Arithmetic Teaching ApparatusTextbooks & Cipher Books
A piece of sheet music from 1946 shows two of the most common tools of arithmetic teaching – the blackboard and the textbook. While these are represented in Smithsonian collections, they are not shown in this group. Also shown here is a handwritten cipher book. Before textbooks became inexpensive, such books were often written out by students. As arithmetic was taught by the same teachers responsible for writing classes, the penmanship in cipher books often is quite elegant.
"Arithmetic Teaching Apparatus - Textbooks & Cipher Books" showing 1 items.
- In the 18th and early 19th centuries, when paper was still expensive and textbooks not generally available, students who learned arithmetic sometimes wrote out their own texts by hand. This volume, covered with yellow, black, and red wallpaper, is such a “cipher book.”
- Jesse Harmon Alexander, who was born in 1810 and lived in Rockland, Delaware, prepared this manuscript exercise book in 1825. Each page contains one or two columns of problems and commentary. The first topic considered was the Single Rule of Three. Alexander went in the wrong direction on the very first problem, but he did reach the solution on subsequent problems. His style was typical of the 18th and early 19th centuries. For example, in division problems, he wrote the divisor, dividend, and quotient in a row from left to right. The remaining topics were also typical of the time: tare and tret (adjustments to the price of goods for the weight of the container and for imputities), the Double Rule of Three, direct and inverse proportion, interest, insurance commission and brokerage, compound interest, discount, equation of accounts, barter, loss and gain, foreign exchange, measurement of surfaces, vulgar fractions, reduction of decimals, alligation, single and double position, involution and evolution, extraction of square roots, cube roots, arithmetical and geometrical progression, annuities, and promiscuous questions.
- Alexander's teacher was likely guided by one of the many old-fashioned arithmetic textbooks still in wide use in the 1820s. He (in 1825 most teachers teaching boys in the mid-Atlantic states were men) would have expected Alexander to memorize rules and examples and thus learn how to carry out the mathematical operations Alexander would use in business. The "vulgar fractions" section is one example of this teaching method, as Alexander copied down case after case rather than any general principles governing all fractions. The teacher probably also hoped Alexander would copy the material neatly. This not only offered practice his penmanship but prepared a reference book the boy could use as an adult.
- Alexander clearly returned to this exercise book later in his life, for dates from the 1830s dates are scattered throughout the book. New computations are written on the fourth page of the "interest" section. It is not clear, though, that Alexander's cramped handwriting and failure to clearly mark many of the solutions were any easier to read in the 19th century than now, when bleeding ink and worn page corners have also damaged the textual content.
- Several pages that are not from the original exercise book have been placed inside the front cover. These contain newspaper clippings (mainly poems and obituaries) pasted over accounts from 1831 and 1832.
- For an appreciation of the importance of cipher books in arithmetic education, see: Nerida Ellerton and M.A. (Ken) Clements, Rewriting the History of School Mathematics in North America 1607-1861: The Central Role of Cypher Books, Dordrecht: Springer, 2012.
- Currently not on view
- date made
- Alexander, Jesse Harmon
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- accession number
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- Data Source
- National Museum of American History, Kenneth E. Behring Center