Rewriting the History of School Mathematics in North America 1607-1861: The Central Role of Cyphering [Repost]

The focus of this book is the fundamental influence of the cyphering tradition on mathematics education in North American colleges, schools, and apprenticeship training classes between 1607 and 1861. It is the first book on the history of North American mathematics education to be written from that perspective. The principal data source is a set of 207 handwritten cyphering books that have never previously been subjected to careful historical analysis.
Two centuries ago, American teachers did not stand at the front of the room and teach, and most students—even those studying mathematics—did not own a mathematics textbook. Written examinations of any kind were not used. Most teachers of mathematics did not have formal qualifications in mathematics. The modern educator might well ask: “If all of that is true, then how were teachers expected to teach and how were students expected to learn mathematics?”
In this book Nerida Ellerton and Ken Clements argue that before 1840 mathematics was taught in North America via a cyphering approach that had been translated from Western Europe to the new settlements. This approach was based on a tradition that had endured since the thirteenth century, and depended heavily on students carefully writing their mathematics in cyphering books. After 1840, schools gradually adopted more teacher-centered whole-class pedagogies for mathematics instruction, and by the beginning of the Civil War, in 1861, the transformation was complete.