James' World 2

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You probably haven’t had to do longhand math in years, but you do mental math every day. Or maybe you google math problems ten times a day, because you’ve forgotten how to do any math beyond your basic multiplication tables. Here are some shortcuts that will help you do more math in your head.

Calculate percentages backward

X% of Y = Y% of X. You can always swap those percentages if doing the math is easier the other way around. So 68% of 25 = 25% of 68 = 68/4 = 17.

That makes a lot of calculations easy, once you’ve memorized the percentages that equal basic fractions:

• 10% = 1/10
• 12.5% = 1/8
• 16.666…% = 1/6
• 20% = 1/5
• 25% = 1/4
• 33.333…% = 1/3
• 50% = 1/2
• 66.666…% = 2/3
• 75% = 3/4

Subtract without borrowing digits

Mental subtraction is easiest when you can subtract each digit without having to borrow from the next place up. If the second number has some bigger digits than the first, it gets more complicated. To avoid borrowing places, you want to get rid of those bigger digits. Here’s how:

 

 

Say you’re calculating 925-734. That tens place makes things a little complicated. It’d be easier to calculate 925-724, and then subtract that extra 10 separately: 925-724 = 201, and 201-10 = 191. There’s your answer.

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Let me think…

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I teach people how to teach math, and I’ve been working in this field for 30 years. Across those decades, I’ve met many people who suffer from varying degrees of math trauma – a form of debilitating mental shutdown when it comes to doing mathematics.

When people share their stories with me, there are common themes. These include someone telling them they were “not good at math,” panicking over timed math tests, or getting stuck on some math topic and struggling to move past it. The topics can be as broad as fractions or an entire class, such as Algebra or Geometry.

The notion of who is – and isn’t – a math person drives the research I do with my colleagues Shannon Sweeny and Chris Willingham with people earning their teaching degrees.

One of the biggest challenges U.S. math educators face is helping the large number of elementary teachers who are dealing with math trauma. Imagine being tasked with teaching children mathematics when it is one of your greatest personal fears.

Math trauma manifests as anxiety or dread, a debilitating fear of being wrong. This fear limits access to life paths for many people, including school and career choices. There are many reasons people may develop negative associations with mathematics. The way students are positioned as “good at math” is often based on non-mathematical characteristics such as gender, race, language, or socioeconomic status. For example, Ebony McGee, an education researcher at Vanderbilt University, describes both fragile and robust mathematics identities that Black engineering and mathematics college students developed in response to negative stereotypes about their ability to learn and do mathematics.

While math trauma has multiple sources, there are some that parents and teachers have power to influence directly: outdated ideas of what it means to be good at math. These include speed and accuracy, which were important in decades past when humans were actual computers.

But research has confirmed what many people share with me anecdotally: Tying speed with computation debilitates learners. People who struggle to complete a timed test of math facts often experience fear, which shuts down their working memory. This makes it all but impossible to think, which reinforces the idea that a person just can’t do math – that they are not a math person.

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Even some teachers suffer from anxiety about math. Undrey/shutterstock.com

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You can find Dolomite all over the world. It’s a calcium magnesium carbonate found in the Dolomite Mountains in northern Italy (obviously), but also at Niagara Falls in North America and the White Cliffs of Dover in the U.K. Altogether, this useful construction mineral makes up some 2 percent of the Earth’s crust.

But in contrast to its relative natural abundance, scientists have failed to recreate dolomite in the lab for nearly two centuries, leading to what experts call the “Dolomite Problem.” But new work from scientists at the University of Michigan (UM) and Hokkaido University in Sapporo, Japan seems to have finally solved this geologic conundrum by leveraging proprietary software and dissolving crystalline defects with an electron beam. The results of the study were published in the journal Science this past November.

“In the past, crystal growers who wanted to make materials without defects would try to grow them really slowly…our theory shows that you can grow defect-free materials quickly, if you periodically dissolve the defects away during growth,” Wenhao Sun, UM scientist and the corresponding author, said in a press statement. “If we understand how dolomite grows in nature, we might learn new strategies to promote the crystal growth of modern technological materials.”

Dolomite is usually found in rocks older than 100 million years, meaning that this mineral take a long time to form. According to the researchers, this slow growth rate can be attributed to how dolomite’s crystalline structure forms. The mineral’s growth edge is made of alternating rows of calcium and magnesium, and in water, these elements randomly attach to the wrong places and prevent dolomite from forming. While the Earth has nearly infinite patience to wait out this slow growth (like, only one dolomite layer produced per 10 million years slow), humans—with their comparatively infinitesimally small lifespans—do not.

To figure out how to speed up this natural process, scientists needed to understand how these defects attach to the dolomite surface. Usually, this would take thousands of hours of supercomputing, but new UM software leverages a novel technique to complete these simulations “in 2 milliseconds on a desktop,” according to one researcher.

“Our software calculates the energy for some atomic arrangements, then extrapolates to predict the energies for other arrangements based on the symmetry of the crystal structure,” UM associate research scientist and co-author Brian Puchala, one of the software’s lead developers, said in a press statement.

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There is a rip in the armpit of Orsola de Castro’s jumper. She raises her hand high in the air so I can see it: a slash of pale skin peeks from tomato-red wool. This “memory hole”, as De Castro describes it, tells the story of the jumper’s long life. It was owned by her cousin, then her daughter. “It is very old Benetton, from when Benetton was still made in Italy. You can’t see it on Zoom, but this is really nice wool,” she says, arm still aloft.

De Castro, 54, is an activist, a lecturer, a former designer, and a co-founder of not-for-profit movement Fashion Revolution. With the release of her book Loved Clothes Last, she has also become a kind of anti-Marie Kondo. She advocates “radical keeping”, not decluttering. “The only antidote to throwaway culture is to keep. So I am an obsessive keeper,” she says.

The book is full of startling facts about fashion’s impact on the planet and its people. It is “as much about mending systems as mending clothing”, says De Castro. She had just four months to write it, so her daughter Elisalex de Castro Peake, who runs the independent sewing-pattern label By Hand London, and her colleague Bronwyn Seier helped with the research. “That meant that all I had to do was vomit words, which were nestling inside me, quite pumping to get out.” Those words are still pumping in today’s interview: she talks rapidly and lyrically, her eyes shining behind thick-rimmed cat-eye glasses, her salt-and-pepper curls trembling as she gestures energetically.

De Castro grew up in Rome. Her mother is an artist and runs a traditional printmaking school in Venice. Her father, who died when she was two, was a businessman. Her Venetian grandmother, whom she calls Nonna Stanilla, taught her how to crochet at the age of six. She moved to London at 16, did her A-levels, then had the first of her four children at 18. She made clothes for years, first with a small line of upcycled hats, then printed textiles.

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Embellish your imperfections. Photo by Iryna Khabliuk / EyeEm

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Maybe you know the routine. Every so often, I go through my refrigerator, check labels on the items, and throw out anything that’s a month, or a week, or maybe a few days past the date on the label. I might stop to sniff, but for my whole adult life, I’ve figured that the problem was obvious — my jam or almond milk or package of shredded Italian cheese blend had “expired” — and the fix was simple: Into the garbage, it goes.

This habit is so ingrained that when I think about eating food that’s gone past its date, I get a little queasy. I’ve only had food poisoning once or twice in my life, always from restaurants, but the idea is still there in my head: past the date, food will make me sick. You’ll probably never catch me dumpster-diving.

I know, on some intellectual level, that throwing away food is probably wrong. The statistics are damning. Forty percent of food produced in America heads to the landfill or is otherwise wasted. That adds up. Every year, the average American family throws out somewhere between $1,365 and $2,275, according to a landmark 2013 study co-authored by the Harvard Food Law and Policy Clinic and the Natural Resources Defense Council. It’s a huge economic loss for food growers and retailers, who often have to ditch weirdly shaped produce or overstocked food that didn’t sell.

Environmentally it’s bad, too. The study found that 25 percent of fresh water in the US goes toward producing food that goes uneaten, and 21 percent of input to our landfills is food, which represents a per-capita increase of 50 percent since 1974. Right now, landfills are piled high with wasted food, most of which was perfectly fine to eat — and some of which still is.

On top of this, I know that in the same country that throws away so much food, about 42 million people could be living with food insecurity and hunger. Yet state-level regulations often make it difficult to donate past-date food to food banks and other services.

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A scene like this greets most supermarket shoppers in the US. But much of what we think we know about food shopping needs an overhaul. Steve Pfost/Newsday/Getty Images

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