The “value of estimating”

Here is another way to help students develop their mathematical skills: learn how to estimate.

Quick, take a guess: how tall is an eight-story building? How many people can be transported per hour on a set of train tracks in France? How many barrels of oil does the U.S. import each year?

Maybe you gave these questions your best shot – or maybe you skimmed right over them, certain that such back-of-the-napkin conjecture wasn’t worth your time. If you fall into the second, just-Google-it group, you may want to reconsider, especially if you’re a parent. According to researchers who study the science of learning, estimation is the essential foundation for more advanced math skills. It’s also crucial for the kind of abstract thinking that children need to do to get good grades in school and, when they’re older, jobs in a knowledge-based economy.

Parents can foster their kids’ guessing acumen by getting them to make everyday predictions, like how much all the items in the grocery cart will cost. Schools, too, should be giving more attention to the ability to estimate. Too many math textbooks “teach how to solve exactly stated problems exactly, whereas life often hands us partly defined problems needing only moderately accurate solutions,” says Sanjoy Mahajan, an associate professor of applied science and engineering at Olin College…

Sharpen kids’ logic enough and maybe some day they’ll dazzle people at cocktail parties (or TED talks) the way Mahajan does with his ballpark calculations. His answers to the questions at the top of this story: 80 ft., 30,000 passengers and 4 billion barrels. To come up with these, he guessed at a lot of things. For instance, for the number of barrels of oil the U.S. imports, he made assumptions about the number of cars in the U.S., the number of miles driven per car per year and average gas mileage to arrive at the number of gallons used per year. Then he estimated how many gallons are in a barrel. He also assumed that imported oil is used for transportation and domestic for everything else. The official tally for U.S. imports in 2010 was 4,304,533,000 barrels. Mahajan’s 4 billion isn’t perfect, but it’s close enough to be useful – and most of the time, that’s what counts.

It sounds like estimation helps with problem solving skills and taking known or guessed at quantities to develop reasonable answers. I tried this question about the barrels of oil with my statistics class today and we had one guess of 4 billion barrels (among a wide range of other answers). This also suggests that there is some room for creativity within math; it isn’t all about formulas but rather takes some thinking.

This reminds me that Joel Best says something similar in one of his books: being able to quickly estimate some big figures is a useful skill in a society where statistics carry a lot of weight. But to do some of this, do people have to have some basic figures in mind such as the total population of the United States (US Census population clock: over 312 million)? Is this a commonly known figure?

The article also suggests ways to take big numbers and break them down into manageable and understandable figures. Take, for example, the national debt of the United States is over 15 trillion dollars, a figure that is perhaps impossible to comprehend. But you could break it down in a couple of ways. The debt is slightly over \$48k per citizen, roughly \$192k per family of four. Or you could compare the debt to the yearly GDP.