Menus Subscribe Search

Follow us


minus-symbol

(PHOTO: SIMINITZKI/SHUTTERSTOCK)

How All the Cool Kids Are Doing Subtraction

• December 11, 2013 • 10:00 AM

(PHOTO: SIMINITZKI/SHUTTERSTOCK)

The number line: it’s subtraction—except it’s addition.

I learned subtraction back in the heady days before global warming, when we trudged uphill both ways to school in three feet of fresh powder. It was a process, both the trudging and the learning, because walking through snow is only fun when you have nowhere to be and because borrowing the one never made much sense.

You may remember. You’re trying to take 99 from 183, so you line them up vertically:

183
-99
—-
=??

Except nine doesn’t go into three, so you need to borrow from the 10’s column, and then nine can go into 13, but then nine doesn’t go into seven so it needs to go into 17 and then, well, whatever, doesn’t someone have a calculator watch or something? Eventually, you figure it out, but it’s a pain and conceptually complex.

Fast forward a number of years, and I found myself on the subway, watching a school-age child dutifully doing his homework, a subtraction problem set, during his commute home. But instead of using the column method, he had some sort of horizontal line on his paper. I was fascinated. I didn’t ask him anything because that would have been creepy and weird and no one needs that on the F train at 3:30 in the afternoon, but I did some investigating when I got home.

He was using a number line, a newfangled way to do subtraction. It’s all the rage, apparently. You could go down the Google vortex in search of details or you could just watch this video, narrated by an unintentionally condescending British dude:

http://www.youtube.com/watch?v=JNo7hxngkDc

That’s fun. The concept has its roots in the discoveries of John Wallis, an English mathematician from the 17th century who served as chief cryptographer for Parliament and the royal court, and who is given credit for inventing the sideways-eight infinity symbol. He also helped develop infinitesimal calculus and has an asteroid named after him. (Impressive, but can he insert a link into a blog post? Doubtful.)

At first I thought it was really cool, and then I realized basically all you’re doing is changing a subtraction problem to an addition problem.

Anyhow. Back in the days of the colonies, the number line helped the masses conceptualize the idea of negative numbers, giving visualization to the fact that there was something below zero, i.e. to the left. Today, it has been co-opted to help youngsters learn subtraction.

It’s not a perfect system. A group of researchers studying the indigenous Yupno people of the Finisterre Range in Papua New Guinea found that number lines were not as engrained into the human brain as previously thought. “Our study shows, for the first time, that the number-line concept is not a ‘universal intuition’ but a particular cultural tool that requires training and education to master,” said Rafael Nunez, director of the Embodied Cognition Lab and associate professor of cognitive science in the University of California-San Diego Division of Social Sciences. “Also, we document that precise number concepts can exist independently of linear or other metric-driven spatial representations.”

At first I thought it was really cool, and then I realized basically all you’re doing is changing a subtraction problem to an addition problem. Someone using the number line gets the correct answer—assuming he or she understands the concept behind column addition and can add up the numbers—but do they understand the theory behind the subtraction? To me, admittedly someone who has never been trained in educational practices, some combination of the line method and the column method would seem like the best practice. But it’s interesting to see how how things like this evolve.

Now, please don’t get me started on the “1 up, 1 down” method.

http://www.youtube.com/watch?v=I6jinLA1AxA

Noah Davis

A weekly roundup of the best of Pacific Standard and PSmag.com, delivered straight to your inbox.

Recent Posts

October 24 • 4:00 PM

We Need to Normalize Drug Use in Our Society

After the disastrous misconceptions of the 20th century, we’re returning to the idea that drugs are an ordinary part of life experience and no more cause addiction than do other behaviors. This is rational and welcome.


October 24 • 2:00 PM

A Letter to the Next Attorney General: Fix Presidential Pardons

More than two years ago, a series showed that white applicants were far more likely to receive clemency than comparable applicants who were black. Since then, the government has spent hundreds of thousands of dollars on a study, but the pardons system remains unchanged.


October 24 • 12:00 PM

What Makes You So Smart, Middle School Math Teacher?

Noah Davis talks to Vern Williams about what makes middle school—yes, middle school—so great.


October 24 • 10:00 AM

Why DNA Is One of Humanity’s Greatest Inventions

How we’ve co-opted our genetic material to change our world.


October 24 • 8:00 AM

What Do Clowns Think of Clowns?

Three major players weigh in on the current state of the clown.


October 24 • 7:13 AM

There Is No Surge in Illegal Immigration

The overall rate of illegal immigration has actually decreased significantly in the last 10 years. The time is ripe for immigration reform.


October 24 • 6:15 AM

Politicians Really Aren’t Better Decision Makers

Politicians took part in a classic choice experiment but failed to do better than the rest of us.


October 24 • 5:00 AM

Why We Gossip: It’s Really All About Ourselves

New research from the Netherlands finds stories we hear about others help us determine how we’re doing.


October 24 • 2:00 AM

Congratulations, Your City Is Dying!

Don’t take population numbers at face value.


October 23 • 4:00 PM

Of Course Marijuana Addiction Exists

The polarized legalization debate leads to exaggerated claims and denials about pot’s potential harms. The truth lies somewhere in between.


October 23 • 2:00 PM

American Companies Are Getting Way Too Cozy With the National Security Agency

Newly released documents describe “contractual relationships” between the NSA and U.S. companies, as well as undercover operatives.


October 23 • 12:00 PM

The Man Who’s Quantifying New York City

Noah Davis talks to the proprietor of I Quant NY. His methodology: a little something called “addition.”


October 23 • 11:02 AM

Earliest High-Altitude Settlements Found in Peru

Discovery suggests humans adapted to high altitude faster than previously thought.


October 23 • 10:00 AM

The Psychology of Bribery and Corruption

An FBI agent offered up confidential information about a political operative’s enemy in exchange for cash—and they both got caught. What were they thinking?


October 23 • 8:00 AM

Ebola News Gives Me a Guilty Thrill. Am I Crazy?

What it means to feel a little excited about the prospect of a horrific event.


October 23 • 7:04 AM

Why Don’t Men Read Romance Novels?

A lot of men just don’t read fiction, and if they do, structural misogyny drives them away from the genre.


October 23 • 6:00 AM

Why Do Americans Pray?

It depends on how you ask.


October 23 • 4:00 AM

Musicians Are Better Multitaskers

New research from Canada finds trained musicians more efficiently switch from one mental task to another.


October 22 • 4:00 PM

The Last Thing the Women’s Movement Needs Is a Heroic Male Takeover

Is the United Nations’ #HeForShe campaign helping feminism?


October 22 • 2:00 PM

Turning Public Education Into Private Profits

Baker Mitchell is a politically connected North Carolina businessman who celebrates the power of the free market. Every year, millions of public education dollars flow through Mitchell’s chain of four non-profit charter schools to for-profit companies he controls.


October 22 • 12:00 PM

Will the End of a Tax Loophole Kill Off Irish Business and Force Google and Apple to Pay Up?

U.S. technology giants have constructed international offices in Dublin in order to take advantage of favorable tax policies that are now changing. But Ireland might have enough other draws to keep them there even when costs climb.


October 22 • 10:00 AM

Veterans in the Ivory Tower

Why there aren’t enough veterans at America’s top schools—and what some people are trying to do to change that.


October 22 • 8:00 AM

Our Language Prejudices Don’t Make No Sense

We should embrace the fact that there’s no single recipe for English. Making fun of people for replacing “ask” with “aks,” or for frequently using double negatives just makes you look like the unsophisticated one.


October 22 • 7:04 AM

My Politicians Are Better Looking Than Yours

A new study finds we judge the cover by the book—or at least the party.


October 22 • 6:00 AM

How We Form Our Routines

Whether it’s a morning cup of coffee or a glass of warm milk before bed, we all have our habitual processions. The way they become engrained, though, varies from person to person.


Follow us


Politicians Really Aren’t Better Decision Makers

Politicians took part in a classic choice experiment but failed to do better than the rest of us.

Earliest High-Altitude Settlements Found in Peru

Discovery suggests humans adapted to high altitude faster than previously thought.

My Politicians Are Better Looking Than Yours

A new study finds we judge the cover by the book—or at least the party.

That Cigarette Would Make a Great Water Filter

Clean out the ashtray, add some aluminum oxide, and you've (almost) got yourself a low-cost way to remove arsenic from drinking water.

Love and Hate in Israel and Palestine

Psychologists find that parties to a conflict think they're motivated by love while their enemies are motivated by hate.

The Big One

One company, Amazon, controls 67 percent of the e-book market in the United States—down from 90 percent five years ago. September/October 2014 new-big-one-5

Copyright © 2014 by Pacific Standard and The Miller-McCune Center for Research, Media, and Public Policy. All Rights Reserved.