The State of the Unit: a documentary film about the redefinition of the kilogram

July 31, 2016 Colonial measures and education in Early America

Photo of cyphering book from the collection of Nerida Ellerton and Ken Clements Ken Clements and Nerida Ellerton with their three Springer books based on research on cyphering books.

After learning about standardization in 1790s France in everything from measures to education, I became interested in what was taught in the American Colonies, and early United States. At that time, we used measures and currency from many countries, and bartering was common in business.

I was happy and lucky to find two experts in Colonial and Early American mathematics education: Nerida Ellerton and Ken Clements, both math professors at Illinois State University. In addition to their regular teaching and advising, Nerida and Ken have studied and compared 500+ cyphering books.

Cyphering books are self-written reference books; students would solve problems on slates, and after reaching the correct answer, students would record the full problem in their own, more permanent cyphering book.

Photo of cyphering book from the collection of Nerida Ellerton and Ken Clements "Practical Questions" is an apt heading. The first question is "Bought 25 lb of coffee for 5 dollars what is that a pound? Answer 20 cents" This cyphering book is one written by a girl student—about 20% of the cyphering books studied these professors were written by girls. The cover is blue fabric, reinforced with newspaper.

Ken and Nerida’s research is new, and their premise is that the cyphering books show what was actually learned and taught. There were popular textbooks through the years, but they would have been quite expensive and out of reach of small neighborhood or homestead schools.

Photo of cyphering book from the collection of Nerida Ellerton and Ken Clements An assortment of cyphering books from the 1700-1800s. You can see some were homemade, with handstitching. Others were purchased blank books, at the bottom left. They were covered in cloth, board, and leather, bottom right.

Nerida explains that after schooling (one winter, one year, whatever the students could afford), a cyphering book was later used by the student both as a reference and “essentially as a CV.” School boards and/or employers would look at your cyphering book to determine your level of education, and thus your suitability for a teaching or clerk/accounting position. “It would have been the second-most important book in the family, after the Bible.”

Photo of cyphering book from the collection of Nerida Ellerton and Ken Clements This page describes "shares" of profit in a "joint adventure" in 68 pounds of tobacco, 80 pounds of cloth, 120 pounds of leather, and 140 pounds of silk hose.
Photo of cyphering book from the collection of Nerida Ellerton and Ken Clements Nerida describes how common bartering was, especially when traveling by sea. This problem asks "What quantity of candles, at $9.50 per [cwt] must be given for 15 [cwt]. 0 [grs] 27 pounds of tobacco at 20 cents per lb."

Bérénice Reynaud, one of my film professors, said that standardization in education and textbooks was one aspect of social equality after the French Revolution—a child in the provinces could have the same education as a child in Paris. We sometimes still see this disparity between wealthy suburban schools and rural schools.

Photo of cyphering book from the collection of Nerida Ellerton and Ken Clements Dark borders made problems easier to identify on a page full of numbers.
Photo of cyphering book from the collection of Nerida Ellerton and Ken Clements Nerida and Ken show a few old containers. The two small are firkins. You may remember them in C.S. Lewis' The Last Battle, "'A firkin or so of good wine in each of these towns would not have been amiss,' said Tirian."

Nerida explains, "Firkins were a common container and of a fixed size for butter, flour. But for different things, a “true” firkin is about 4 times this size. It should be one cubic foot in internal volume." The larger container is a kilderkin. Ken said they found it at a local estate sale and "Nerida measured it all out and it was exactly 2 cubic feet," as a kilderkin should be. Nerida explains that a kilderkin is "half a barrel, and you need two barrels make a hogshead.” But Ken adds that in some places “three barrels make a hogshead.” Nerida continues “And it depends whether you’re measuring beer or wine or ale. Or solid measures. You can imagine the confusion. If you’ve one hogshead and half a kilderkin and firkin, and you try to do some bartering."

Thomas Jefferson worked to install decimal currency and reform education, to build an educated citizenry who could easily perform and understand fundamental transactions of daily life. Ken and Nerida have published a book about Jefferson’s mathematics reforms, listed below. They find more decimal problems in cyphering books after the U.S. adopted decimal currency, but not in English cyphering books because England was still using pounds, shillings, and pence.

Their research in cyphering books reveals trends in political policy, for example, with respect to decimal currency. Another cyphering book was written during the American Revolutionary War, and messages related to the Colonials' insurgency was hidden inside. If you're interested in reading further about the implications in education, mathematics, and weights and measures, you might continue with one of their books:

Abraham Lincoln's Cyphering Book and Ten other Extraordinary Cyphering Books by Nerida F. Ellerton and M. A. Ken Clements. 2014.

Rewriting the History of School Mathematics in North America 1607-1861: The Central Role of Cyphering Books by Nerida F. Ellerton; M. A. Ken Clements. 2012.

Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics by M. A. Ken Clements and Nerida F. Ellerton. 2015.