... in the Years following the War for Independence. Joel Silverberg. Dept of Mathematics. Roger Williams University. Bristol, Rhode Island. USA. June 2, 2003 ...
Higher Mathematics Education In the United States: The Role of the Academy in the Years following the War for Independence Joel Silverberg Dept of Mathematics Roger Williams University Bristol, Rhode Island USA June 2, 2003
Delivered to the Annual Meeting of the Canadian Society for the History and Philosophy of Mathematics held at Dalhousie University, Halifax, Nova Scotia, Canada
Introduction An examination of nearly one hundred “cyphering books” created by New England students during the 18th and early 19th centuries and other manuscripts giving evidence of their mathematical studies, together with representative textbooks published in America for the teaching of mathematics during that period, reveals a lively and widespread interest in higher education of a practical nature, including mathematical studies of quite a different type than those undertaken within the collegiate environment. Though students often engaged in these advanced studies privately with individual tutors or at ephemeral private–venture schools, these manuscripts and textbooks bear witness to the widespread influence of an institution of higher learning which has all but disappeared from the educational landscape : the Academy. First introduced to this country through the efforts of Benjamin Franklin (Penn., 1753), Lt. Governor William Dummer (Mass., 1782), and the Phillips brothers (Mass., 1778,1781), these institutions approached their calling with impressive creativity and energy. Their goal was “to induce habits of thorough and patient study, to expand and discipline the intellectual and moral powers,” to provide useful and practical knowledge, “but more especially to learn them the great end and real business of living.” [21, 22] By 1850 ten times as many students were enrolled in academies as were enrolled in colleges and universities[2]; and yet their very existence is largely forgotten, and they are scarcely mentioned in the histories of education that have been written since the rise of the public high school in the decades following the Civil War. [22] In this paper we will outline the nature of the mathematics taught by private tutors and Academies. However, we will focus, not so much on the mathematical content of these studies, but on the social and cultural conditions that gave rise to the Academy and its sister institutions which were the dominant cultural and educational forces in United States from the time of the Revolution until the decades following the American Civil War.
William Cranston of Warren, Rhode Island My interest in these materials begin with my chance discovery and purchase of a late 18th century cyphering book at an antique show five or six years ago. The volume contained over 350 pages of detailed explanations and calculations recording the mathematical studies of one William Cranston of Warren, Rhode Island. The young man frequently signed and dated the pages of his workbook and these notations show the studies to have been for the most part undertaken and completed in 1797, with minor and sporadic additions in the years up to
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1801. The material included matches neither the curricula of the colleges of his era [16, 7], nor the curricula of the common or district schools 1 . The first page of the cyphering book detailed the workings of “the rule of three,” a topic sometimes covered at the end of one’s elementary education. From there it proceeded to explore the intricacies of the mathematics of trade and commerce. The mathematical techniques employed were as surprising as the subjects studied. The document is remarkable for its total lack of algebra or algebraic thinking. Relatively sophisticated topics, which we would today approach algebraically were studied using clever manipulations of rules of proportion, including many variants on the rule of three.
Figure 1: William Cranston, His Cyphering Book, 1797 1 The majority of district school students, including practically all girls, cyphered only through addition, multiplication, subtraction, and division, with a short excursion into vulgar fractions. It was a mark of distinction to have penetrated the mysteries of the Rule of Three, and to cypher through “Old Pike” was to be accounted a prodigy. [12]
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Mathematical Content The contents of the cyphering book are summarized below.
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• Rule of Three Direct, Rule of Three Inverse, Compound. Proportion • Single Fellowship and Double Fellowship • Practice • Simple and Compound Interest • Barter, Discount, Loss and Gain • Tare and Trett • Insurance • Equation of Payments • Commission and Brokerage • Buying and Selling Stocks • Alligation Medial and Alligation Alternate • Involution and Evolution: Extraction of Square Roots and Cube Roots • Strength of Anchor Cables • Single Position and Double Position • Reduction Ascending and Reduction Descending • Arithmetic of Federal Money • Conversion between various currencies and units of measure Some of these topics are familiar, others unfamiliar. Together they form a comprehensive and fairly sophisticated compendium of everything an eighteenth century gentleman or lady might need to know about financial calculations. The techniques are made considerably more difficult than they would be today by the arcane systems in use for both currency and measurement. The cyphering book displays a strong preference for the use of denominations rather than fractions, proportions rather than algebra, and separate tallies rather than signed arithmetic. Despite the apparent mathematical naivet´e, many of the problems approached are not easy and would challenge many a college student today. 2 Similar manuscript cyphering books include additional topics such as rebate, arithmetic and geometric progressions, permutations and combinations, compound arithmetic, vulgar fractions, gauging of casks, and duodecimals.
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The Search for Context I had long been interested in the history of the New England colonies, especially their political and architectural history. But I had never explored the history of mathematics or mathematics teaching during that period. How typical or atypical were the studies revealed in Mr. Cranston’s manuscript? Where might such material have been studied? At what age? For what purpose? By what kinds of people? My initial goals were to identify the sources from which Mr. Cranston was taught and to seek out similar manuscripts and identify such patterns as might arise.
Who was William Cranston? After some genealogical research and a visit to the Warren town archives, I was able to identify William Cranston, along with his parents, wife, and children. I was unable to determine his occupation or where he undertook his schooling. William was born in 1783 in the year following his father’s return from service in the local militia and the Continental Army. William married, lost several children in infancy, and had a son born the year before his death in 1812. His sole surviving child went on to have 12 children. At the time he wrote this manuscript Master Cranston was the 14 year old son of a prominent, but not wealthy man from a small seaport town — a typical child of a middle class family of his time.
What was he studying? In the 18th century it was most likely that only the teacher had a printed text. In fact, these cyphering books are created in large part by copying out specified sections of the teacher’s textbook into one’s own copy-book. By comparing the manuscript with various texts available to American scholars at that time and matching up exact language and assigned exercises, I was able to determine that he was taught from the newly authored textbooks by Nicolas Pike and by Nathan Daboll – two of the most important arithmetic texts written in America following the revolution. [20, 10] The importance and influence of Nicolas Pike’s Arithmetic can not be overstated. Prior to its publication in 1788 there had been only two texts published in America, both around 1730 [13, 26]. Neither text (one in English and one in Dutch) received much notice or circulation. In the following sixty years there were no such texts authored in America, although several popular English texts were reprinted in Philadelphia and New York. 3 At the time of its publication, Pike’s work was believed (incorrectly) to be the first arithemetic written and published in America. Pike’s encyclopedic work, running 512 pages, was endorsed by George Washington as a great contribution of American science and ingenuity, and the promotion of this work was 3 American editions of English arithmetics included works by John Hodder [1719], Thomas Dilworth [1781] John Bonnycastle [1786], John Gough [1788], and Daniel Fenning [1795]. Dates given are the dates of the American reprinting
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couched in unabashedly patriotic terms. An abridged version of 371 pages was published in 1793 and Pike served as the model of many texts to follow and was in popular use until the middle of the 19th century. A signed copy exists from which Abraham Lincoln taught himself mathematics. The preface to the 1793 abridgment refers to the original, larger work as “that celebrated work, which is now used as a classical book in all the New England Universities.” That Pike’s book was known and available in Rhode Island is attested to by the fact that Benjamin West, who ran his own private–venture school in navigation in Newport and was from time to time a Professor of Mathematics at the College of Rhode Island (now Brown University) in Providence was one of the luminaries quoted in the first edition as praising its value 4 – along with Governor James Bowdoin of Massachusetts and the Presidents of Dartmouth, Harvard, and Yale. The second half of William Cranston’s course of study was clearly taught from Nathan Daboll’s 5 Schoolmaster’s Assistant, first published in New London in 1800, despite the fact that the student notes were written in 1797 — three years before the publication of the text. Another Rhode Island [Brown University] connection may supply the explanation. The Recommendations printed in the first edition include one by Asa Messer, Professor of the Learned Languages and teacher of Mathematics at the College of Rhode Island. Professor Messer shortly afterwards was appointed President of the University. Other recommendations were written by Professor Josiah Meigs at Yale, the famous Noah Webster, and teachers at Phillips Academy, Plainfield Academy, and Billerica Academy. Thus Professor Messer, soon to become President Messer at the University in Providence had access to a manuscript copy of Daboll’s work several years before its publication. To circulate a manuscript some years before publication to garner endorsements and recommendations was a common practice – one followed as well by Nicolas Pike. It is entirely within the realm of possibility that William Cranston was taught or tutored by Asa Messer or one of his students in order to supplement his income from the college. [23, 2]
How common were such studies? In order to understand the purpose and nature of Cranston’s studies in mercantile mathematics and how they fit into the larger picture, it was necessary to locate more cyphering books to determine whether his studies were typical or unusual. 4 “ . . . This volume contains, beside what is useful and necessary in the common affairs of life, a great fund for amusement and entertainment. The Mechanick will find in it much more than he may have occasion for; the Lawyer, Merchant and Mathematician, will find an ample field for the exercise of their genius; and I am well assured it may be read to great advantage by students of every class, from the lowest school to the University. More than this can not be said by me, and to have said less, would be keeping back a tribute justly due to the merit of this work.” [20, Recommendation by Benjamin West] 5 Nathan Daboll was a teacher of navigation and a writer and publisher of nautical almanacs in New London, Connecticut
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The Search for Cyphering Books The search for further examples of cyphering books started in the research libraries, special collections, and archives of the New England colleges of colonial times: Harvard, Yale, Brown, and Dartmouth. Although these libraries contained a small number of mathematical manuscripts, a far richer source were local and state historical societies and the research librarians of historical museums such as Old Sturbridge Village and Mystic Seaport. The cyphering books were frequently saved by their authors either as a ready reference for practical calculations or as a sentimental memento of their years of study. These were sometimes inherited by decendants and eventually donated to libraries, historical societies, genealogical societies, and similar institutions as part of the “family papers.” Whether or not such items ever surface again for study depends in large part on how these family papers are cataloged. Most often these mathematical manuscripts are either uncataloged (miscellaneous family papers) or are classified in a general “arithmetic mss” category together with business ledgers, day books, miscellaneous receipts and bills, etc. I was fortunate to find one source that appears to have been sorting through family papers donated to them with a separate category for such materials for well over a century. Thus, although most libraries I visited turned up two or three such manuscripts, and occasionally eight or ten, in the manuscript division of the Rhode Island Historical Society I was able to identify and study approximately seventy-five such manuscripts, dating from 1720 to about 1830. It is the study of this body of manuscripts from Rhode Island families that forms the basis for this analysis.
The Context Discovered An overview of the manuscripts in the Rhode Island Historical Society [RIHS] revealed a number of patterns, some expected and others surprising. The manuscripts dated from 1720 to about 1840 with the largest part of these dating between 1780 and 1825. Despite the existence of Brown University within the state from 1764 onward, only one of these manuscripts contains any evidence of collegiate studies. The percentage of manuscripts containing evidence of elementary studies is likewise very small (less than 10 %). Another 10 %, nearly all of which date from the 1820’s and 1830’s deal with algebra, mensuration, infinities, and other advanced topics. Of the remaining 80 %, two-thirds of the manuscripts are devoted to a course of study in commercial mathematics and one-third to the study of a certain body of navigational techniques. Although there was no body overseeing the nature of student instruction, the manuscripts clearly reveal a common curriculum. They present the same topics, covered in much the same order and approached in the same way. There appear to have been two business curricula, one a simplified version of the other for less talented or less ambitious students [or teachers]. The more complete business curriculum appeared twice as often as the less complete one. Secondary sources state that education for females was extremely limited during the 18th and early 19th
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centuries. They report that the wealthier families might send their daughters to either “dame schools” or finishing school to study manners, dancing, French, needlework and embroidery. The daughters of less wealthy families would either be taught only how to read and write or would receive no education at all. This is a widely published assumption that needs to be reexamined. In the RIHS collection about 10 % of the manuscripts are by females. I have found a similar characteristics and identical curricula among the Massachusetts and Connecticut manuscripts that I have examined. Furthermore, the female students are completing exactly the same courses in mercantile mathematics that their male counterparts are. While among males, two-thirds of commercial students completed the more challenging curriculum, among the female students, that percentage was closer to 50 to 60 %. I did not find any manuscripts of female students undertaking the navigational course of study. The careful study of the student manuscripts yielded a variety of insights not available from either the study of the textbooks or the secondary sources on the history of textbooks and education in this era. From the manuscripts I learned how these students were actually taught; what books were really used; which topics and problems were emphasized and which were ignored; which teaching approaches were preferred; what the students knew and how they knew it. I came to understand how they looked at mathematical things. The manuscripts also occasionally reveal the personal side – from sketches by artistically talented youth to the doodles of the artistically challenged; from philosophical musings to eye-witness reports of the major events of their time; from love sonnets to a favored friend to hints of personal hardship and tragedy. Most of my preconceived notions about how things were and how they worked were incorrect. Many of the secondary sources reporting this history were misleading or incorrect — sometimes through ignorance, sometimes through bias, as will be discussed later in this paper. In summary, most Rhode Island cyphering books reflect neither an elementary nor a classical education. They reflect instead the model of education advanced by a quintessentially American institution of higher learning — the Academy — whose potent influence can be seen and felt in these manuscripts despite the fact that for most of this period there were few if any academies in Rhode Island 6 . It is far more likely that these manuscripts reflect studies at private–venture schools, with individual tutors, or in some cases with more ambitious town schools. Returning to the question of whether Cranston’s studies were unusual or not, it is clear that his studies were very typical of what the vast majority of students in New England were doing who chose to pursue additional education beyond the rudiments of literacy and numeracy provided by the elementary schools. Over 80 % of the cyphering books examined, male and female, reflected a four year course of study, either of mercantile mathematics or of the elements of geometry and trigonometry applied to problems in surveying and navigation. The 6 Rhode Island did not embrace academies as quickly as its neighboring states. I have found evidence of only one or two Academies in Rhode Island prior to 1800. However, by 1828 there were at least 15 academies [23], and by 1850 there were 46 academies in the state.[2]
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Figure 2: Dates of Rhode Island manuscripts students who wrote these cyphering books, whether male or female, whether in town or country, whether individually tutored, instructed at a private–venture school, or boarding at an Academy were all studying the same material from the same group of texts. These authors of these textbooks understood their mathematical studies in the context of a broader education that included both classical and practical elements, delivered increasingly through the establishment of Academies in villages and small towns across the nation. If we are to understand at all the nature of higher mathematics education in America before the 1870’s we must understand better the nature of the Academy. It is to that institution: its origins, evolution, context, and decline that we now turn our attention.
The Academy The Academy, as it developed in America from 1780 to 1880 was a residential institution of higher learning, often located in a town with population between 2,500 and 5,000 people. Scholars came from many surrounding towns and counties, occasionally from other states to study. Most of the students came from farming families, and attendance varied with the demands of farm life. In New York academies, 65 to 85 % of the students came from out of town. [4] Many academies accepted both men and women. A substantial number of their stu-
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Figure 3: Subjects Studied dents were adult learners. The average academy taught 40 to 60 students and employed 2 to 4 teachers. In contrast, the typical college of the time enrolled about 200 students, taught by 8 to 10 faculty members. The academies were also distinguished from other types of school by their governance system and by the nature of the curriculum. They were started and governed by private self–perpetuating boards of trustees. Most often these were the leading citizens of the town or village, and these academies were institutions of local pride and civic boosterism. Many academies were chartered by either town or state, thus providing for more permanence and local control than the private–venture school. They not infrequently received some level of public funding despite their private governance, but relied primarily on tuition and philanthropy to meet their expenses. The age and level of preparation of students entering the academy was similar to the age and preparation of students entering the college or university. The curriculum contained a utilitarian component much desired by the American populace, but lacking in the Latin schools and in the colleges. The academies offered a breadth of study in preference to a narrowly focussed curriculum. They served a far wider range of students, including adults, females, farmers, sailors, merchants, and tradesmen. Many students came only at certain times of the year, or studied only certain parts of the curriculum. Each was welcome to take as little or as much of what was offered as they wished or as they were able. The best of the academies offered a combination of classical and applied education typified by the Montpelier Academy (VT) in 1828, which required for a diploma, courses in Orthography, Reading, Writing, Composition, Geography, Grammar, Arithmetic, Rhetoric, History of Vermont, History of the United States, General History, Logic, Moral Philosophy, Astronomy, Chemistry, Drawing, Evidence of Christianity, Natural Philosophy, Geometry, Algebra, Surveying, Mensuration of Surfaces and Solids, Linear Drawing.[23, p 28]
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Figure 4: Subjects Studied over Time “Opportunistic and laissez-faire in the extreme are the only ways one can describe the curricula of the academies. Anything and everything could be put into a six-week course.” [23, p 28] More opportunistic academies offered courses in such areas as needlework, phrenology, waxwork, conchology and optics. This approach of teaching a little bit about a large area of subjects, broken down into six-week sections that one could take at will as the demands of work allowed, proved very popular, and these institutions grew, flourished, and multiplied. Although these descriptions may give the impression that the academies provided a trivial experience, the evidence of the cyphering books is that these students were involved in serious study and demonstrated considerable discipline and determination in their approach to the material. Nancy Beadie’s study of the women students’ diaries and correspondence reveals how important academy attendance and learning were to the women of the early nineteenth century. Many women whose attendance was interrupted went to great lengths to maintain social contacts and to continue their academy studies on their own. If a private tutor was unavailable or not affordable, they often continued their studies at home with the academy curriculum as a guide and studying common academy texts. [4] Perhaps the fundamental attraction of what the academy represented was that it appealed to the American’s desire for the ability to turn his educational and intellectual efforts to practical ends. This was one of the American academy’s distinguishing characteristics since the very first Academy was established by Benjamin Franklin. Unlike the colleges, the Academy would teach you not only Latin and grammar, but how to speak French, Italian, or German – skills most useful to the sons and daughters of the merchant class. They would teach you not only classical geometry, but how to calculate annuities, returns 10
on investment, and compound interest. One would come out not only educated, but competent in those skills which allowed one to make his or her way in the world. Specialized academies also developed, including female academies, seaman’s academies, military academies, and Indian academies. Many academies also contained Normal Departments within which students were trained to be teachers in the common schools.
Origins The origins of the academy stretch back to the English Civil Wars and the influence of philosopher John Milton. In his 1644 tractate On Education [17], Milton proposes the establishment of academies for the education of“our nobler and our gentler youth”. His aim was the traditional aim, the molding of boys into enlightened, cultivated, responsible citizens and leaders. His academy, which would take the place of both secondary school and college, was to concentrate on instruction in the ancient classics, with due subordination to the Bible and Christian teaching. Milton also emphasized the sciences, and physical and martial exercise had a place in his curriculum as well. [Encyclopedia Britannica]. Milton proposed to teach modern subjects through the study of the classical authors of ancient Rome : agriculture learned from Cato, law from Moses and Licurgus, etc. Milton’s revolt against the education of Oxford and Cambridge was not a protest against the wisdom of the ages, but against the abuse of their writings through rote study and busywork in the Schools and Universities. He wished to “provide a desire to search for and seize every opportunity to serve and to oblige – what is the Foundation of what is called Good Breeding.”[17] Since attempts to make the philosophers into Kings had not succeeded since Plato’s Republic, Milton outlines a plan for turning the future Kings into philosophers. Following the Restoration of the monarchy under Charles II in 1660, those unwilling to take a pledge of loyalty to the Church of England were excluded from the Schools and Universities of the country. Thereupon followed the establishment of a number of Protestant Dissenting or Nonconforming Academies, presumably named after Milton’s proposed institutions. Nearly a century later, Benjamin Franklin, inspired by Milton’s essay and the Protestant experiment, established the first American academy, the Philadelphia Academy in 1751. Although naming his institution an Academy and citing Milton extensively in order to gain authority and legitimacy for his proposed school, Franklin did not share Milton’s goal of perfecting the sensibilties of the ruling class. Franklin instead seizes upon Milton’s support for learning in the practical and applied arts and severs it from its ties to the ancient classics. The goal of the American academy was to bring higher education away from its tradition of in depth study in the Classics and in Theology and to move it into closer consonance with “the great and real business of living,” [21], closer to areas that relate to this world and the challenges and opportunities it presents. Franklin’s academy promotes the study of modern languages, literature, history, geography, 11
chronology, navigation, mathematics, natural and applied science, agriculture, and the like. For many decades the families of the rising merchant class had found the education provided by the Latin school and by the University lacking, preferring to prepare their sons for everyday living through private tutors, and these newly established schools soon were patronized by these classes. A second English antecedent which is relevant for mathematical teaching in particular is the English Commercial School. Founded at the same time as the dissenting academies and for the same reasons, these schools provided technical training in penmanship, writing, arithmetic, bookkeeping, etc. It’s teachers produced the first English Arithmetic texts, and it is these texts and their American descendants that determined the mathematical curriculum both of the academy and of the early college. The earliest texts which are know to have influenced American teaching were written by writing masters Edward Cocker (1678) and James Hodder (1661). The first American written arithmetic by Isaac Greenwood (1729) [13] is essentially a reworking of Hodder, and the subjects contained in the mercantile curriculum reflected in the copy books and in American arithmetic texts starting with Pike and Daboll remains essentially unchanged from 1678 until 1824 when the pioneering work of Warren Colburn breaks its hold, although the pedagogy used has varied through that period. An analysis of the evolution of arithmetic texts and their transmission form England to America lies beyond the scope of this paper and is the scope of work in progress by this author.
Evolution Throughout most of the eighteenth century the great competitor to the Latin school and the college was the private–venture school. Following the establishment of the earliest academies in this country, many venture schools sought to be chartered or incorporated as academies. This provided benefits and stability to community, school, and schoolmaster. The transition was most successful in rural areas, with the academies located in small towns and villages. The support of a governing board of influential citizens provided the resources for permanent facilities and additional faculty. On the part of the teachers, this transition required a broadening of curriculum and the sharing of decision making and responsibilities with a governing board of community leaders. This brought the teachers into closer sympathy with the needs of the host communities and made for more successful educational ventures. The nature of the academy was defined by three factors. The academies were nearly universally residential institutions, providing students with room, board, and instruction. They were governed by private, self-perpetuating boards of trustees, although they not infrequently received a state charter and possibly a modest level of government financial support. The curriculum was more modern and more secular than that of the Latin school or the College. The more prestigious academies offered a classical curriculum supplemented by the study of modern languages and literature, modern history, and practical science and mathematics. 12
The Academy became the dominant institution of higher learning during the first decades of the 19th century. According to a report by Henry Barnard, in 1855 there were 235 colleges but 6,185 academies. The colleges enrolled approximately 20,000 students in the entire country, but the academies enrolled 263,000. New York State alone enrolled nearly 50,000 students in 887 academies. Even Texas had 97 academies in 1850, only 15 years after the battle at the Alamo. [2]
Sister Educational Institutions Colleges & Universities There were but nine colleges or universities established in the American colonies prior to 1776: Harvard 1636 Congregational William & Mary 1688 Anglican Yale 1701 Congregational College of New Jersey (later Princeton) 1746 Congregational Kings College (later Columbia) 1754 nondenominational with strong Anglican influence College,Academy,Charitable School of Philadelphia (later Penn) 1755 nondenominational College of Rhode Island (later Brown) 1764 Baptist Queens College (later Rutgers) 1766 Dutch Reform Dartmouth College 1769 Congregational Four of the nine colleges were in New England, with another four from New York, New Jersey, and Pennsylvania. All but two were formally denominational Protestant institutions. The only one of the nine that was truly nondenominational was founded by Benjamin Franklin who envisioned a different role, reflected in the original name of the school. The curricula at the colleges, reflecting their primary mission of training new generations of ministers and clerics for the colonies, was comprised primarily of the study of Latin, Greek, classical authors, theology, oratory, and rhetoric. The role of modern languages and literature, science, and mathematics in the curriculum was minimal. A Brown University catalog from 1797 lists the course of study for students. The first two years were devoted to the study of Classics, rhetoric, and oratory. In the third and fourth years they studied theology, natural science, and mathematics. The mathematical entrance requirement for first year students was to be able to perform addition, “substraction”, multiplication, and division and to be able to work with simple fractions. They studied no mathematics until their final year when “they were exposed to Fenning’s Arithmetic, Hammond’s Algebra, Stone’s Euclid, Martin’s Trigonometry, Love’s Surveying, and Wison’s Navigation.” Clearly, exposed to was an accurate description. I would speculate that this was a list of texts owned by the professor or the library and that students were shown a few problems from each book, watching as the instructor demonstrated how the problems could be worked out. Certainly there is evidence of
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the study of fluxions and the like by individual students with special interests or talent, but even the study of algebra was not part of the education of the vast majority of students at universities and colleges in America during the Eighteenth century. Latin & Grammar Schools The Latin grammar schools in New England were town schools, governed by an elected board, supported by town and (often) state grants which were established to “prepare scholars for ye college.” They were among the earliest institutions established in Massachusetts [Boston Latin School, founded by town meeting, 1635]. In 1647 the Commonwealth of Massachusetts specified that every town of more than 100 families provide for a Latin school or its equivalent, although in fact such institutions were only founded in the larger towns. These schools admitted boys who could already read, and within these schools boys spent six to seven years reading arithmetic and Latin texts. The goal of parents supporting these schools was either to prepare their sons for entry into college or to provide them with the gentlemanly polish needed to maintain or improve their standing in society.[25] Town and Church Schools These schools provided instruction in basic literacy and numeracy and were supported by the institution which founded them. During the nineteenth century these institutions evolved into common schools or district schools, supported by town and state and providing free elementary education to all who wished it. Private-venture Schools These schools were a dominant force in education throughout the eighteenth century. These schools were run by individual men and women offering their services for instruction. Sometimes they offered instruction in only one or two subject areas (e.g. dancing, navigation, French and Italian, needlework, violin), but some offered instruction in a wide range of subjects that went beyond the basics of reading, writing, and arithmetic. These institutions were supported entirely by tuition and therefore tended to be very entrepreneurial and market driven in nature. Their very existence often depended upon the availability and interest of a single instructor. These ephemeral institutions are frequently known through their newspaper advertisements or through broadsides printed to attract students. They appeared and disappeared with astonishing frequency and were present in very large numbers in most cities. Little is known about what was taught in these institutions and how it was taught. None of these schools survive, and few if any records were kept. They were the creation of individual teachers, not established institutions, and the details of their operation has passed away with their creators. This study of Rhode Island cyphering books, however, provides strong evidence of the nature of mathematical study
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at the venture–schools in Rhode Island and suggests that it was indistinguishable from what was taught in the academies of the neighboring New England states. Religious Academies Within the middle and southern colonies, schools called “academies” were established that were similar to the Latin Schools in the northern colonies. These institutions were church schools designed to train students for the ministry. A number of such institutions were founded in Catholic Maryland as early as the seventeenth century, and at least 44 Irish Presbyterian schools of this type had been founded before the revolution, primarily in the middle and southern colonies. [25, 3] The use of the term Academy in this paper does not refer to these religious schools, but to schools founded based upon a specific educational model formulated by John Milton and modified in America by Benjamin Franklin [17, 11].
Sister Cultural Institutions: private action for the greater public good The preferred institutions for early Americans were those with a direct utilitarian nature : the Academy, the Lyceum, and the Subscription Library. All three institutions were originally privately supported, but for the purposes of enhancing the public good. The goal of an involved and informed citizenry was viewed as essential for the success of the American experiment in self government. In time, each of these gave way to institutions receiving direct public support and under direct public control, but at the time of their founding, the electorate, with the notable exception of Massachusetts, was not comfortable with direct support of such endeavors. With declining tax-payer support for public universities and libraries, it may be asked if such models will have a role to play in the future. The Athenaeum or the Proprietary or Subscription Library The earliest libraries in the American colonies were proprietary or subscription libraries (also known as social libraries, library societies, or library associations.) The first such library in this country was started by Benjamin Franklin. In 1730 Franklin and other members of the Junto (a debating society which eventually became the American Philosophical Society) pooled their books. This experiment soon failed and the next year Franklin tried a different approach. He established a stock company in which each of fifty proprietors was to pay forty shillings for a share and thereafter 10 shillings a year in fees. This entity became the Philadelphia Library Company. Several similar libraries formed in Connecticut and Rhode Island. By 1776 there were at least 64 such libraries in the colonies, 38 of them in New England. Some still exist to this day as subscription libraries in which members pay a yearly fee and have a direct voice
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in the running of the libraries. The Redwood Library in Newport, RI was one of the earliest of such libraries [1747]. The Providence Athenaeum is a direct descendant of the Providence Library Company [1754]. The Lyceum Another institution that burst on the national scene and quickly spread across the country was that of the lyceum. The goal of the lyceum was to provide for an environment that supported mutual education and furthered intellectual and cultural activities for the citizens of the community. The first lyceum was introduced in Milbury, Massachusetts by Joshua Holbrook in 1828. The idea was drawn from the Mechanics Institutes established in England. The idea was to give people an opportunity to hear debates and lectures on topics of current interest. At first the lyceums were local ventures with speakers supplied from the community, but they soon became professional organizations with outside lecturers to whom fees were paid. By 1834, the number of lyceums in America had grown to 3,000. One of the most successful of the lyceums was the Salem Lyceum Society (Salem, Massachusetts). Over a 60 year period the Salem lyceum sponsored over 1,000 lectures featuring the most prominent Americans of the day. These included Richard Henry Dana Jr (author of Two Years Before the Mast) speaking of “The Reality of the Sea”, former United States President John Quincy Adams on “Faith and Government”; Oliver Wendell Holmes on “Lyceums and Lyceum Lectures”; abolitionist Frederick Douglas on “Assassination and its Lessons” (shortly after the shooting of Abraham Lincoln); and James Russell Lowell on “Dante”. Nathaniel Hawthorne never spoke at the Lyceum, but served as corresponding secretary for the 1848–1849 lecture series recruiting Horace Mann, Henry David Thoreau, Ralph Waldo Emerson, and Daniel Webster. Emerson spoke nearly 30 times at the Salem Lyceum alone. Alexander Graham Bell’s first public demonstration of the telephone was given at Lyceum Hall (although sponsored by the Essex Institute.)
The Decline of the Academy and its sister institutions These institutions were born of the 18th century enlightenment inherited from Europe combined with early American optimism and practicality. America believed itself to be a place where the common man could educate himself to be the equal of any privileged European. This engendered the formation of institutions born of private initiative to advance the public good. Prominent among these institutions were the subscription library, the academy, and the lyceum. All three of these institutions faded in the decades following the Civil War and have largely disappeared from the American scene. It took until 1880 before the number of students in public high schools equalled the number enrolled in academies, but by 1900 the academy had largely disappeared from the institutional scene. Some academies became the public high school. Others became colleges or universities. Some simply closed their
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doors, and others became preparatory schools or boarding schools. In these same decades the proprietary library was replaced by the public library, and thousands of Lyceums and Mechanics’ Institutes simply vanished. The causes for the simultaneous, rapid and near universal disappearance of these institutions — which were among our country’s most vital and flourishing ones — is not clearly understood. Among the influences and changes that have been suggested are the demographic changes from a rural to an urban population (the flight from the farm to the city), the effects of the industrial revolution, and changes in immigration patterns. To these I would add the economic, social, and psychological effects of the Civil War, the rise of mass marketing and consumerism, and the loss of the sense of newness and optimism engendered by the Revolution. The academy was always an institution of the countryside and the small town. The necessity of boarding at the school was acceptable because no one village by itself could supply sufficient numbers of students to support a school of this type. Transportation limited the distance one could travel if returning home each day. As more and more of the population moved to the cities to seek the jobs that industrialization could provide, there were sufficient numbers within a single town to support a school of advanced study. Improved roads and transportation made access to these schools easily available for those within the city. The expense of residing at the school was no longer necessary. As the movement to public tax–supported education grew, the academy could no longer compete economically with the high school. For many years public high schools were only viable in the city and academies continued to operate in the rural countryside. Even today, there are functioning academies in rural states such as Maine, where they operate along side of and in competition with public high schools. However, it is not solely an effect of urbanization, but a change in the way in which the world and man’s place within it were viewed and understood that resulted in the decline, not only of the academy, but of its sister institutions as well. The concept that each citizen is master of his or her own fate and can in fact change the world was no longer the prevailing world view. The bitter experience in the Civil War and the Reconstruction period that followed destroyed what what left of eighteenth century optimism. A new set of challenges faced the country, and new institutions and new approaches would replace the old.
Descendants of the Academy Although academies, lyceums, and athenaeums have largely vanished from the American landscape, their influence can be detected in many areas. Many communities proudly support local museums, libraries, and historical societies. The public library is perhaps unique in the remarkable level of public support it receives for an educational or intellectual institution. The high school, community college, and the university have borrowed heavily from the lead of the academies. The public high school serves the need for post-elementary education for those not wishing to pursue collegiate education — a need once filled by the 17
academy. The community college both provides career–oriented applied studies and preparation for college. The college and university for the most part no longer define themselves in classical or religious terms, but provide a mixture of liberal foundation, applied knowledge, and professional or career training. The comprehensive college or university in particular continues to evolve along the model established by the academy. But for all those similarities, something unique has been lost and the educational landscape is impoverished by its absence. Our current system of secondary education, based upon public support and control and the goals of universal access and a professional teaching corps have been purchased at a price.
Conclusions Documentary evidence shows that the Academy, not the College was the dominant American institution of higher education from the last quarter of the 18th century to the middle of the 19th century. This was true in mathematics education as well as in other areas, and that even in locales with few academies, the agenda for the education of American youth was framed by the experiment undertaken by the Academies. The characterization of the Academy as a proto–high school, or an outgrowth of the common schools, or as an exclusive preparatory school easing the wealthy student’s way into the most prestigious colleges was a categorization and characterization of a much later era ... one with its own agenda ... that of establishing a uniform national system of public, mandatory education in schools supported by public tax dollars and staffed by the professionally trained graduates of normal schools and teacher’s colleges. This characterization would not have been recognizable to those students whose work is reflected in these manuscripts. The earliest leaders in the efforts to reform the educational system were Horace Mann 7 and Henry Barnard 8 . Between them, these two men served as state and national legislators and as state and national commissioners of education. Both men wrote extensively and worked tirelessly on educational reform, Barnard over a period of nearly fifty years. 7 Horace Mann (1796-1859), a graduate of Brown University, played a leading role in establishing state-supervised, state-funded, mandatory-attendance school systems in the United States. He served in the Massachusetts legislature from 1827 until 1837 when he became secretary of the newly established Massachusetts State Board of Education. As secretary, his speeches and 12 annual reports on education were influential in changing the definition of common school. The term had long applied to one-room, community-based schools. After Mann’s work, only tax-supported schools graded by age and organized within township units were called common or public schools. In 1839, Mann helped found the country’s first statesupported normal school (teacher-training school), in Lexington, Massachusetts. He served in the U.S. House of Representatives and was the first president of Antioch College from 1853 until his death. [World Book Multimedia Encyclopedia 2003] 8 Henry Barnard (1811-1900), served as the first United States commissioner of education from 1867 to 1870. Previously, he had been commissioner of education in Connecticut and in Rhode Island. He also served in Connecticut’s legislature. In these offices, he did much to improve public schools and to arouse public interest in them. He edited and published the American Journal of Education, through which he contributed to educational thought. [World Book Multimedia Encyclopedia 2003]
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The influence of these two educational leaders and reformers was enormous and persists strongly even to this day. It is their views on the academy that informed the early writers on educational history in the United States. They were not objective observers, but reformers in a battle to replace the privately supported institutions of their day by a nation–wide system of tax–supported public schools, taught by the graduates of the Normal Schools and Teacher’s Colleges that they would found. They also sought to feminize the teaching establishment, arguing that women were uniquely endowed by their creator with just those characteristics most needed in teachers. At the same time they observed that women would work for much less money than their male counterparts and thus the nation could obtain many more teachers for the same expenditure. It is also the case that most of the histories of education were written by people trained in the very institutions of which Mann and Barnard were the intellectual founders. A study of these cyphering books brings many commonly held notions about education at this time into question. It also brings many commonly held notions about the Academy into question. It has been written that the academies provided the veneer or appearance of education without the substance [22, pp 29–36], that their mathematics courses were taught through the uncomprehending memorization of rules without understanding [7, 18], and that the Academy gave way to the high school through the inevitable democratization of American institutions [6]. Let us offer an alternative set of explanations. In the years following its successful break with mother England, eighteenth century America, inspired by the thinking of the European Enlightenment and still strongly influenced by its founding mixture of utopians, religious idealists, and opportunists, enthusiastically embraced a heady optimism in the ability of the common man, the self made man, to remake both himself and the world he lived in through his own efforts at self and community improvement. This resulted in an explosion of local efforts, financed through the generosity of individuals, to remake the civic climate. These efforts manifested themselves on many fronts, from Mechanics’ Institutes to Subscription Libraries, from Concert Halls, Museums, and Lyceums to Academies and Seminaries. In education we see a desire for broad knowledge, broadly shared. We see an appreciation of the contributions of the mechanic and the craftsman as well as for the minister and the lawyer, and appreciation of the practical and useful as well as for the intellectual and the other-worldly. It is possible that such optimism and enthusiasm could not be sustained in the long run and that these movements faded from sheer exhaustion and the cynicism that can set in when working to achieve idealistic ends in the real world. Newer generations without the experiences of the colonization of a new continent or the founding of a democracy, were more willing perhaps to settle for more easily achievable, more modest and realistic goals. This new approach required less involvement from individuals and local communities as the state and local governments, together with the professional teaching organizations came to play a more important part. Once individual citizens relinquished the initiative for community improvement to the expert, the professional, and the government, 19
those institutions founded and sustained through local private action “for the common benefit of all” faded from the American civic landscape.
Web Links to Images A few institutions of the types discussed in this paper still exist and function in their original buildings. In other cases the institutions have disappeared but their buildings still exist, having been modified to serve other purposes. I feel that being able to see what these schools, libraries, and lyceums looked like will help the reader to understand something of the nature of the institutions. Due to the difficulty of clearly reproducing these photographs in a journal format and the difficulties inherent in gaining permissions to reproduce possibly copyrighted materials I have instead included a table of internet links (URLs) which will provide the interested reader with a view into these remarkable 18th and early 19th Century institutions.
Academies Andover MA [1778] Albany NY [1813] Exeter VT [1781] Governor Drummer MA [1763] North Yarmouth, ME [1814] Troy NY Female Seminary [1814]
andover.edu albany-academy.org exeter.edu thegovernorsacademy.org nya.org emmawillard.org/
Lyceums Salem, MA [1830] Alexandria, VA [1839] Mechanics Hall, Worcester, MA [1857]
salemweb.com/tales/Lyceum.shtml alexandriava.gov/Lyceum mechanicshall.com
Subscription Libraries Newport, RI [1747] Providence, RI [1754] (building 1838) Boston, MA [1807]
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redwood1747.org providenceathenaeum.org bostonathenaeum.org
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[11] Franklin, Bejamin, Proposals Relating to the Education of Youth in Pennsylvania (1749), from Leonard W Labaree, et. al., eds, The Papers of Bejamin Franklin, II 397-421, New Haven CT, 1959, reprinted in Sizer. [22] [12] Freeman, Ruth S, Yesterday’s School Books, Century House, Watkins Glen, NY, 1960. [13] Greenwood, Isaac, Arithmetick vulgar and decimal: with the application thereof, to a variety of cases in trade, and commerce., Boston, 1729. [14] Karpinski, Louis Charles, Bibliography of mathematical works printed in America through 1850, Ann Arbor, The University of Michigan Press; London, H. Milford, Oxford University Press, 1940. [15] Lancaster, Jane, Inquire Within: A Social History of the Providence Athenaeum since 1753. The Providence Athenaeum, Providence, RI 2003. [16] Mitchell, Martha, Encyclopedia Brunonia, Brown University Library, Providence, RI 1993. [17] Milton, John, Of Education (1644), from Browning, Oscar ed., Milton’s Tractate on Education (Cambridge, England, 1883, pp 1–23. ) Reprinted in Sizer [22] [18] Nietz, John A, Old Textbooks, University of Pittsburgh Press, 1961. [19] Nietz, John A, The Evolution of American Secondary School Textbooks, Charles E Tuttle Company, Rutland, Vermont, 1966. [20] Pike, Nicolas, New and Complete System of Arithmetic. Composed for the Use of the Citizens of the United States., Newbury-port [Mass.], printed and sold by J. Mycall, 1788. [21] Constitution of Phillips Academy (1778), The Constitution of Phillips Academy in Andover, Andover, Mass., 1817, reprinted in Sizer [22] [22] Sizer, Theodore R, The Age of the Academies, Bureau of Publications, Teachers College, Columbia University, New York, 1964. [23] Stockwell, Thomas B, A History of Public Education in Rhode Island from 1636 to 1876, Providence Press Company, 1876. [24] Tolley, Kim & Beadie, Nancy, Reappraisals of the Academy Movement, Hisotry of Education Quarterly, Vol 41, No 2, 2001, 216-224. [25] Tolley, Kim The Rise of the Academies: Continuity or Change, History of Education Quarterly, Vol 41, No 2, 2001, 225-239.
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[26] Venema, Pieter, Aritmetica of cyffer–konst, volgens de munten maten en gewigten te Niew-York: gebruykelyk als mede een kort ontwerp, van de algebra, New York, 1730.
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