One of the Three R's

ARITHMETIC IN THE EARLY SCHOOLHOUSE

by Michael Day

We often talk about the "the 3 R's" as being "reading, 'riting and 'rithmetic", but for the young scholars in the 18th and early 19th centuries, the "3 R's" were "reading, 'riting and religion". While Bible readings and religious exercises were basic elements of school life, arithmetic (generally referred to as "ciphering") was scarcely dealt with at all.

Prior to the beginning of the 19th century, arithmetic was considered more of an occupational skill than an appropriate subject for general education, and was largely relegated to private evening schools. If instruction in arithmetic was offered in the public schools at all, it was reserved until the later years. Children below the age of twelve or so were generally considered intellectually incapable of leaning arithmetic. Warren Burton in his District School As It Was By One Who Went To It (1833), reported that, "At the age of twelve, I commenced the study of Arithmetic, that chiefest science in Yankee estimation. The entering on arithmetic was quite an era in my schoolboy life. This was placing me decidedly among the great boys, and within hailing distance of manhood." Those who did have occasion to study arithmetic did not get far, at least not by modern standards. The upper limit even for good students was "the rule of three" as proportion was then known. As one writer put it, "To cipher beyond the rule of three was deemed a notable achievement and mere surplusage among the average of country scholars".

In the years before the Revolution, the arithmetic book most widely used was Thomas Dilworth's Schoolmaster's Assistant. Despite a title that would suggest a broader range of focus, this was exclusively a math book, and like many other books of this period, it covered all the math concepts that the average person would need to know in a lifetime. In addition to the four basic operations, the student was introduced to weights and measures, proportion, factions and decimals, pensions and annuities, extraction of cube roots and the exchange of foreign currencies. No one expected the student to learn much of this in class, but the information was there if he cared to pursue the study on his own. The book was first published in 1761 and went through dozens of editions before its final American edition in 1827. From the modern perspective (and particularly from the perspective of a museum interpreter) the only part of Dilworth worth sharing with a visiting class today is a small section at the back of the book called "A Short Collection of Pleasant and Diverting Questions". Here we find nine "brain teasers" such as the classic problem of the farmer who has to get a fox, a goose and some corn across the river in a small boat. You may want to consider challenging your visitors with the same "brain teasers" that perplexed students six generations ago.

But Dilworth was an Englishman, and his book contained many references to places and units of measure that had little relevance in America. The Revolution led to a general distaste for all things English and Dilworth's book rapidly began to lose favor. Clearly there was a need for a book that more closely reflected the conditions and ideals of the new Republic. Nicholas Pike was one who saw this as an opportunity, and in 1788 published The New and Complete System of Arithmetic which, according to its full title, was "composed for the use of the CITIZENS of the UNITED STATES". It offered very few pages of introductory arithmetic, and large sections on commission, extraction of square roots, annuities, and other more advanced topics. In 1793 he issued a simpler, abridged version, "Adapted to the Commerce of the Citizens of the United States for Use of Schools." Pike's book was the first commercially successful arithmetic book written and published in the United States. It was one of the few schoolbooks studied by Abraham Lincoln.

An alternate text vying for the same market was Nathan Daboll's Schoolmaster's Assistant. Like Dilworth's earlier book of the same title, this was comprehensive text that covered everything from simple addition to compound interest. Daboll's book achieved great popularly, in large part due to the fact that it introduced "Federal Money" and showed how to calculate the value of goods using this new means of exchange. Noah Webster highly recommended it.

Often there was no textbook at all, either for the teacher or for the students, and much of the instruction relied on the "ciphering book" approach. The master would dictate a "rule" which would be written down by the student in his ciphering book, (i.e. a set of folded papers sewed together into a "book"). A "sum" (i.e. math problem) would then be written into the ciphering book by the master and the student would solve the sum using the rule. A number of writers reported using birch bark instead of paper for their preliminary work. The learning was mostly rote memorization with little effort made to understand the logic and reasoning behind the process. A lot of class time was spent just waiting for the master to "set the sum" or to check the work, and this time was often used by the student to elaborately decorate his ciphering book. Many of these have come down to us as treasured family heirlooms. A teacher who did not possess an arithmetic book of his own (and there were many who didn't) would use as a teaching text the ciphering book that he had created as a student.

With the opening of the nineteenth century there was a growing recognition that arithmetic was an appropriate study for all children, and that an understanding of why things were so would lead to better education. Not everyone agreed. One teacher, writing in the 1830's noted that, "Until within a few years, no studies have been permitted in the day school, but spelling, reading and writing. Arithmetic was taught by a few instructors one or two evenings a week. But in spite of a most determined opposition, arithmetic is now permitted in the day school". Another innovation taking place at about this same time involved how large numbers were written. European mathematicians recognized that it was easier to read very large numbers if the digits were separated into smaller groups. English mathematicians began separating large numbers into groups of six digits; the French divided large numbers into groups of three digits. American intellectuals, still harboring ill-feelings left over from the Revolution, tended to prefer French ideas, rather than English. While it was common up to the time of the Civil War for arithmetic books to show large numbers with no separation, the French innovation gradually took hold, and to this day we divide our large numbers (such as 1,000,000) into groups of three digits.

A major reform in the teaching of arithmetic occurred in 1821 with the publication of Warren Colburn's First Lessons: Intellectual Arithmetic Upon The Inductive Method. Colburn was the first to provide what today we would call "developmentally appropriate" instruction. Where Dilworth (and others) gave rules to be memorized, Colburn gave simple word problems that allowed the student to develop their own understanding of the process. Dilworth introduced his lessons with the didactic: "Arithmetic is the art or science of computing numbers, either whole or in fractions"; Colburn began with the simple questions: "How many thumbs have you on your right hand? How many on your left? How many on both together?" Most of the 170 or so pages were devoted to such simple word problems that explored the four basic functions plus "vulgar fractions"; higher mathematics was eliminated entirely. Colburn encouraged oral recitations and his word problems reflected common childhood experiences. In this and in other books, there were also a number of word problems that referenced English money (pounds, shillings and pence). This reflected the fact that England was the most powerful nation on earth and the English economy was the standard by which all others were judged. The success of this little book was extraordinary. It is estimated that over three and a half million copies were produced in the fifty years that it was in common use, and it forever changed the way in which arithmetic was taught.

The word problems used in Colburn's First Lessons can readily be extracted and used today with a visiting class. They will give modern students an opportunity to experience authentic early American education, and will give insight into the daily experiences of early 19th century children. For additional examples of arithmetic that can be shared with a visiting group, see "Sharing 19th Century Arithmetic with your Schoolhouse Visitors" in the October 17, 2006 issue of this CSAA Newsletter.

Artwork: Homework by Winslow Homer; Copybook: Huguenot Historical Society,NY