After Failing Math Twice, a Young Benjamin Franklin Turned to This Popular 17th-Century Textbook

Before Benjamin Franklin became a printer, newsman, author, inventor, philosopher, diplomat and founding father of the United States, he failed math twice.

In 1715, Franklin’s money-conscious father removed his young son from the Boston grammar school that might have led to a college education and sent him to learn writing and arithmetic in preparation for a printing apprenticeship. As Franklin later recalled, he “acquired fair writing pretty soon, but I failed in the arithmetic and made no progress in it.”

By age 16, “being on some occasion made ashamed of my ignorance in figures, which I had twice failed in learning when at school,” Franklin continued, “I took Cocker’s book of arithmetic and went through the whole by myself with great ease.”

This brief account of the statesman’s mathematical education is a well-known digression in Franklin’s autobiography. Few authors have failed to spot the irony in one of the 18th century’s most recognizable polymaths struggling with basic number skills. Yet the story of the “book of arithmetic” that finally helped Franklin master the subject is little known today—another irony, because in his day, it was every bit as famous as he was.

Cocker’s Arithmetick was probably the most successful elementary math textbook published in English before the 19th century. It epitomized an age in which the expanding worlds of commerce and capitalism, education and Enlightenment, coalesced to make basic arithmetic the classroom staple it is today. In many ways, the story of its success mirrors that of the man whose face now adorns the $100 bill.

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Though perhaps unfamiliar to modern readers, in the 18th century, Cocker’s Arithmetick was as close to a household name as any math textbook is likely to ever be. Edited from the writings of London-based teacher Edward Cocker and published posthumously in 1678, the book included lessons on basic arithmetic with a commercial slant, posed as a set of rules to be memorized, as was typical of educational books of the day.

Cocker’s lessons covered addition, subtraction, multiplication and division, as well as calculation with pre-decimal British currency and a gentle introduction to 17th-century England’s bamboozling array of weights and measures. Many pages were devoted to the “rule of three,” which permitted the reckoning of a fourth value in proportion to three others: For example, “If 15 ounces of silver be worth 3 [pounds] 15 [shillings], what are 86 ounces worth at that rate?” Finally, the textbook taught arithmetic skills for business, such as dividing profits equitably between partners.

This was hardly riveting stuff, even for an inquisitive mind like Franklin’s. But Cocker’s Arithmetick possessed crucial advantages that made it a best seller from its earliest days. Priced at 1 shilling, it was within almost any budget, and it was highly portable, barely larger than today’s smartphones.

More significantly, in the cutthroat world of the London book trade, Cocker’s Arithmetick was available to a vast audience in search of short, cheap and popular printed material. The book’s first publisher was Thomas Passinger, whose shop, the Three Bibles, was perched on the medieval London Bridge. In the 17th century, the bridge was not only the most important crossing point over the River Thames but also a bustling shopping district.

The Three Bibles wasn’t the place to purchase pricey scholarly tomes. It was where book buyers and traveling sellers picked up the latest pamphlets, storybooks, almanacs and ballad sheets for pennies apiece.

This was the market to which Cocker’s Arithmetick belonged. Judging from contemporary catalogs and advertisements, booksellers saw the text not as a mathematical treatise or schoolbook, but rather a piece of popular literature worthy of mass attention.

And they were right: Cocker’s Arithmetick was an instant best seller. Its second or third impression appeared within a year, and thereafter, it was continually reissued at a rate of roughly one new edition annually until the mid-18th century. Edward Cocker, who had been dead since 1676, became a household name as his book surpassed the status of a mere educational text. It was now a cultural icon.

In 1755, the great literary figure Samuel Johnson borrowed some of Cocker’s terms for his monumental Dictionary of the English Language. A play published the following year deemed the text the “best book that ever was wrote.” Cocker’s work also provided the first steps in arithmetic for the 18th-century mathematician Thomas Simpson, the Romantic poet John Clare and the radical reformer Samuel Bamford. Such was the ubiquity of Cocker’s Arithmetick that by the late 18th century, the phrase “according to Cocker” had come to mean “exactly right.”

The book’s 1787 edition was the last of roughly 70 that had come before, produced not only in London but also Edinburgh, Glasgow, Dublin and Belfast. The 19th-century bibliographer Thomas Frognall Dibdin can hardly have been exaggerating, then, in his assessment that Cocker’s Arithmetick had “probably made as much stir and noise in the English world as any [book]—next to the Bible.”

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Cocker’s Arithmetick had taken the British Isles by storm, but what was its fate across the Atlantic? Franklin’s was an age in which arithmetic was not yet a core part of American elementary education. The number of schools teaching the subject was growing in the first half of the 18th century, but it remained low, and the quality of tutors was often dubious. Although Franklin was fortunate to have a master in his writing and arithmetic teacher, George Brownell, whom he remembered as “very successful in his profession generally,” still the young man failed to learn arithmetic in the classroom.

Yet it was exactly these limitations that bolstered the success of books like Cocker’s Arithmetick. They were designed for self-teaching and could be used in those few spare hours afforded by a busy working week. Many such books were published in England, and America’s first equivalents were often imports or reprints of English titles. Franklin’s elder brother James Franklin printed one of the first in 1719, an edition of the English Hodder’s Arithmetick. An American impression of Cocker’s text may have even been printed in Philadelphia in 1779, although no example is known to survive.

Whatever the case, a copy of Cocker’s Arithmetick found its way to Franklin around 1722, predating his first visit to England in 1724. It was an encounter of the sort that was becoming ever more common during the 18th century, as wider cultural developments propelled arithmetic into the mainstream. The emergence of a capitalist market economy put ever greater demand on quantification (the act of counting or measuring the quantity of something), calculation and bookkeeping skills. At the same time, arithmetic became central to the educational ambitions of the Enlightenment.

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Franklin is now synonymous with a quantitative, capitalist spirit of which the famous “time is money” dictum is just one illustration. Cocker’s Arithmetick must have played at least some part in the formation of this worldview. Like so many of his generation, Franklin grew up around the idea that Cocker was arithmetic. At age 7, well before he used the book to teach himself, he received a poem from his uncle imploring him to “excel great Cocker with thy quill; / So imitate and [his] excellence rehearse / Till thou excel his cyphers, writing, verse.”

Cocker’s Arithmetick depicted a world that was commercial and utterly quantifiable. It was both a popular commodity, likely to fatten the margins of any bookseller, and a text that exalted the value of commerce on every page. Lucrative transactions were the scenarios presented in many of the book’s example questions: a grocer selling peppers, a draper reckoning his profits. Even the plumber was depicted selling lead rather than using it. On the book’s value to the merchant, Cocker’s preface was bold and unambiguous: “Let his own profitable experience be judge.”

It's little wonder, then, that once established as a printer and publisher, Franklin counted arithmetic books among his wares. Though he never produced copies of Cocker’s Arithmetick, it was available for purchase at his shop at the Post Office on Market Street in Philadelphia. Later, in 1753, Franklin published an edition of George Fisher’s The American Instructor, which also contained lessons on arithmetic.

By then, as Franklin well knew, the growing cultural value of arithmetic had enabled the mathematics branch to surpass the status of a mere utilitarian skill. Now, it was a subject of general mental refinement, the epitome of the “useful knowledge” so cherished by Enlightenment educationalists. Franklin’s 1749 pamphlet on the education of Pennsylvania’s youth laid out a proposed curriculum synthesizing the ideas of some of the era’s weightiest authorities on educational matters, above all John Locke, whose vastly influential 1693 treatise, Some Thoughts Concerning Education, was unequivocal in stressing arithmetic’s importance.

Whatever else a student might learn in Franklin’s grand scheme of general instruction, which included everything from oratory and ancient customs to drawing and geography, he maintained that arithmetic was “absolutely necessary.”

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Toward the end of his life, in a well-known letter of 1784, Franklin reflected in satirical fashion on the importance of waking early in order to save money that would otherwise be spent burning candles at night. As he wrote, his “love of economy induced me to muster up what little arithmetic I was master of, and to make some calculations.”

Franklin, then serving as America’s first diplomat, estimated that Paris was home to 100,000 families, which each burned candles for seven hours per night. Over the six months between March and September, this equated to 128,100,000 hours, requiring 64,050,000 pounds of wax at a cost of 96,075,000 French livres.

Perhaps Franklin’s arithmetic wasn’t so bad after all. At the very least, he had a deep appreciation for the importance of quantification, which was visible in his highly successful annual almanac, Poor Richard, with its calendars and astronomical information, as well as his pioneering work on demography and his wide array of mathematical interests.

But this modesty regarding the “little arithmetic” that Franklin understood suggests a self-consciousness of the limits of his abilities in calculation. Perhaps it stemmed from his struggles learning the subject in childhood. More certainly, he understood that arithmetic was both a genuinely useful subject and an increasingly fashionable enterprise. When it came to preparing his autobiography, therefore, the tale of his struggle to overcome these difficulties fit perfectly with the image he was trying to create as a determined, self-made, enterprising man of letters.

The complementary forces of print and profit, commerce and calculation, converged in Franklin’s life story as in the pages of Cocker’s Arithmetick. He had mastered the subject using that very textbook after school lessons failed. He achieved commercial success as a publisher who sold arithmetic books, an author exalting the importance of math education and a thinker to whom the world was quantifiable. It was a tale of which Edward Cocker himself would have been proud.

James Fox | READ MORE

James Fox is a historian and postdoctoral researcher at the University of St. Andrews in Scotland and a co-editor of the history of knowledge blog Scilicet.