Algebra and Tom Sawyer's Fence

[Thanks to PBS for hosting this excerpt.]

We educators -- especially those math educators who more and more are apologizing for math and even suggesting we should not teach Algebra -- could learn something from Tom Sawyer. So could Mark Twain. Twain wrote the unforgettable passage in which Tom Sawyer coaxed other boys into paying him to do his fence-painting chore, then drew from it the wrong lesson on human motivation:

In order to make a man or a boy covet a thing, it is only necessary to make the thing difficult to attain.

True, the story begins with Tom trying to buy Jim's assistance to no avail. Later Tom refuses to let Ben paint the fence, and later still he has the whole neighborhood lined up to paint the fence, paying him for the privilege. So what makes me think Twain got it wrong?

Twain missed a critical link from his own tale, one germane to the importance of doubling down on Algebra even as we struggle to find a way for kids to master it: why did they want to paint the fence? Because Tom said, No? Um, no. Look closely at the seminal exchange and see if you can spot the true motivational engine at work. Beginning with Tom:

“What do you call work?” 

“Why, ain’t that work?” 

Tom resumed his whitewashing, and answered carelessly:

“Well, maybe it is, and maybe it ain’t. All I know, is, it suits Tom Sawyer.” 

“Oh come, now, you don’t mean to let on that you like it?” 

The brush continued to move. 

“Like it? Well, I don’t see why I oughtn’t to like it. Does a boy get a chance to whitewash a fence every day?” 

That put the thing in a new light. Ben stopped nibbling his apple. Tom swept his brush daintily back and forth – stepped back to note the effect – added a touch here and there – criticised the effect again – Ben watching every move and getting more and more interested, more and more absorbed. 

Presently he said:

“Say, Tom, let me whitewash a little.”

Tom has not said, No, but the bait has been taken. Now Tom will set the hook (and drive monetization) by saying No, but his success hung on first highlighting the intrinsic reward of work done well. Here is the key bit again:

Tom swept his brush daintily back and forth – stepped back to note the effect – added a touch here and there – criticised the effect again  – Ben watching every move and getting more and more interested, more and more absorbed. 

Twain's cynicism, I wager, would be lost on anyone in the painting craft.

"Of course," they would think. "There are a hundred details to get right, details one knows only after painting a thousand fences."

And Mark does seem to know that:

You see, Aunt Polly’s awful particular about this fence – right here on the street, you know – but if it was the back fence I wouldn’t mind and she wouldn’t. Yes, she’s awful particular about this fence; it’s got to be done very careful; I reckon there ain’t one boy in a thousand, maybe two thousand, that can do it the way it’s got to be done.

Thus Tom is saying No, but it is a reluctant No driven by concern for performance: this work is hard and it matters and I would love to say Yes but this has to be done right.

Tom did not turn fence-painting into a game, nor did he make fence-painting somehow relevant to the boys' larger lives. He did not reward them -- he charged them! -- and he did not say they would need fence-painting skills later in life. He simply made it challenging.

We all take pride in a job well done and thus are drawn to challenges at which we might succeed. Look at video games, the single-player kind. The worst thing you can say about a game is that it is too easy to beat. Graphics, music, sound effects, and all the gamification in the world cannot save a game that is too easy to beat.

Why is that? Because the key lure of single-player games is the endorphin rush of success after substantial struggle, and the more struggle the bigger the rush. (Enhancing learning retention, research shows..) There is nothing like mastering something hard, nothing like performing well, meeting an unbending standard. When I complete a level it is because I can perform at that level: one does not pass the Professional Driver's License exam on Gran Turismo by luck.

Tom understood how to make hard work attractive: magnify for your audience the satisfaction of excellence. But US educators today are apologizing for Algebra, the doorstep to one of our greatest cultural wins, mathematics. We strive to make this purest of sciences relevant, as if it were not. We create games that teach mathematics and from that kids learn that we do not think math is worth learning in its own right. We even argue that one should be allowed a college degree without passing Algebra.

That is a losing game. If we want kids to stop showing up for college without fundamental skills in the three Rs, we will need their help: their hard work, their satisfaction in mastering skills that do not need to justify their worth.

We are apologizing for learning being hard. Tom knew that that is half of learning's appeal.