A Quaker Education: William Gawthrop's Arithmetic for Young Ladies

Some of my favourite books to have in the shop are the ones that combine my interests in science and women's history, and today I had the pleasure of cataloguing a rare and delightful book on mathematics for "the use of young ladies". The Scholar's Introduction to Arithmetic; Designed for the Use of Young Ladies and the Junior Classes in Boys' Schools was published by William Gawthrop in Liverpool, probably in the 1820s or early 1830s (an owner's signature in this copy is dated 1832). It speaks to us not only about mathematics teaching in early-19th century Britain, but also about the history of women's education and the role that the Quaker religious community played in its advancement.

This charming volume covers all areas of arithmetic, including addition and subtraction, simple and compound multiplication and division, and fractions. Written with a thoroughly practical outlook, the practice problems (and tables of weights and measures in the appendix) focus on day-to-day situations that would be encountered by the children of the working classes, especially young women who would one day manage households.

There's a very good reason for this focus on practical mathematics, and it's connected to the author's religious background. William Gawthrop was a member of a Liverpool Quaker family. His 1781 birth is recorded in that city’s Quaker Registry, and he attended the renowned Ackworth School, a Quaker institution that was founded in 1779, was co-educational from its inception, and is still operating today (Ackworth School Catalogue, 1831).

According to a note on the verso (back) of the title page, at the time this book was published Gawthrop was living in Liverpool’s Brownlow Street (in what is today the University quarter) and was “instruct[ing] young Ladies in Writing, Accounts, English Grammar, Geography and History, Ancient and Modern, the Use of the Globes, the Construction of Maps, and Chronology”.

It is also likely that this was the same Gawthrop who, in October 1841, began publishing Gawthrop’s Journal of Literature, Science and Arts, a bi-weekly magazine devoted to educational and uplifting content for a broad range of readers, including women and working men. Probably the first such publication local to Liverpool, it offered poetry and prose, scientific information, political opinions, philosophical essays, and reports on the lectures given at educational  institutions in Liverpool and Manchester, including the Mechanic’s Institution for working men. The Journal was printed by Hugh Gawthrop, who was almost certainly William’s brother (his father’s name also being Hugh). Advertised next to the printer’s details is Gawthrop’s Arithmetic and Table Book, “which may be had from the Booksellers”, and is possibly a later version of the present book.


Gawthrop’s interest in education, particularly female education, would surely have arisen from his background as a Quaker, or member of the Society of Friends, the group that did so much to advance the causes of universal education, women’s rights, and the anti-slavery movement.

“From the beginning of Quakerism, individual Friends viewed the extension of learning to all, regardless of class, race, or gender, as a religious obligation… As with other reform and philanthropic movements, Friends appear to have had an impact out of all proportion to their small numbers in the wider society" and they "have often been associated with educational ideals that appear years ahead of their time” (The Oxford Handbook of Quaker Studies, p. 412).

Quaker education was strongly practical, meant to equip the student to be a productive member of society. Quaker girls received a more academic education than most other women at the time, but their roles were still circumscribed by gender. “A man might need mathematical skills to calculate a ship’s tonnage. A woman would also need mathematics, but she would put her knowledge to a more domestic use: calculating cloth yardage or recipe ingredients” (Branson, Those Fiery Frenchified Dames, p. 15).

As we have seen, household measurements and expenses are the main theme of the practice problems in this book, but the examples also reflect the author’s teaching and social welfare interests...

Bought at a sale, Johnson’s Dictionary for 3l. 7s. 9d., Blair’s Lectures for 1l. 4s, 8d., Gregory’s Mechanics for 1l., 5s. 6d., Moore’s Fables for 3s. 5d., Wilkinson’s Atlas for 1l. 9s. 10d., Hume’s England for 5l. 18s.; Sterne’s Works for 2l. 13s. 9d…. what did they all come to?

The clothing of 100 charity children costs £173l. 6s. 8d. what was the expense of each?

...as well as his preoccupation with publishing. There are a number of questions about the price of paper and cost of publishing books:

A bookseller intends to publish 1204 copies of a new work, each copy contains 12 sheets, how many reams of paper will it require?

This book is rare in part because most copies would have been used to destruction by children. A worldwide library catalogue search locates no copies of the first or second edition, and I was only able to find one copy of this edition (the third), at James Madison University in Virginia. This copy also includes some interesting pencilled annnotations demonstrating that at some point it did fulfill its purpose as a textbook (see photo above), but it is still in remarkably fresh condition given its intended use. Most suggestively, there is a faint ownership inscription on the cover which appears to read "Miss Mary [Edward?]", indicating that it was owned by a young lady at some point (see photo below). This volume is indeed an evocative record of the Quaker drive for universal education and the history of mathematical education for women.


Laura Massey
Laura Massey


Alembic founder Laura Massey holds a bachelor's degree in the history of science from Georgia Tech and a master's in book history (focusing on medieval and early modern scientific and medical books,) from the Institute of English Studies at the University of London. She has worked as a cataloguer, bookseller, and blogger in libraries and bookshops in the United States and Britain.

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