The Age of Bartjens. Advancing Numeracy in the Dutch Republic.

Fokko Jan Dijksterhuis In 1988 John Allen Paulos coined the term innumeracy for mathematical illiteracy. He saw a widespread incompetence in dealing with numbers among citizens, which he found worrisome given how crucial quantitative practices are in modern society. The importance of numeracy had started to grow in early modern society when measures and numbers became increasingly significant in trade, warfare, and government. The Dutch Republic was particularly advanced in this regard. Originally skills in dealing with numbers were mainly found among the lower professions; which is reflected in the place of mathematics in the curricula of Dutch, French, and Latin schools. In the course of the 16th and 17th centuries, numeracy became to be regarded as a general competence required of all. At the same time ideas about numbers and quantities were changing with a marked trend towards abstractedness. From pennies to ciphers, from numbers to symbols, from tricks to structures; numeracy acquired the feature of a general cognitive faculty. The changing meanings of 'quantity' informed and transformed mathematical education and ongoing debates about the proper way of learning quantity. The 'Cijfferinghe' of Willem Bartjens is but one, albeit iconic, product of Dutch mathematics teaching. From the clever methods of reckoning that Marjolijn Kool has exhaustively discussed, to the fanciful tools of accounting, and the new logic of geometry developed by the moderns, new ways of advancing mathematical literacy pervaded early modern Dutch society. In this paper I want to map the didactic developments regarding numeracy onto the conceptual transformations regarding quantity in the Dutch Republic.