in 1824. The precedent set by Boston was followed by New York, when a high school for boys was established in 1825, and a similar school for girls in the following year; both of which, however, suspended operations in 1831.

The growth of the High School was very slow until 1860, when United States Commissioner Harris estimated that there were about forty in the country. Since that time the growth has been almost phenomenal. In 1870 there were 160 high schools; in 1880, 800; in 1890, 2536; in 1900, 6005; in 1911, 10,234.

It is to be remembered that when the high school was started there was no relation between it and the college. The original aim of the high school was that it should serve only those who did not want to go to college. Naturally, such a standard was thought to be too narrow as time went on. The feeling that a course should be introduced into the high school which would prepare for college became stronger and stronger. The colleges were not slow to realize that the high schools might become larger contributors to their respective student bodies, so they brought a powerful influence to bear upon the introduction of college preparatory courses. The argument was that what was a good preparation for college was a good preparation for life. This influence became so great that, for a long time, the colleges practically dominated the high schools and arbitrarily dictated entrance requirements, which the high schools had to meet.

The natural result of such an extreme position is that the pendulum has started to swing back, so that the argument of the colleges has been reversed, and the high schools contend that what is a good preparation for life is a good preparation for college.

As an outcome of this attitude on the part of the colleges, the high schools have demanded that certain changes be made in the college entrance requirements. At this point two questions present themselves:

1. What are the elements which have caused this revolt on the part of the high school?

2. What is the function of the college, or rather, what are the functions of college entrance requirements? Are they to determine the student's knowledge of certain branches, or are they an attempt to determine his fitness to do college work?

In relation to the first question, it is a well known fact that within the last forty or fifty years the entrance requirements in almost all of our colleges have been doubled. A brief review of the mathematical requirements will show this very clearly. In 1802, a knowledge of mathematics was, for the first time, required for entrance to Harvard. Even then the candidate was only required to cover Arithmetic up to the "Rule of Three." After 1816, the whole of Arithmetic was required for admission. In 1819 a trifling amount of Algebra was added. The catalogue of 1825 specifies the requirements as follows: Fundamental rules of Arithmetic; vulgar and decimal fractions; proportion, simple and compound; single and double fellowship; allegation, medial and alternate; and Algebra; to the end of simple equations, comprehending, also, the doctrine of roots and powers, and arithmetical and geometrical progression. In 1841, Euler's Algebra or the "First Lessons in Algebra" was required. No other changes were made until 1843. The catalogue for that year mentions for admission, Davies' "First Lessons in Algebra❞ to extraction of square root and an introduction to Geometry, from the most approved Prussian text books, to VII of proportion.42

As taken from the university catalogue, the minimum requirements in mathematics for admission in 1888-1889, were as follows: Algebra, through quadratic equations, and Plane Geometry. The requirements at the present time are essentially the same. But Harvard is more liberal in these requirements than most of the colleges and universities. The majority require Algebra, through progressions, Plane and Solid Geometry. The technical schools require even more advanced Algebra and Plane and Spherical Trigonometry in addition. In a little over a hundred years, the requirements have advanced from absolutely nothing to the list just given. The increase in the requirements in many of the other subjects have been proportionate.

In the second place, the high school is a tax-supported institution. Since there is less than one in six of those who go to the high schools that go to college, the community has a right to

42 Cajori, "The Teaching and History of Mathematics," p. 131.

demand and the high school teachers appreciate the justice of the demand, that the courses of study should be so constructed as to be of the greatest benefit to the individual when he takes his place in the community.

Many colleges refuse to give credit for such courses. They suggest that if the high school feels obliged to meet the above condition it should establish a college preparatory course and a course which shall prepare for life. Such a policy is impracticable in the small communities, because of the greater expense that would be incurred. The high schools have endeavored to adapt themselves to new conditions which have arisen, whereas many colleges and universities have maintained their time-honored customs, have made no attempt to meet new conditions, and will give no credit for new subjects which have been introduced into the high school courses.

The second question presents greater difficulties. It ought to be fair to assume that one of the functions of a college is to permit a pupil to show that he can do college work, irrespective of how much knowledge he has in different subjects. Of course, certain college courses require a definite amount of preliminary work which is continued in college. For instance, it is not to be expected that a boy who has pursued a non-classical course should be admitted to the classical course in college. This work should be considered as essential under the favorable conditions, recommendations, etc., necessary before he is considered eligible to entrance in college. But I wish to emphasize the fact that when a student has completed his high school course satisfactorily there should be a course in the college or university ready to receive him.

The University of Illinois, a short time ago, sent the following statement to every high school principal in the State: "The chief purpose of your high school is to prepare the boy for the business of making a living, and the university believes, on the whole, that it will require as good a training to make him a success in life as it will to make him a success in the university. We propose, therefore, to leave you free to determine the needs of your community and to prepare your boys and girls for success in that community. We shall then admit them to such courses in

the university as will best supplement the education you have given them and best fit them for larger spheres of influence and of service." The stand taken by the University of Illinois is in accord with the recommendations of the Committee of Ten, which was appointed to investigate the articulation of the High School and College. In its report for 1893, we find the following: "There is a general principle concerning the relation of the secondary schools to colleges, which the Committee of Ten, inspired and guided by the conferences, find it their duty to set forth with all possible distinctness.

"The secondary schools of the United States, taken as a whole do not exist for the purpose of preparing boys and girls for colleges. Only an insignificant percentage of the graduates of those schools go to colleges or scientific schools. A secondary school program intended for national use must therefore be made for those children whose education is not to be pursued beyond the high school. The preparation of a few pupils for college or scientific school should in the ordinary secondary school be the incidental and not the principal object. At the same time it is obviously desirable that the colleges and scientific schools should be accessible to all boys and girls who have completed creditably the secondary school course-in order that any successful graduate of a good secondary school should be free to present himself at the gates of the college or scientific school of his choice, it is necessary that the colleges and scientific schools of the country should accept, for admission to appropriate courses of their instruction, the attainments of any youth who has passed creditably through a good secondary school course, no matter to what group of subjects he may have mainly devoted himself in the secondary school. As secondary school courses are now too often arranged, this is not a reasonable request to prefer to the colleges and scientific schools; because the pupil may now go through a secondary school course of a very feeble and scrappy nature, studying a little of many subjects, and not much of any one, getting perhaps a little information in a variety of fields, but nothing which can be called a thorough training."'43

43 J. F. Brown, "The American High School," p. 58.

Unquestionably, there is a great deal of truth in the final sentence of this general principle. In order that the demands of the high schools may have a hearing and be approved it is the duty of every high school principal to see to it that his course is such a one as may be included under the heading of a good secondary school course.

In some districts, notably the South, the high schools are not alone to blame. We find colleges catering to pupils who have not finished their high school course. As an illustration, I quote a statement from a recent report of Prof. William H. Hand, inspector of high schools of South Carolina. He states: "Reports show that the colleges of this and nearby states have in their college classes, from the schools of this state, nearly 200 pupils from the ninth grades and more than forty pupils from the eighth grades. One half the colleges of this state have now last year's tenth grade pupils in their sophomore classes." Under such circumstances it is not a surprise that the high schools in those districts were for a long time in a state of lethargy.

The demands of the high school may be briefly summed up as follows:

1. That the number and amount of required subjects be cut down.

2. That colleges admit by certificate.

3. That credit be given for standard subjects taught in high schools.

I. Many colleges and universities have recognized the reasonableness of the first demand and have diminished the number of required subjects. On the other hand, however, the number of specified subjects is so numerous and the fixed requirements so great in many instances that the high school principal is severely handicapped in the preparation of his course of study.

Some idea of the diversity of practice in the number of specified units for admittance to college may be had from a review of the statistics collected by the "Carnegie Foundation for the Advancement of Teaching." In 1909, there were 64 institutions on the accepted list of the Foundation, each of which required at least 14 units for admission.

The number of specified units required range all the way from none at Clark University to 14.5 at the New York University.