Books / History

Can you solve these 19th-century math problems?

In 1895, a little book the size of an unambitious romance novel was published in Boston. Bound in mud-brown cloth, it was to become the bane of legions of American schoolchildren.

The deceptively slim textbook, titled Mental Arithmetic, is divided into just five chapters, each of which contains about forty brief but increasingly dispiriting lessons covering the topics of addition, subtraction, animal husbandry, berry picking, haberdashery, child labor, and the class struggle between the agrarian proletariat and the suit-buying, omnibus-riding, quire-of-paper-buying urban bourgeoisie.

Mental Arithmetic book

What can a 21st-century student expect to learn from Mental Arithmetic? Not much … at first.

5 minus 0? Of course you can do that in your head! 1 plus 8? Easy! No pencil or quire of paper required. But all too soon, the simple formulae give way to story problems, and 1895 America unfolds in all its countrified glory.

Author G.A. Wentworth was hep to the hobbies and habits of the bucolic brats of yesteryear; thus many bushels of potatoes change hands in Mental Arithmetic, Durham and Jersey cows are counted, boys tally hornets and flies for fun, and nobody ever seems to have more than 18 cents to their name.

Work your way through Mental Arithmetic and you will learn that you can get a suit for $30 and a gun for $11. A Bible, however, will set you back just $9. Which is worth more in this rural sphere?

All is rosy while we’re adding mittens and gloves knit by some overworked spinster eking out a living in the Heartland. But then subtraction is introduced in Lesson 17, and things take a dark turn.

Six horses have distemper! Five peach trees are blighted! A fox carries off eight turkeys! Our farm is ruined! We must seek work off the homestead. A man earns $30 for a week’s work, while a boy gets but $9. How many of the farmer’s fourteen children must be sent out to engage in child labor for the family to survive the bitter winter?

Berry picking seems to be the dominant form of employment for children in Mental Arithmetic; it’s a career pursued by a multitude of mathematically-inclined boys, including a trio unironically named Tom, Dick and Harry. For the book-learned, a job in an office downtown (oh, dirty, dirty city!) might give you the chance to write seventy-two letters in six days, or copy eight pages of business text before sundown while praying that the photocopy machine gets invented soon.

Mental arithmetic problems

Though we read about the comings and goings of many rustic children in Mental Arithmetic — including Maggie, Maud, Frank, Joseph, and the triune berry-reaping machine Tom, Dick and Harry — a strange character gradually makes his or her presence felt. That person is simply referred to as “I,” a terrible foe who tempts the starry-eyed students of the 19th century to roll around in a patch of poison envy.

I’m a boss; I’ve got it all goin’ on. I pay just $5 per week in rent, own not one but two suits, and am saving up to buy a bicycle. As the lessons fly by, I make extravagant claims, boasting that I memorize poetry and only play for 19 minutes a day. I can read 98 pages between dinner and bedtime. And I can “skate up the bridge against the wind” in just 15 minutes, which simply sounds like the mad boast of a sociopath.

And then, just out of spite, our peculiar first-person narrator tosses out a Zen koan:

“If I had 9 children, I should have 14; how many children have I?”

Wha…t?

But to return to the actual purpose of Mental Arithmetic, all of the problems in the opening pages are quite doable sans paper or calculator by a modern third-grader or mildly intoxicated adult.

But live in fear! It won’t be long before the insidious arithmetical pedagogue slyly demands, “On Monday, I sold 3/7 of my pears; on Tuesday, I sold 16 more than 1/2 of the remainder, and had 20 pears left. How many had I at first?”

And then, “A piece of cloth measured 12 2/3 yd. before sponging and 11 5/6 yd. after sponging. How much did the cloth shrink?”

And yet again, “if a boy weighing 70 3/4 lb. rides a bicycle weighing 20 2/3 lb., what is the weight of both?”

Quick! How many pears? How much cloth? How much boy and bicycle? Do you want Teacher to get the paddle? How many? How much? The farm is counting on you!

Oops, you just failed 19th-century elementary school. Better pray you can get a job picking berries.

the-delve blog