Small, Compared to All that Work
I spend a lot of my time as a stay-at-home-mom as a chauffeur, shuttling my kids between school, playdates, and activities like art class, karate and ballet. All that time in the car makes for a wonderful opportunity to listen to books on tape. Most recently we have been listening to the Little House books by Laura Ingalls Wilder and I was particularly struck by a story about work in Farmer Boy.
Farmer Boy tells the story of a nine year old boy named Almanzo. The child lives and works on a farm with his family in New York in 1866. At the independence day celebration in the small town near the family farm, Almanzo watches his cousin Frank, a city boy, buy a glass of lemonade for a nickel. Frank brags that his father gives him money any time he asks and dares Almanzo to ask his father for money. When Almanzo asks his father for money, the answer is not simple but it is powerful.
“Almanzo, do you know what this is?’
‘Half a dollar,” Almanzo answered.
‘Yes. But do you know what a half a dollar is?’
Almanzo didn’t know if was anything but half a dollar.
‘It’s work, son,’ Father said. ‘That’s what money is; it’s hard work.’”
Almanzo’s father asks him to describe the long hard process of raising potatoes to sell, which he does. Then his father asks,
“‘How much do you get for a half a bushel of potatoes?’
‘Half a dollar,’ Almanzo said.
‘Yes,’ said Father. ‘That’s what’s in this half-dollar, Almanzo. The work that raised half a bushel of potatoes is in it.’
Almanzo looked at the round piece of money that Father held up. It looked small, compared with all that work.”
That last point, “It looked small, compared to all that work,” stuck with me. In the days that followed hearing it for the first time, my mind tumbled it around and settled on a tangentially-related experience I had as a math teacher at a small university in the Pacific northwest. It was an argument I had with another teacher about whether or not students should learn to do arithmetic with pencil and paper when calculators could do it for them.
It should be known that I love math. I love the patterns, the logic, the comfort of answers that can be right or wrong. When I complete a calculation or other problem and it doesn’t feel right or I otherwise know that it is wrong, I like hunting for and finding my errors. I enjoy the mental work of it. In fact, I believe in the value of that mental work. I think it makes people better, more confident, smarter than they were before learning math. I also believe that wrestling with the math develops an intuition about number, quantity and space that can only happen through experience.
As you might imagine, when I taught math I did it “old school.” I insisted that they write numbers and letters and symbols on paper, demonstrating the mental work they did to make calculations, simplify algebraic expressions, or solve equations. I considered it my responsibility to empower my students to do math and demonstrate their knowledge this way. I believed that they became more confident, smarter, and better people for making that time-honored journey through the material. Plus, that is why they were enrolled in college, right? To practice and perfect a better way of thinking.
So when my colleague told me that he does not bother teaching his students how to compute fractions by hand, only to calculate them with a machine, I thought he was robbing them of learning they deserved. By limiting the students’ math lessons to punching keys on a calculator, he deprived them of the opportunity to work, to become smarter. Which is the entire point of being a student.
Not only that, but as an algebra teacher, I thought he was handicapping their future math learning. If they could not compute numerical fractions like ½+⅓ then they would be at a huge disadvantage when I asked them to simplify the expression x/2 + x/3. And the inability to perform such a small task has huge ramifications when you consider that x/2 could represent half of anything - half of your grade, half of the milk in your refrigerator, half of your salary, half of your time, half of your tank of gas, half of the votes for president.
Making math students dependent on a calculator to add fractions is like making babies dependent on walkers. It may seem like a good idea immediately - a fun technology to mess around with - but it is in fact detrimental to natural development, natural learning.
Don’t get me wrong. I realize that in order to thrive in modern life, people need to learn to use calculators (and the computer counterparts). However, I also believe that we have right and responsibility to understand technology and the work it does for us. If we do then we can make informed choices about when and how to do our work: When is it appropriate to “goggle in” (a phrase I found in the book Snow Crash) to a computer screen and when is it time to wrestle with mental work of the day? Should we drive a car when walking would suffice?
If, like Almanzo recognized that a half dollar is small compared to the work it took to earn it, we recognize that punching keys on a calculator to compute numbers is small compared to all the mental work of adding fractions then we will realize the true value of the technologies we have at hand.
We will be less dependent on technology, less likely to be crippled without it, and more likely to be unafraid of work.