that the same attainments be secured to all who have an equal opportunity for instruction, and in the same length of time. We have emphasized unity and equality to such a degree that we are in danger of forgetting that there is also variety. Freedom has not been too greatly emphasized, and it is the glory of our time that we recognize the duty of training the capacity for freedom to its highest expression.

There are children to whom the language arts are so difficult that they will leave school and work at the hardest and most disagreeable manual employment, rather than try to master the art of reading upon its most elementary plane. The mind cannot make the adjustment to what requires so complex and intense a mental process. Most of these pupils can be taught to read by the insight, skill, and patience of the expert teacher but not in the same length of time that is required to teach children who have average aptitude for learning written and printed forms, and interpreting their meaning. The teaching of language, both oral and written, should not be postponed with these pupils, and they should not be abandoned by the school. There should be a large element of manual and motor expression, and definite manual training, which is mental training also, and which may form a gradual approach toward what must be the closer mental adjustment required in learning to read. The child who has learned to read and to spell the words of a First Reader, and to write his name with a fair degree of legibility, has a vast advantage, in his equipment for life, compared with the entire lack of such skill, elementary as this preparation seems, and inadequate as it really is. We know that this is not preparation for citizenship in a republic.

The demand upon the part of the public that these pupils all be taught to write a well-balanced and sensible letter, perfect in mechanical form, to fit any occasion, will not be soon fulfilled. This means some maturity of judgment-the ability to distinguish the important from the unimportant. Our use of language reveals our degree of development, and language cannot be improved without improving the quality of mind.

Much of the work of our modern business world requires quick discrimination, concentration, accuracy, and rapidity in execution. To make a combination of endurance and fine discrimination is a problem of growth which superficial thinkers have yet to consider. Fine and quick execution requires physical strength, and quick and accurate judgment. Compare the work of the expert shorthand reporter and typewriter with the ordinary employments requiring the use of the large movements of the body, little mental discrimination, and slow execution. The machine, and expert training, have raised the standard of accuracy in writing and spelling beyond what can be attained by a considerable minority with our present system of penmanship and an unphonetic language.

Perhaps the greatest evidence of progress during the year is in the increased recognition of the value of the teacher, as compared with the value of buildings and equipment. More money for the teachers of the elementary schools is

now one of the most important measures to be considered in the development of the school in our country. The teacher is the school. Money will not make good schools, excepting in so far as it enables the best people to give their services to teaching. Bishop Spalding says:

A message of the nineteenth to the twentieth century is this: "So mold public opinion that it shall lead the best men and women to choose teaching as a vocation." Can we reduce the amount of money invested in drugs, prisons, and battleships, and make a condition of civilization in which these things will not use so great a part of the energy and creative force of life?

Some progress has been made in the adjustment of the work of the elementary school to the high school. This has been made possible by the departmental plan of teaching in the higher classes of the grammar schools, and also by a better understanding of the capacity of the pupils, and better teaching in grades below the grammar schools.

While there is great waste in trying to get little children to think beyond their capacity, there is equal waste in failing to require abstract thinking up to the pupil's maturity of development. While the time given to arithmetic and grammar should probably not be increased, these subjects should be emphasized by the manner in which they are taught, both as to method and extent. I believe that Latin in the seventh or eighth grade would bring a more exact study of English, and that the beginnings of algebra would assist in understanding some of the more complex processes of arithmetic.

A very marked advance has been made in the recognition of the value of play. School grounds in cities have been enlarged, and outdoor play has been encouraged by intelligent direction and organization. The meaning of play is not yet understood. Froebel has done more than anyone else to explain its meaning and to show us its value, its necessity, in the life of the child. Its value to all stages of development needs to be recognized, and the school should show that play can be recreation. There is a tendency to organize play into a strenuous employment, and to use up all the forces of life in preparation for battle, which requires savage alertness and ferocity. Play should teach temperance in action, and should form a habit of normal and healthful reaction.

Progress has been made in the appreciation of the value of individual instruction. The preceptor idea was inaugurated at Princeton University a year ago.

These preceptors are to take students, individually or in small groups, and train them to work. This work is to consist, not primarily in preparing lessons, but rather in reading, and preparing written reports upon the matter read.

This individual help is necessary for the college student; there is no machinery which will take the place of the personality of the teacher. It is necessary for the little child in the primary school, and for the maturing youth in the elementary school.

There is an effort, in all progressive school systems, to give closer individual

instruction, either by dividing the school into small groups, or by employing an assistant to teach special classes or individuals. President Eliot's demand for the enrichment of the course of study meant more teachers, smaller classes, more individual instruction, and better preparation for teaching. It means that we can no longer teach children mechanically and in the mass.

Back of the demand for the enrichment of the course of study is the nature, the capacity, of the child, which has never been met by an adequate environment. That atrophy of power may set in very early, for want of the adaptation of conditions to growth, we all believe. That the school is striving to meet this demand, this great meeting of earnest teachers is evidence.

The teachers of the primary and elementary schools speak to the whole nation. There is no more inspiring sight, nothing which brings such hope, nothing that gives such evidence, that the man of the present has, to a great degree, power over the future, as this annual meeting of the teachers of the nation.

THE TEACHING OF ARITHMETIC IN ELEMENTARY SCHOOLS M. A. BAILEY, NEW YORK TRAINING SCHOOL FOR TEACHERS The principal factors in the teaching of arithmetic are the course of study, the text-book, and the teacher. The office of the course of study is to indicate the order in which the topics shall be considered, and to assign the time within which each shall be completed; the office of the text-book is to indicate the order of the topics, and to present them in such a manner that the learner may master them without other assistance; the office of the teacher is to give the same instruction by word of mouth which is given in the text-book by the printed page, and to direct the learner. Thus the course of study and the textbook have the order of topics in common, and the text-book and the teacher have the imparting of instruction in common.

The outline in both the course of study and in the text-book should be the same, that the learner may have before him in consecutive order everything that he has studied, and that he may be able to find readily whatever he may need. Otherwise he is obliged to keep a notebook, to study pages widely separated, and, it may be, to use several text-books at the same time. The practice in most of the large cities of outlining a course of study in detail, and of authorizing the use of one or more text-books no one of which follows the prescribed order, is indefensible in theory and unsatisfactory in practice. One of two things should be done: either a series of text-books should be selected, and the course of study should be made to conform to its outline; or a course of study should be approved, and a series of text-books should be written to carry out its provisions.

What shall be the order of the topics? Every step in mathematics has been taken in response to a need and as a means to an end. The satisfaction

of a need has given rise to other needs, their satisfaction to still other needs, and so on. The adaptation of means to an end is the law of human development. Hence the order of topics may be found by investigating the workings of this law. The first need in connection with number is to find how many individuals there are in a single group. After this need is satisfied, there are only five primary problems, and each may be solved by counting:

I. To find how many individuals there are in two or more groups, from the numbers in the groups.

2. To find how many individuals are left, from the number in the original group and the number taken away.

3. To find how many individuals there are in two or more equal groups, from the number in one group and the number of groups.

4. To find how many equal groups there are, from the number of individuals in all and the number in one group.

5. To find how many individuals there are in one group, from the number in all and the number of equal groups.

Hence the first stage may consist of notation and numeration thru some definite limit, as a hundred, and of the solution of the five primary problems by counting.

As soon as the numbers become large, the need is felt for shorter methods. The need of a method shorter than counting for finding the sum of two or 'more numbers is satisfied by calling from memory the sum of the first two numbers in each order, the sum of the result and a third, and so on. This necessitates memorizing the sums of the first nine numbers taken two and two, and of applying these combinations to increasing numbers of two orders by a number of one order. The need of a method shorter than counting for finding the difference between two numbers is satisfied by calling from memory the differences between the numbers in each order separately. This necessitates memorizing the differences in the combinations of subtraction which grow out of the combinations in addition. Hence the second stage may consist of the addition and subtraction tables, and of their applications to problems involving these operations thru some difinite limit, as a thousand.

The need of a method shorter than counting for multiplication is met by addition, and the need of a method shorter than addition, by calling from memory the products of the numbers in the several orders of the multiplicand by the numbers in the several orders of the multiplier. This necessitates memorizing the products of the first nine numbers taken two and two. The need of a method shorter than counting for the two cases of division is met by subtraction, and the need of a method shorter than subtraction, by calling from memory the quotients of the numbers in the orders of the dividend by a number of one order. This necessitates memorizing the quotients in the combinations of division which grow out of the combinations in multiplication. Hence the third stage may consist of the mutliplication and division tables, and of their applications to problems involving these operations thru some definite limit, as a million.

The fourth stage may consist of the mastery of the fundamental operations upon integers thru some definite limit, as a quadrillion. Integers must precede fractions, decimals must precede percentage, and percentage must precede interest, because each is the basis of its follower. Hence the fifth stage may consist of common fractions; the sixth, of decimals and denominate numbers; the seventh, of percentage and interest; and the eighth, of mensuration and miscellaneous topics. The tendency during the past fifteen years has been to carry the spiral method to the extreme. Eight-book series have been used, and the children have been whirled about in this merry-go-round so rapidly as to make them dizzy. The work has never been well done; the only wonder is that it has been done at all. It is encouraging to note that the pendulum is now swinging toward the topical plan and a two-book series.

The plan of instruction to be followed both by the text-book and by the teacher should be the same, in order that the learner may acquire the power of mastering a subject from the printed page, and in order that he may be able to refer to a topic and to find a method of treatment with which he is familiar. Great care should be exercised in the selection of the text-book in the first place; but after the book has once been selected, the teacher should be required to follow its presentation.

What is the proper method of instruction? This question will be discussed under subject-matter, operations, and problems, because everything in arith- • metic falls under one of these heads, and because each demands a method of treatment different from each of the others.

The subject-matter includes integers, fractions, decimals, per cent. expressions, denominate numbers, lines, surfaces, solids, commission, interest, and other terms found in problems. Since they are mental products, they should not be brought to the attention of the learner, like minerals, plants, and animals, as entities ready formed in nature, but they should first be created in the mind. The steps are: developing, to create the product in the mind; naming, to secure ease in reference; and defining, to give expression to the mental product.

We will present the subject-matter of common fractions:

Developing.-Fold a piece of paper thru its middle line. Into how many equal parts has the paper been divided? One of the folds is what part of the whole? We write one-half by placing the figure 2 under a horizontal line to show that the unit has been divided into two equal parts, and by placing the figure 1 above the line to show that one part is considered. Fold the paper again. Into how many equal parts has the paper been divided now? One of the folds is what part of the whole? Three of the folds are together what part of the whole? How shall we denote the number of equal parts into which the unit has been divided? How shall we denote the number of equal parts that are considered? Write three-fourths.

Naming. The number written under the line is the denominator; the number above the line, the numerator; the whole expression, a fraction.

Defining. What is a fraction? the denominator? the numerator?

Ability to define accurately and concisely should be gained by the study of arithmetic. To emphasize the way of accomplishing this end, we will