A History of Trigonometry Education in the United States: 1776-1900

Abstract

A History of Trigonometry Education in the United States: 1776-1900 Jenna Van Sickle This dissertation traces the history of the teaching of elementary trigonometry in United States colleges and universities from 1776 to 1900. This study analyzes textbooks from the eighteenth and nineteenth centuries, reviews in contemporary periodicals, course catalogs, and secondary sources. Elementary trigonometry was a topic of study in colleges throughout this time period, but the way in which trigonometry was taught and defined changed drastically, as did the scope and focus of the subject. Because of advances in analytic trigonometry by Leonhard Euler and others in the seventeenth and eighteenth centuries, the trigonometric functions came to be defined as ratios, rather than as line segments. This change came to elementary trigonometry textbooks beginning in antebellum America and the ratios came to define trigonometric functions in elementary trigonometry textbooks by the end of the nineteenth century. During this time period, elementary trigonometry textbooks grew to have a much more comprehensive treatment of the subject and considered trigonometric functions in many different ways. In the late eighteenth century, trigonometry was taught as a topic in a larger mathematics course and was used only to solve triangles for applications in surveying and navigation. Textbooks contained few pedagogical tools and only the most basic of trigonometric formulas. By the end of the nineteenth century, trigonometry was taught as its own course that covered the topic extensively with many applications to real life. Textbooks were full of pedagogical tools. The path that the teaching of trigonometry took through the late eighteenth and nineteenth centuries did not always move in a linear fashion. Sometimes trigonometry education stayed the same for a long time and then was suddenly changed, but other times changes happened more gradually. There were many international influences, and there were many influential Americans and influential American institutions that changed the course of trigonometry instruction in this country. This dissertation follows the path of those changes from 1776 to 1900. After 1900, trigonometry instruction became a topic of secondary education rather than higher education.