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Mathematics Education at West Point: The First Hundred Years
Teaching at the Academy
An 1869 article in The New Englander by Robert Keep describes the teaching at West Point during the nineteenth century so well that we will quote it at length.
These weekly grades were also used to resection the cadets. This idea of grading the cadets every day, is at the core of Thayer’s philosophy. And this method of instruction, which quickly became known as the ‘Thayer method’, was in use in all departments for the entire century. In the technical subjects such as mathematics, science and engineering, cadet boards were graded on a daily basis through the 1980s.
Given a very limited faculty, this class-intensive form of instruction would have taken its toll on the professors. Thayer outlined his solution to this problem in a letter to President James Monroe dated October 10th, 1828.
As Thayer indicates, these assistant professor were recent graduates, and in some instances, cadets from the upper classes who had shown a strength in mathematics. As we will mention latter, some of these cadet instructors went on to other academic posts and helped to spread the USMA curriculum across the country.
In order to facilitate this style of instruction, the classrooms at the Academy were, and are to this day, fairly unique. The 1896 Annual Report of the Superintendent describes them as follows:
This means that there was a blackboard for each student (photo c. 1900) and several at the front for the instructor. Several sources claim that Claudius Crozet introduced the blackboard to West Point in 1817, and that West Point was the first place the blackboard was used in the country. However, as noted earlier, the blackboard was in use at USMA in 1801. Whether this was the first use of the blackboard in the United States is unclear. It was in use in various areas of the country by the second decade of the century: Philadelphia 1809, Boston 1812, Salem 1820, Bowdoin College 1824. By the 1830s they were in common use in most schools.
Blackboards (c. 1900)
Another of Thayer’s additions to the Academy was the institution of bi-annual exams, in the style of the École. Cadets were examined twice each year, in December and June. This took place in front of the Academic Board and, in June, the Board of Visitors also. One section of cadets was examined at a time. In advance, the instructor wrote the main topics of the course on slips of paper and then drew them randomly to decide which question was asked of each cadet. For example, there is an 1877 copy of Davies’s Algebra in the West Point Library that was owned by Cadet Acton. On the endpapers is written
Examined Jany 2nd 1879.Subject – “Logarithms” “Fessed cold”
The cadet slang “fessed cold” means that Cadet Acton failed the exam. This is confirmed by his Cullum listing as x1882, a non-graduating member of the class of 1882. The question asked of him was to explain the topic of logarithms. Curiously, this section of the text is heavily annotated in a way that indicates the writer understood the nuances of the subject. But perhaps this is not Cadet Acton’s handwriting. The failure does not seem uppermost in his mind, for he continues the annotation:
This study was ordained in hell
To torment those who on earth dwell
And it suits its purpose well.
Along with setting firm guidelines for academic instruction, Thayer set to work immediately to bring the curriculum to a higher level. The topics taught during this period were: analytic geometry, plane and spherical trigonometry, mensuration, logarithms, conics, surveying, and fluxions. In particular, the precursor to technical drawing, descriptive geometry became a mainstay of the curriculum for many years. The Committee on Military Affairs of the Academy in 1834 describe descriptive geometry as: “a science peculiarly necessary in civil and military engineering, and which has been nowhere else cultivated with advantage or assiduity, save in France.” The first professor of descriptive geometry was Claudius Crozet.
Keep, R., The System of Instruction at West Point: Can it be Employed in our Colleges, The New Englander, XXVIII (CVI), 1869, pp. 4-18. Available online at Cornell University Library “Making of America” website.
The West Point Thayer Papers 1808-1872, ed. C. Adams, 1965. Available online the USMA Library and at: http://www.dean.usma.edu/math/people/rickey/dms/doc/1828-10-10-Thayer-Monroe.htm
Annual Report of the Superintendent of the United States Military Academy, 1896, p. 75.
Edwin L. Dooley, Jr., Claudius Crozet: Disseminator of French Technical Education to the United States, Proceedings of the Consortium on Revolutionary Europe, 1750-1850, 1986, p. 452.
Anderson, C., Technology in American Education: 1650-1900, 1962.
George Cullum was an 1833 graduate, who among other things compiled a comprehensive list of all cadets, graduates and non-graduates, and information about their time at the Academy and the Army career.
Annual Report of the Superintendent of the United States Military Academy, Washington, 1896, p. 47.