Can A New Symbol Make You Better At Math?

Math popularizer Rob Eastaway thinks his "zequals" sign will help people get better at back-of-the-envelope calculations.

"Mental math" is a pain. Totting up simple sums like 1,900 + 700 is easy enough to do in your head (just drop the zeros), but what about 248 x 84? To do that, you’d have to mentally simulate the tedious algorithm you were taught how to do on paper in elementary school. No wonder we just whip out our calculators, even for simple arithmetic. But math popularizer Rob Eastaway thinks this is a shame, because outsourcing even simple sums to software robs us of the opportunity to build a "feel for numbers" that keeps us connected to what these digits actually mean. He’s invented a new mathematical symbol called "zequals"--and a little mental estimation trick to go along with it--that he hopes will encourage normal people to do more math in their heads, and become more number-literate in the process.

Estimation, Eastaway says, is the key to getting a grip on math. You already do it all the time, but you don’t learn it in school as a distinct mathematical skill because math is supposed to be, well, exact. "After all, estimates are inevitably the ‘wrong’ answer, and most people are struggling just to come up with the ‘right’ answer that’s in the back of the textbook," Eastaway tells Co.Design. At the same time, estimation is how math often looks in the real world. "Many people develop the knack of estimating when they discover a real need for it: business people assessing the viability of a project, engineers looking at how long a job is going to take," he says. "In these examples, it’s the ballpark figure that’s important, not the number to its third decimal place."

But if this "back of the textbook" thinking has made your feel for numbers crap in the first place, you’re not going to be able to even do estimations very well. Eastaway wanted to train teenagers to be better estimators, "and I thought it would be more memorable to have a symbol," he says. "I wanted something that looks like equals but is ‘sharper’ (it’s as if you are sawing off all the other digits) and discovered there’s a standard Aquarius symbol that looks like that, and which can be found on any keyboard as the letter h in Wingdings font."

Of course, a new symbol isn’t much use if it doesn’t mean anything. Eastaway intends zequals as a kind of graphic mnemonic device for a simple but surprisingly accurate estimating procedure he calls "ruthless rounding." "The rule is that whenever you encounter a number, you 'zequal’ it by rounding it to a single digit followed (if it is larger than ten) by zeroes," he wrote in The Guardian. In my example above, 248 x 84 becomes 200 x 80. Easy enough to multiply: That’s 16,000. What makes the estimation "ruthless" is that you zequal the answer, too: It rounds up to 20,000. Which brings it pretty darn close to the exact answer (20,832).

Why does this matter? Like Bret Victor’s Kill Math project, Eastaway’s zequals sign is a reaction against the learned helplessness that most of us have accepted in our relationship with numbers. In a very real sense, the "interface" for math is broken for regular people: Numbers are abstruse, abstract, and best left to computers. There’s nothing wrong with having software crunch numbers for us, but when it’s at the expense of our own basic numerical literacy, that’s not a good thing. Having a "number sense," Eastaway writes, "helps you to interpret the numbers that are fed to you by politicians, the media and your financial adviser and to decide whether those numbers deserve to be challenged (as they often do)."

Zequals may never make it into the pantheon of "real" mathematical notation, but that’s fine. Even if it persists as a kind of graphic-design reminder that numbers don’t have to be intimidating to regular people, we’ll be better off for it.

[Read more about Zequals]

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  • Random

    I think you mean 250 * 80 is 20,000 which is a good estimation.

    The symbol for approximate (a tilde over a tilde) has been used in exactly this way for a LONG time as VIXBRO says though I have no complaint about popularizing mental estimation techniques and relevance.

  • Rob Eastaway

    The approximation symbol has indeed been used in a similar way, but not in EXACTLY this way, because the approx symbol does not have strict rules attached about the number of significant figures. In fact the approx symbol has no official rules at all. You might use the approx symbol to say "382 x 9.1 is approximately 3800 (380 x 10)" and that's fine.  The difference with Zequals is that it DOES have rules, that you always have to round a number to one significant figure.  The end approximation may be less accurate (or it may be more accurate) but what Zequals does do is always reduce every calculation to one that involves no more than a knowledge of basic times tables.

  • Helen Purves

    What's wrong with using something that already exists, if it means the same thing?  Which it does, in this case. Why reinvent the wheel?