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REPORT OF SUBCOMMITTEE 2
MATHEMATICS IN SCHOOLS FOR THE TRAINING OF NAVAL OFFICERS, INCLUDING SCHOOLS FOR GRADUATES OF ANNAPOLIS
The United States Naval Academy, at Annapolis, Md., is under the supervision of the United States Navy Department and has for its purpose the training of officers of the Navy. The students of the Naval Academy are called "midshipmen." According to the present law two midshipmen are allowed for each Senator, Representative, and Delegate in Congress, and two for the District of Columbia; in addition to these, the President appoints five each year from the United States at large.
Candidates are required to pass mental and physical examinations to qualify for entrance. The first mental examination is held on the third Tuesday in April and is conducted by the Civil Service Commission at certain authorized places in each State; the second examination is held only at Annapolis, Md., and is under the direction of the Superintendent of the Naval Academy. Mental examinations are given in the following subjects, and applicants may be rejected if found deficient in any one of them: Punctuation, spelling, English, grammar, geography, general history, United States history, arithmetic, algebra through quadratic equations, and plane geometry.
Candidates passing the mental examinations are examined physically at the Naval Academy by a board composed of three medical officers of the Navy. A candidate must be of good moral character, physically sound, well formed, and of robust constitution; any one of 20 stated physical defects is sufficient to cause his rejection. He must be between 16 and 20 years of age. Candidates passing both the mental and the physical examination are admitted as students to the academy. On admission, each midshipman must sign articles binding him to service in the United States Navy for eight years, unless sooner discharged.
1 Beginning with the year 1912, both examinations will be conducted by the Civil Service Commission.
COURSE OF INSTRUCTION
The instruction given in the academy extends over a period of four years and includes work in mathematics, mechanics, descriptive geometry, drawing, physics, chemistry, engineering, navigation, ordnance and gunnery, history, English, and modern foreign languages. The following outline indicates only the ground covered in theoretical and applied mathematics during the course:
Algebra and geometry
Mechanical drawing and descriptive geometry-
Analytic geometry and the calculus_
First term, theoretical mechanics_
Astronomy and navigation____
First term, theory and practice of navigation__.
Theory of compass deviations, surveying, and practical navigation____ Engineering mechanics
Integral calculus, spherical trigonometry, and stereographic projection_ 5
DISTRIBUTION OF TIME
The academic year begins October 1 and closes the first week in June. The members of the three undergraduate classes are sent on a cruise each summer for a period of three months. On these cruises the midshipmen are required to perform all the general duties of a navigator, with particular reference to the adjustment and use of the navigational instruments on board, to practical pilotage, and to the determination of the ship's position by observation.
During the academic year each class in mathematics requires a period of two hours for recitation; classes recite in sections of 12 students each.
Midshipmen complete the courses in pure mathematics during the first two years in the academy and the courses in applied mathematics in various other departments during the last two years.
PURPOSE OF TEACHING MATHEMATICS
In the teaching of mathematics at the Naval Academy, as in any technical school, the aim is purely practical, the course consisting essentially of the solution of problems which a midshipman must understand in order to become a naval officer.
All of the textbooks used in the department of mathematics have been written expressly for the midshipmen by men in the department. No more theory is presented in these books than is absolutely necessary. The recitation work, which is strictly competitive, consists of solving numerous problems on the blackboard; and perhaps 90 per cent of all monthly, semiannual, and annual examinations are composed of practical problems.
Instruction in the Naval Academy is carried on through the following departments: Mathematics and mechanics, navigation, seamanship, physics and chemistry, marine engineering and naval construction, electricity, English and modern languages. Each department is supervised by a naval officer. Teaching is done in some departments by naval officers detailed for such duty and in others by both naval officers and civilian instructors. In the department of mathematics there are 13 instructors, of whom 7 are naval officers, and 6 civilian instructors, having been appointed from civil life.
METHODS, REVIEWS, AND EXAMINATIONS
Accurate marking of work done by the midshipmen during their four years' course at the academy is of the utmost importance, for their marks or credits determine the order of their promotion after graduation; consequently all of their work is strictly competitive, and all possible care is taken, therefore, in assigning lessons, in organizing new sections with different instructors each month, and in marking daily recitations and examination papers, so that any advantage or disadvantage in the methods of instruction may be equally shared by all.
The lessons for each day of the month are assigned by the head of the department at the beginning of the month; these assignments are noted by the instructors and given to the midshipmen at each recitation, so that all midshipmen in the same class study and recite precisely the same work at the same time.
A further effort to give all of the midshipmen an equal opportunity in the recitation room is made by a new arrangement of sections and instructors each month. The 12 midshipmen receiving the highest marks in the monthly examination constitute the first section for the following month; the 12 receiving the next highest,
the second section, and so on.
The instructors are assigned different sections from month to month, so that all midshipmen are placed on an equal footing so far as advantages or disadvantages of different sections and different instructors are concerned.
Midshipmen are marked on a basis of 2.5 for passing, or satisfactory, and 4 for perfect. They receive daily marks for their work in the recitation, and the average of the daily marks is taken as the weekly mark; the average of four weekly marks is taken as the monthly recitation mark. An examination is given at the close of each month and the examination mark is combined with the monthly recitation mark, the former counting one-third. For the information of the midshipmen, a sheet is posted giving the final monthly mark and class number or standing of each member of the class. This plan is followed each month during the year except the months of January and May, when the monthly examinations are omitted, because these months immediately precede the semiannual and final examinations. The semiannual examination mark is combined with the average of the monthly marks from October to January, inclusive, to determine the final mark for the first half year; the semiannual examination mark counting one-fourth. Similarly for the second half year the final mark is combined with the average of the monthly marks for the final mark of the second half year, the final mark counting one-fourth. Semiannual and annual sheets similar to the monthly sheets are posted, giving the mark and rank of each member of the class. The monthly examinations are two hours in length, while the semiannual and final examinations are each five hours. All examination papers must be marked independently by two instructors, the mean of the two markings being taken as the mark for the examination. In case there is a considerable difference between the two markings, the paper is re-marked by the head of the department, and the different marks are then properly adjusted. Instead of regular recitations on Saturday morning, the classes of the first and the fourth years have written recitations of two hours each. The mark received on this paper is counted as the recitation mark for that day. Such recitations are not so frequent in the other two classes.
When a midshipman is badly deficient in one study and fails to make a satisfactory mark (2.5) in any other subject for either the first or second half year, he is dropped from the academy; the vacancy of course is not filled until the following year.
The final term average of every midshipman in each branch of study is multiplied by the coefficient assigned that branch for the term, and the sum of the products is the aggregate mark for the
1 In the upper classes there are usually not more than 8 or 10 midshipmen in each section.
year. Coefficients are assigned to the different branches according to the time devoted to these branches. For mathematics these coefficients are as follows: Algebra and geometry, 3; trigonometry, 3; calculus, 5; applied calculus and stereographic projection, 6; and mechanics, 11.
The merit roll of the graduating class is prepared at the completion of the four years' course; the names of the graduates are arranged in the order of merit according to the graduating mark, which is the arithmetical sum of the final marks of the four years of the course.
After graduation midshipmen are sent to sea for two years, after which they are given the final graduating examination, and if found satisfactory are eligible for promotion to the commissioned rank of ensign.
THE NATURE OF THE COURSES IN MATHEMATICS
The Naval Academy is a strictly technical school, and the courses in mathematics are essentially practical problem courses. More condensed courses in mathematics have been necessitated at the academy during the last two years by the increased time devoted to the professional subjects of marine and electrical engineering. All subjects ordinarily treated in mathematical courses, but which are not adapted to the needs of a naval officer, are omitted, while certain other important features are given greater emphasis.
In the algebra, particular emphasis is placed upon the following: Computation by logarithms, the graph of the general polynomial and its use, the tracing of curves of the first and second degree, the theory of equations, identities, undetermined coefficients, and series. The subject of choice and chance is merely touched upon, while the subjects of harmonic progression, interest and annuities, continued fractions, theory of numbers, and determinants are omitted. Special free-hand methods are used for tracing curves of the second degree by means of limiting tangents, diameters, and asymptotes.
The work in trigonometry emphasizes particularly accurate logarithmic work in the solution of plane and spherical triangles—the oblique spherical triangles being solved by means of a perpendicular and Napier's rules. The text includes a course in stereographic projections covering as a special feature the projection and solution of the astronomical triangle.
Except for its subsequent use in the calculus, analytic geometry occupies a very small place in the academy compared with that usually assigned it in colleges and universities. The tracing of curves of the third or higher degrees by use of the analytical triangle. may be mentioned as a special feature.