Guest Notebook: Back to School special! (2) A little history of American math books

by Robert Rosenfeld

Opening of Joseph Ray, The Little Arithmetic (1834)

Read Part One of this post here!

Nathan Daboll’s experience-based approach to teaching mathematics is a harbinger of a new philosophy of education growing from European Enlightenment ideas expressed in Jean-Jacques Rousseau’s controversial 1762 book, Emile, or On Education. In the preface to Emile Rousseau writes, “the wisest writers devote themselves to what a man ought to know, without asking what a child is capable of learning.” Joseph Neef, a protégé of the Swiss educational reformer, Johann Pestalozzi, a follower of Rousseau who developed a curriculum in every discipline designed to imitate the way a child learns naturally in the real world, was invited to start a new school in Philadelphia after an American diplomat visited his orphanage school in Paris. Neef opened America’s first progressive school in 1809. Before it opened, he published the New World’s first strictly pedagogical book, its title showing both the influence of Rousseauean ideas and American national aspirations: Sketch of a Plan and Method of Education founded on the Analysis of the Human Faculties and Natural Reason, suitable for the offspring of a Free People and for all Rational Beings. Here are some passages from the description of mathematics instruction showing the influence of Rousseau:
From the moment a child learns to make the first use of its nerves, nature presents, unceasingly, to its eyes, a variety of objects; from which, at a very early period of its existence, it abstracts the notions of unity and plurality.

The power of combining numbers, is one of the noblest powers that have been given to man … how comes it then, that a power so noble has been debased in our schools to a merely mechanical, may I say, machine-ical operation?

As it is evident, that all our numerical notions proceed from objects, we shall, of course, begin our studies by them. Easily moveable things, as beans, pease, little stones, marbles, small boards, shall be our first instructors. To one bean we shall add one more, and after having carefully verified the sum resulting from this addition, we shall say, not one and one make two, nor one bean and one bean are two beans; but one time one bean, more one time one bean, is equal to two times one bean.

His “easily moveable things” are the 1808 version of modern manipulatives. By the 1850s Rousseauean educational ideas were dominant in the US and have remained so.

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