The public school arithmetic for grammar grades, based on McLellan and Dewey's "Psychology of number "—By J. A. MCLELLAN, A. M., LL. D., and A. F. AMES, A. B. New York: The Macmillan Company, 1902.

For the last fifteen years all sorts of books and manuals, as well as innumerable articles from newspapers, school-journals, and magazines have been written for the avowed purpose of improving arithmetical teaching in the schools of the United States. With such a profusion of literature emanating from diverse sources, it is not strange that conflicting opinions have been advanced and pushed with enthusiasm. So far, however, as the writer is aware, the Psychology of number never assumed gigantic proportions among educators till within the last few years. While it is true that Americans started in immediately after the close of the American Revolution to make arithmetics, and they have gone on with accelerated velocity ever since, yet they did not bother themselves much about the underlying philosophy of the science, but they kept the pupils working at arithmetical principles and problems till light, either obscure or clear, dawned in their minds.

It was assumed by our early schoolmasters and the people generally that the boy who could not learn arithmetic did not have sense enough to know his own father, and that such a one, in legal parlance, was properly called a "fool." However, the discovery was made and then announced that the time given to the subject of arithmetic did not produce expert arithmeticians. This statement is a sort of psychological joke, because the most expert arithmeticians in the world are Americans, and the most difficult arithmetics ever published, or ever ciphered thru, have been used and are still used as text-books by many Americans boys and girls. Literally, we take to figures.

The book before me is planned along the lines indicated in the Psychology of number, and the keynote of the text is based upon these two negatives: "No number without measurement, no measurement without number." This statement is immediately followed by the two sentences: "This implies three factors in the number process-a whole to be measured, a unit of measure, and how many of the unit in the whole. The idea is nothing but an application to quantity of the fundamental

principle common to all thinking." It might be pertinent to ask what the first negatives mean, and also a query may arise in the minds of some whether quantitative thinking is the only kind of thinking there is. The measuring unit, I am inclined to think, has not been found for all kinds of qualitative thinking, not to speak of counting sheep, cattle, ears of corn, and so on.

Putting aside the preface of this arithmetic, it does not appear that the book, as a work on arithmetic, is better than the average arithmetics that have been issued during the last ten years. The borrowed thought from Kant, tho put in another set of words, is his old unity, plurality, and totality business, dressed up for supplementary purposes.

The contrast between the authors' conception and that of a plain arithmetician will be apparent by observing the following definition; the first definition in each case being the one given by the authors, and the second, the common definition usually given for children to learn in the upper grammar grades: 1. (a) A unit is a quantity used to measure a quantity of the same kind. (b) A unit is one thing, or one. 2. (a) Addition may, therefore, be considered as the operation of finding the quantity, which, as a whole, is made up of two or more given quantities as its parts. (b) Addition is the process of uniting two or more like numbers into one equivalent number. 3. (a) Subtraction may, therefore, be defined as the operation of finding the part of a given quantity that remains when a given part has been taken from the quantity. (b) Subtraction is the process of finding the difference between two numbers of the same. kind. 4. (a) Multiplication is the operation of finding the number of primary units in a quantity expressed by a given number of derived units, or more briefly, Multiplication is the operation of finding the product of two numbers. (b) Multiplication is taking one number as many times as there are units in another. Whether the pupil can understand the new definitions better than the old ones need not be discussed in this connection. They speak for themselves and forcefully enough. It should be remarked that the definitions in the last half of the book are not so stilted as those in the beginning.

The problems cover rather an extensive range of topics, and

about one-half fit into the mental scheme outlined by the authors. Taken as a collection thruout, they are on a level with those in Moore's Grammar school arithmetic-no better, perhaps no worse. A large number of the exercise problems. may be classed as "straight arithmetic."

The book as a whole is scrappy, introducing a little of a subject here, using perhaps a term or two, and further on, it may be, the subject is taken up with some additional explanations. As compared with Kirk and Sabin's Oral arithmetic, in which one number is compared with another, the book is of a much weaker order. The idea of making arithmetic an information study, as outlined by Pliny E. Chase and Horace Mann some fifty years ago, has not been so well done in the present instance as by the original workers. Yet the book contains some strong chapters, especially the "Miscellaneous exercises" and the "Appendix." The chapter on mensuration is also good, but there is no valid reason why it should not have been introduced earlier. Why square root should have been placed near the beginning of the book, and the chief exercises 190 pages further on, even tho the footnote speaks of an alternative, is one of the peculiarities of the arrangement. The book would be just as strong with a less pretentious title, and the straining for effect would have been avoided. The title, no doubt, caused the book to be published-certainly not its contents, definitions, illustrations, principles, or arrangement of subject-matter. It is a good book for a teacher to have on his desk as an excellent illustration of how the human mind, under certain restrictions, works when trying to make a very simple subject very psychological. It is not constructed out of that kind of philosophy that teaches one how to live, or how to die, "like a gentleman."

SUPERINTENDENT OF SCHOOLS,

KANSAS CITY, Mo.

J. M. GREENWOOD

Judicial Control of Colleges

VIII

NOTES AND NEWS

During the discussion of President Draper's paper, printed in this issue of the REVIEW, the fact was brought out that the Supreme Court of Ohio had recently voided the charter of a college for misuse of its corporate powers. We take pleasure in reproducing the essential part of the court's decision as a contribution to the history of American education of unusual significance and hopefulness. If this precedent is followed, the day of the fiat college is nearly over:

THE STATE OF OHIO ex rel. THE ATTORNEY GENERAL VS. THE MT. HOPE COLLEGE COMPANY

Trustees of educational institution—Sign diplomas in blank-Officer sells them and confers degrees-Dissolution of corporation required.

When the trustees of an educational institution, incorporated under the laws of this State, sign diplomas in blank and leave them within the control of one of its officers who sells them, and thus confers degrees without regard to merit, there is such a misuse of the power conferred as requires the dissolution of the corporation.

(Decided November 13, 1900.)

IN QUO WARRANTO:

The attorney general filed a petition to oust the defendant of its franchise upon the ground now insisted upon that such franchise has been abused and misused. The grounds specified in the petition are sufficiently. indicated in the following abstract of the report of Robert H. Day, Esq., to whom the cause was referred, after issue joined for the purpose of taking and reporting the testimony with his findings of fact and conclusion of law: That report condensed shows that the defendant was incorporated as a corporation for profit on the 23d day of January, 1893, for the general purposes, as alleged in its certificate of incorporation, of promoting education, religion, morality, et cetera. Shortly after its incorporation it proceeded to conduct a college called Mt. Hope College, at Rogers, in Columbiana County, employing for that purpose teachers, and receiving and graduating students; that on or about the 11th day of December, 1897, it entered into a contract with one A. A. Galbreath by which it leased the college to him for a term of five years for an annual rental of one hundred and eighty dollars, the property to be used for school purposes, to be con

ducted under the management of said Galbreath as president, he to receive all incomes from tuitions and diplomas and to pay all expenses of the operation of the college. Under said contract said Galbreath conducted the institution up to the filing of this suit, maintaining a number of departments at least in name, that it included a "Home Study Department" which was conducted as follows: Pupils who could not arrange to pursue their studies as residents of Rogers were invited to matriculate in the institution and send by letter to the principal a statement of what studies they had pursued and what degree they desired; in reply to which the student was given a grade and informed as to the amount of work necessary to secure his degree, together with the necessary fees which should be paid before the diploma was granted and the degree conferred. The post-graduate course was conducted largely in the same way; a list of studies was submitted to the applicant and he notified the principal of those which he had pursued, what grades, if any, he had from another school or college, upon consideration of which the defendant would confer upon him such degree as the applicant desired, upon the payment of fees and the performance of certain conditions. If the applicant had attended a school whose standard warranted it, a degree would be conferred without further requirement by the defendant except the occasional writing of a thesis or digesting of a book. No records were kept of the operation of the college since April, 1898, by the trustees or the faculty, of the students attending the college, nor of their classification, standing, or work in said college, nor of the degrees conferred, except as the same were kept in a private ledger in the control of said Galbreath. Prior to that date occasional records had been kept. The board of trustees did not authorize nor organize the so-called Home Study Department" established by Galbreath, but did sign diplomas with full knowledge that they were to be used in such department. They knew of its existence from the catalog and from a publication called The Mt. Hope Anchor. The records of the board of trustees do not show that any curriculum was ever adopted. Students were admitted to all departments of the college as applicants for degrees upon their own statement as to the studies which they had pursued, and sometimes upon the grades received from other schools, but nowhere does it appear that any entrance examination was ever required. The diplomas were granted and degrees conferred in the "Home Study Department" upon examination of the applicant by examiners appointed at or near the home of the applicant. In the postgraduate course degrees were conferred without examination, but upon the preparation of a digest of some book or the writing of a thesis, and in some instances in both departments the applicant received his degree upon the payment of fees and a promise to do work in the future. Such diplomas were signed and degrees conferred by the board of trustees upon the verbal request of Galbreath, and sometimes such diplomas were signed in blank to be afterwards filled out. No grade or statement of the standing of the applicant or his accomplishments was submitted to the trustees, nor was there any vote or record of any faculty proceedings communicated to the board. That one Chester Ralston, who had secured from Oberlin College the degree of M. A., asked the requirements of