statement is found: "While number work in the first grade may be largely incidental, it ought not to be accidental. The teacher should have a clear conception of the work to be done, and of the order and method by which the child may step by step reach the desired end. When the child enters school the number sense is alert; he is, roughly speaking, in the counting stage of development. Upon the principle, strike while the iron is hot,' this counting power should at once be used for further growth by applying it to more definite measurements. Such application arouses fresh interest in number and is in a high degree educative.”

Wallace Thornton of Jersey City, in the Journal of Education, says: "In none of the fads grafted on to our curriculums is the departure from the rules of right reason more marked than in the teaching of arithmetic. It has become the recognized rule that primary, intermediate and grammar grade classes differ, not in the nature of their several divisions of arithmetic, but simply in the numerical value of multipliers, divisors, denominators or decimals. The child of six is now confronted with the whole field of arithmetic the first term he enters school. He is taught to form correct ideas of number in the integer, the fraction,

the decimal. Is not this absolutely wrong? The matter difficult of comprehension for the child is not the size of the number, it is the number itself. . . It is a monumental task for the infant intelligence to grasp the idea of unity, of combinations of units. It is a tedious task to build up a proper idea of five, six, ten, twenty. When these numbers are lastingly moulded into the brain-matter, the step to hundreds, to thousands, is necessarily short. And yet, now we essay to teach simultaneously three distinct divisions of arithmetic, and all to the six-yearold tyro! Is not the result, by necessity, such as teachers now find it-a confused medley? A medley that pursues the child all through the school course, blunting the faculties, stunting the mindgrowth, and giving us graduates of our grammar schools devoid of reasoning power."

SALIENT THOUGHTS FOR PRIMARY TEACHERS.

THE PROBLEM.

Here is your problem: Given fifty children, more or less, and one teacher eager to apply the newest and best educational thought in teaching them the three R's; how shall it be done?

One thing is certain; you must have the whole child with you if any kind of good work is to be accomplished. This means that not only the child's body must be present in the school-room, that his mind must in some degree be responsive to yours, but that the soul of the child, the feeling, willing, motive-making part of him, must be with you also. For his own good you want him to do certain things. You have the power to make him do them; that is, you can control his body and, in a degree, his mind, by virtue of the authority vested in you as a teacher; but the soul of the child, the part that makes him want to do the thing that should be done, must be won. It cannot be driven or coerced in any way. Authority cannot reach it, but it comes forth gladly, more than half way, in response to the teacher who has the heaven-given power of drawing it to herself.

It is so common a thing to see a child in school in the body only that we have ceased to notice it, the rest of him roaming far afield, God knows where, creating a world of his own more in accord with child-nature than the every-day schoolroom. "Johnny is a good boy," the teacher says, 'but very dreamy. He does not learn very quickly. I think I will have to put him back with the C class."

When a teacher, by reason of inspiration or good training, brings to her children the right thing, they respond so freely and fully that half in ecstasy, half in despair, she exclaims: "Why can

not they always be like this?" If they could, the millennium would indeed be here, ushered in by an army of perfect teachers. Our present work is to find out what this "right thing" is in song, in story, in play, and in working methods, that we may give it to our children and keep them "with us" for periods of longer and longer duration.

If you have ever taught little children you know what I mean when I say that often we have only the body of the child with us; you know what I mean when I say we hold the child's mind or attention as well; you also know that even then, unless we have the soul, the will, the love of the child in addition, our work is but imperfectly done.

What should you do first of all, to give yourself to the children, and to get them to give themselves freely into your hands? Play with them. I do not mean by that that you are to learn some pretty little kindergarten games and teach them to the children; I do not mean that you are to play for them, play at them, or make them play. I mean you are to play with them.

You have learned, perhaps, that "Play is the first creative utterance of man;" that "Play is the expression of self-activity." You know that the child comes to you from a world of play in which he has lived for six years; that its atmosphere is his native air. Now the whole child plays. Body, mind, and soul are all present when he is playing happily. Why can we not use this tremendous fact, and, instead of taking the child out of his play-world all at once and plunging him into a school-work atmosphere, go down into it ourselves to meet him on his own ground, live and play with him there, and, after nature's own method, make him so at one with us that we can lead him where we will?- KATHERINE BEEBE: The First School Year. The Werner Company.

PRIMARY READING.

Divide the time allotted to reading into two periods as widely separated from each other as possible.

In the first of these teach all the new words, and drill upon them thoroughly. Too much emphasis cannot be laid on the importance of this preparatory study.

In general, the following methods will be satisfactory with second and third-year pupils :

I. Write upon the board a new word with all the diacritical marks that may be necessary to enable the pupil to pronounce it correctly.

II. Teach the meaning of the word.

III. Proceed in the same way with several other words.

IV. Drill on the instant recognition of these words without diacritical marks.

V. Let the pupils mark the words from dictation, marking the sounds and accents, and dividing it properly into syllables.

Later in the day let him read the lesson for the sake of the thought. Do not take it for granted that no further teaching is necessary, but remember, too, that it is now the pupil's time to talk.

If he does not read well now, it is because he fails to grasp the thought. A word, a question, will often clear up the obscurity in his mind. Lead him to think, not to imitate.

It is a good idea to have a systematic plan for silent reading. Many of the short stories in this little book will lend themselves easily to this device. On this work may be based a subsequent oral and written language lesson.

Above all do not neglect to cultivate his taste,his literary and artistic instincts. "What stanza, or what line, or what part of this did you like best? Why?" are questions always in order and always interesting.-MRS. L. L. W. WILSON: Nature Study in Elementary Schools. Macmillan & Co.

THE STAR AND THE LILY.

One evening an old chief sat at the door of his wigwam smoking his pipe.

A crowd of little Indian boys and girls gathered about him and begged for a story.

This is what he told them: Once all the people were happy. sickness and no war. The white

come.

There was no man had not

There was plenty of game in the forest. There was plenty of fruit on the trees.

The earth was covered with a carpet of flowers. There were birds of more beautiful plumage than now.

The red man loved the stars. For he believed that in them the good people lived who had been taken home by the Great Spirit.

One night they saw a star that shone brighter than all others.

Night after night, as they watched it, it came nearer and nearer.

At last it rested on the top of a tree like a beautiful bird.

One morning it spoke to a young warrior of the tribe and said:

"Young brave! I have looked down upon your people for a long time. I have grown to love them and their beautiful land, with its flowers and birds and rivers.

"I have left my two sisters, the Morning and Evening stars-in the sky, and have come to live with you forever.

"Ask your wise men what form I shall take, and where I shall live to be most loved."

The star was asked to choose for herself. "I know where I shall live" she said joyfully, -"in the lap of the water, where I can see the gliding canoe. Then I can kiss the naked feet of the little children as they play on the bank of the stream."

With these words she flew down to the water, where she saw herself reflected.

Children, when you see the water-lily, take it in your hands and hold it to the skies, that it may see its sisters in heaven.-MRS. L. L. W. WILSON: Nature Study in Elementary Schools.

PRIMARY ARITHMETIC.

1. Counting.-Counting is of course the first thing to look after; the child can probably count a little when he enters school, but there is now to be counting with a definite end in view-the growth of the relating process which gives rise to number; there is a whole to get an idea of, there are its parts; there is the how-many; e. g., the child is counting something.

(a) Start with a whole and count by single things. For instance, count the number of girls in the room. Of boys. Of children. Test how far the number names are significant; e. g., name the number and have corresponding objects selected, etc.

(b) It may be that the children cannot countcannot give the consecutive number names and apply them to corresponding groups of objects. In this case the starting-point is the vague muchness (ideas of more and less) and the vague howmany which must be in the children's minds. Have them make comparisons involving ideas of more and less; e. g., the length of the desk is greater than the width, etc. Also practice in the how-many idea; e. g., compare the how-many cubes (say 8) in this group with the how many (say 6) in that. They will be led to see that the muchness of a quantity is determined by the how many parts in it, etc. Have constructive exercises, bringing out relations in consecutive numbered objects (how many five differs from six, etc.), and arousing interest in number names; e. g., have them make a picket (two splints); try to make a triangle with two splints; they will need one splint more, and will express the how-many as two and one," or as "one, and one, and one." Similarly, try to make a square with three splints; they will need one more splint, and the how-many in the square will perhaps be expressed as "three and one," or "two and one and one," or (as we have often seen) "one and one, and one and one," with some rhythmic movement. They will now fully appre

ciate the simple number names which are substituted for the round-about expressions.

The children will hence soon be ready to see that we cannot find how much one quantity (as a line, area, etc.) differs from another without finding the how-many of some one thing (unit) in each.

2. Not to be confined to single things.-Count this two rows of girls; of boys; of all,-how many twos? Count pairs of hands,-how many pairs? Similarly, count groups of 3,-how many threes, etc? Also appeal to the ear: taps with stick, strokes of bell, vocal sounds (as letters, etc.), this both with single sounds, and groups of sounds (i. e., sounds rhythmically marked off).

3. Test this relating process; e. g., start counting with 4; i. e., 4, 5, 6 (units of any kind). Show by fingers or marks or dots what preceded the 4.

4. Count the same quantity with different units of groups; e. g., these 12 pupils: by 2's how many? (6). By 3's, by 4's, by 6's, how many in each case? This lot of 24, by 2's, by 3's, by 4's, etc., to determine the different numbers (how many) that measure the same quantity. Also count different quantities with the same unit of measure. This lot of 6 (pupils, etc.) by 3's. This group of 12 by 3's, this group of 15 by 3's, etc. Use many familiar units. MCCLELLAN AND AMES: Primary Arithmetic. The Macmillan Company.

FAMILY LIFE.

The dependence of each member of the family upon the whole.

The similarity of family life as seen in comparing our own homes with those of the birds as to: Paternal and maternal care.

Life of the young: Infancy, activity, growth, responsibility.

The bond of common sympathy springing from similar experiences which unites all family lives. Preparation for winter, as seen in the making of winter homes by caterpillars chrysalis or

cocoon.

First Week.-OUR OWN FAMILY LIFE. Second Week.-OCCUPATIONS OF THE HOME. Third Week.-SPECIAL STUDY OF FRUITS. Fourth Week.-PREPARATION FOR WINTER. -CANNELL AND WISE: Outlines for Primary and Kindergarten Classes. E. L. Kellogg & Co.

When sectional feeling is past, when the sons of South Carolina are styled Yankees' by the Spaniards, and the Massachusetts boys march with joyous step to the tune of "Dixie," when educators meet from North and South and East and West, with never a thought of sectional differentiation, it is most fitting that this convention should close with the singing of "My Country, 'Tis of Thee," with the emphasis on the "My."-E. ORAM LYTE, President-elect N. E. A.

THE WASHINGTON MEETING.`

At Philadelphia, four years before the Civil War broke out, leading teachers from various sections of the Union organized the National Teachers' Association. In 1870 the name was changed to the National Educational Association, and in 1886 it was incorporated with a permanent fund of $60,000. Its purpose, as stated in the charter, "To elevate the character and advance the interests of the profession of teaching, and to promote the cause of popular education in the United States," has been fairly well realized, though the enormous size of the conventions tends to make them unwieldy, while politics, the inevitable, has already intruded, impairing in a measure the greatest usefulness of the organization.

It may be urged, too, against this as against large associations generally, that the papers and discussions deal too much with the general and too little with the particular; yet it is a great help and a source of inspiration to attend if one's mind is open to influences and impressions. There is always the enthusiasm of numbers, and there is the uplift due to close contact with the best minds of the profession. If some eminent speaker happens to disappoint our expectations it is encouraging to find ourselves not hopelessly inferior. But there are always prevalent fine influences which make us ill satisfied with past efficiency and ambitious to advance, and in the strength of such ambition we go many days.

A wholesome rivalry among the most attractive cities usually locates the association at some desirable place, and it seems only fair that as Washington and the East had it this year, Los Angeles and the West should have it next year.

The newly-elected president is E. Oram Lyte, principal of the State Normal School at Millersville, Pennsylvania. The office of permanent secretary was created, and Irwin Shepard, who has been secretary for several years, was elected to this office for four years with a salary of $4,000. Secretary Shepard will hereafter devote his entire time to this work. No better selection could have been made. This body has grown so large, and the work of the secretary so heavy, that this move had become a necessity. The attendance this year was very large-10,000 teachers are said to have been present. The time and the place were both favorable. The teachers were delighted with their stay in Washington. The program was carried out as previously announced. It is impossible to do justice to such a meeting with a mere report, and we commend our readers to the bound volume of the proceedings when it shall

appear.

In this volume we are to study, under Professor Henderson's direction, some of the facts, problems and institutions which come to us from our association in human society. Every intelligent teacher is aware that in every stage of its development society is continually presenting a scene of strife and conflict. There are evils to be opposed, wrongs to be righted, dangerous movements to be circumvented and brought to naught. Society is made up of advocates and reformers, dangerous radicals and stupid conservatives, noble men of benevolent designs, unscrupulous demagogues with evil intent, shrewd and selfish men who would pervert and corrupt the State for private gain, of a great army of honest workers who are toiling for their daily bread, of busy men and idlers, of geniuses and scholars, of men of business affairs, of society swells and worthless dudes, of philosophers and saints and sinners. Contention and agitation,-which are essential to social progress,-keep the great complex mass in movement and turmoil. Many causes and reforms, many parties and classes are brought to the teacher's attention. The spirit with which the teacher approaches these themes will measure the benefit which he is to receive and impart from their study. The spirit of the teacher should be impartial, but never indifferent. Divesting himself not of conviction, but of selfishness, partisanship and prejudice, he should cultivate a fair, calm and judicial spirit,-a spirit which will lead him to appreciate the point of view of all parties and classes. It is especially important in the study of society and its problems that that spirit should be cultivated in the teacher which will lead to the realization of the noble motto: "In essentials, unity; in non-essentials, liberty; in all things, charity."

II. THE SCOPE OF THE SUBJECT AND THE POINT OF VIEW. 1. Fix clearly in mind the institutions to be considered: a. The Family, b. The School, c. The Industrial Organization, d. The Church, e. The State. pp. 4-5. 2. Consider by what forces and organizations, present and past, these institutions are worked. What should be the method of study? The relation of sociology to the other sciences? pp. 4-8.

3. In what sense must future social changes be based upon the present constitution of society? pp. 10-12. Explain what is meant by historical development and the empirical method.

III.-NATURE AND SOCIAL LIFE. Ch. II.

1. Why should we consider astronomy, the physical sciences and biology in connection with a study of society? Set forth several specific illustrations of the influence of physical, geographical, and geological elements on man. Are material and physical influences of less importance than formerly? pp. 12-21.

2. Write out a statement of the law of "diminishing returns," and of the "Malthusian theory."

3. Illustrate the law of competition and natural selection. pp. 25-29.

4. State the social race problem, from the physical point of view. pp. 29-30.

5. Give a brief discussion of Nature. a. As an obstacle to man.

b. As an ally of man.

Show how man has used and overcome nature. pp. 30-37.

IV. THE SOCIAL MEMBER. Ch. III.

Show how social study is related to the study of the human body.

a. As to the demands of the natural body.
b. As to bodily growth and decay.

c. As to the contribution of the senses to our social
life.

d. As to the development of human emotions. pp. 43-50.

Note the differences and likenesses among individuals, and their social significance. pp. 51-55. Consider the influence of heredity and individuality in society. pp. 56-61.

COMMENT.

At the request of the editor I am to present a few articles for teachers in connection with readings, studies and discussions relating to social problems of knowledge and of action. These articles will not be systematic, nor take the place of a programme; but they will be suggestive reminders, illustrative of principles, and encouragement to renewed endeavors.

TEXT-BOOKS.

It happens that a text-book has been prepared, and a book may be so used as to do great harm. A book is an instrument and not an object. We use a telescope to look through, not to look at ; to see stars and planets, not to gaze upon its polished glass and brass and endless clockwork. The author sincerely hopes that the book will be outgrown; that it will in time make itself useless, as scaffolding is taken down when the walls are up. When a guide has taken a company to a spring they can afterward dispense with his direction and make a path for themselves. Each student can become an original investigator. The world is his laboratory. The book is a slave, not a lord. Use it and use it up. Make a better one for your

self.

THE SUBJECT.

The subject is "Social Elements," not sociology