Promiscuous Problems and Vulgar Fractions:
The Early-Nineteenth Century Schoolbook of Sarah DuBois

(New Paltz, NY: The Huguenot Historical Society)
Joan Hollister, Marist College
Sally M. Schultz, SUNY New Paltz

© 2001The Academy of Accounting Historians
The Accounting Historians Notebook
Vol. 24, No. 2, October 2001

Integrating accounting history into the classroom is one way to motivate students in financial accounting courses, to help them gain an appreciation of the evolution of accounting, and to challenge them to conceptualize and think constructively [Bloom and Collins, 1988; Coffman et al., 1993]. This paper presents examples of some familiar and some unfamiliar business and accounting concepts as they were taught in the early-nineteenth century to help accounting students and faculty members to gain further insight into how today's practices evolved.

In early American education, bookkeeping and arithmetic were closely connected [Sampson, 1960, p. 462]. While arithmetic books did not always cover accounting in its present-day sense, various mercantile topics were often included [Sheldahl, 1985, pg. 4, 9]. During this period the lack of a sound monetary system required that accounting accommodate not only a variety of monetary units, but also other items of value that served as a medium of exchange in barter [Previts and Merino 1998, p. 26].

Student workbooks from the early American period examined by the authors typically included the study of basic topics in arithmetic, including vulgar (common or non-decimal) fractions, as well as some basic business and accounting concepts. Such concepts would include calculating simple interest and commissions, computing the total cost for a quantity of goods at a given unit price, and translating foreign and domestic currencies. The schoolbook of Sarah DuBois is of interest because it includes not only the business topics commonly seen in such schoolbooks, but also several more advanced business concepts.

Perhaps Sarah DuBois received more extensive instruction in business topics because she was the daughter of a mercantile family that had operated a general store in New Paltz, New York for several generations. Sarah was descended from Jean Hasbrouck, one of the original twelve French Huguenots who settled in New Paltz, New York. A whole street of stone houses built by the early settlers of New Paltz has been uniquely preserved to the present day. Jean Hasbrouck's stone house, completed around 1712, would become the site of a thriving general store and tavern that his son Jacob opened in one of its front rooms. Sarah DuBois was Jacob Hasbrouck's great-great-granddaughter. Sarah's mother, Elizabeth, who operated the store with her husband Josiah DuBois, was the last Hasbrouck generation to run this store.

The mercantile topics studied by Sarah DuBois are comparable to those covered in a 1788 text by Thomas Sarjeant, The Elementary Principles of Arithmetic, with their application to the Trade and Commerce of the United State of America, In Eight Sections. In addition to basic arithmetic topics, Sarjeant's text covered mercantile arithmetic topics such as exchange of money, weights and measures, simple and compound interest, determination of a time for joint payment of sums due at different dates (equation of payments), discount for early payment, gross gain or loss on an individual sale, and fellowship [Sheldahl, 1985, 9-10]. As the eighteenth century drew to a close, a number of texts also sought to address the nascent Federal monetary system [Sheldahl, 1985, p. 21-24]. The schoolbook of Sarah DuBois illustrates how the concepts contained in texts of the era would be transcribed by a student in the classroom. The schoolbook also shows how these concepts were applied in exercises, and helps to inform us about business instruction in the early part of the nineteenth century.

This schoolbook comprised one half of a cloth bound volume. The other half was completed by another student and included the date 1821. Sarah's side is undated, but it is likely that her work would have been completed within a few years of 1821, since she was born in 1806. The title page of the workbook bears the inscription: "The Elements of Arith'c, Commenced by Sarah DuBois, Gilbert Cuthbert Receptor." Receptor is apparently a variant of preceptor, or teacher. This book is in the archives of the Huguenot Historical Society in New Paltz, New York.*

Among the topics that Sarah DuBois studied were simple interest, compound interest, discount, and equation of payments. Her transcription of each of these concepts appears below, accompanied by one of the many promiscuous (mixed; unordered) but numbered problems solved in the schoolbook to illustrate the concept. Sarah's schoolbook also included supporting calculations, which have been omitted here because of their length. We have endeavored to adhere to the spelling, capitalization, and punctuation of both words and numbers used in the original document. The document's use of the words vulgar and promiscuous, used in a context different than today, highlights shifts in our lexicon over time. In the compound interest problem, note that the final answer has been calculated in dollars, cents, and mills (one tenth of a cent), which is typical of the period.