Lessons from Extraordinary Cyphering Books.

Six lessons about school mathematics, and its history, are drawn from the analyses of the 11 extraordinary cyphering books. These lessons relate to: (a) the intended curriculum that the <italic>abbaco</italic> and Sacrobosco traditions, and the British and North American textbook authors, defined for school mathematics during the period 1600 through 1880; (b) the implemented curriculum, as evidenced by entries in cyphering books; (c) the lack of hard data with respect to the attained curriculum–that is to say, with respect to what was actually learned by students during the cyphering era; (d) the remarkable value that many students placed upon their cyphering books; (e) the ethnomathematical circumstances which surrounded the preparation of the extraordinary cyphering books; and (f) the educational significance of qualitative differences between British and North American cyphering books. [ABSTRACT FROM AUTHOR]