U.S. Education by the Numbers

Today, more students are enrolled in school than ever before. And the trend is accelerating. In fact, all of the population numbers in this article have increased by about ten percent in the past ten years; in the next decade, the acceleration will increase. For the moment, let’s focus on the U.S., and, in time, in future articles, the view will expand. Note that much of his information comes from the National Center for Education Statistics.

Before we dig deeply, I suppose it’s interesting to note that there are about 99,000 public schools (including just over 5,000 charter schools), plus more than 33,000 private schools.

640px-College_graduate_studentsThis year, there are slightly fewer than 50 million public school students, including about 15 million high school students in public school. Add another 5 million students in private school, including over 1 million in private high schools.

Each year, about 4 million students start high school. (Actually, the number is about 3.7-4.0 million). Remember that number: it’s the basis for some arithmetic below.

There are many ways to calculate high school graduation rates, and the Federal government has been improving the reliability, accuracy and precision of these metrics. Distribution is uneven: students in some ethnic groups, who live in some states or cities or districts, may fare better or worse (as poorly as 1 in 2 graduating, for example).

In our simple (and, perhaps, simplistic) calculation, it would be fair to assume that about 4 million students start high school and about 3 million finish high school.

About 2 in 3 males, and about 3 in 4 female, enroll in college.

Each year, just under 2 million bachelor’s degrees, plus just short of a million earn an associates degree. And although not everybody earns a bachelor’s degree in four years or an associate’s degree in two years, on average, the vast majority of people who graduate high school–that is, about 3 in 4 of the people who started ninth grade–earn a college degree.

What’s more, nearly one million advanced degrees (masters, doctorate) are awarded every year. It’s fair to assume more than a half million people earn these degrees each year–or about 1 in 6 f the people who graduated high school.

Taking this into the workplace, in 2010, nearly 3 out of 4 college graduates were employed, in comparison with just over 1 in 2 people with only a high school diploma. On average, those college graduates also earned more money: over $45,000 for the college graduates compared with just under $30,000 for high school graduates without a college degree.

All of this sounds terrific, but I wonder whether the numbers are correct.

Last spring, The Atlantic published an article that placed just over 40 percent of 18-24 year olds in college, and offered a graduate rate (within a generous six years) of just 56 percent. If I understand this story correctly: roughly 20 percent of 24 year olds earn a college degree. The Atlantic story was inspired by a report prepared by Reuters.

So why does the National Center for Education Statistics report 1.8 million bachelor’s degrees per year? (I may not be comparing [teacher’s] apples to apples, but this discrepancy seems to be quite large.)

The purpose of this article is not to challenge these sources, but instead, to try to get a fix on the actual numbers, and the state of U.S. education today. Why? If 3 in 4 people are indeed graduating high school, then we’re working on the right problem, especially if the vast majority of high school grads finish college and earn a good wage. However, if only 3 in 4 high school grads are attending college, and only 1 in 2 of them are actually finishing college, that only 1 in 4 Americans are college graduates.

Gee, those numbers seem wrong to me–the number of college graduates is probably over fifty percent–so why don’t the numbers add up?

(Help?)

The Multiplier Effect

Quickly now… If you multiply 633 by 11, what’s the answer?

No doubt, you recognize the pattern, and you may recall the mental math process:

633 x 10, plus 633 x 1, or 6,330 plus 633, or 6,963, which is the answer (or, in terms used by math teachers, the “product”).

There is another way to solve the problem, a faster way that assures fewer computational errors, and does not involve any sort of digital or mechanical device. It does, however, involve a simple rule and a different way to write the problem down.

The rule is: “write down the number, add the neighbor.” The asterisk just above each number is there only to help you to focus. If you prefer, think of it as a small arrow.

Here’s how it works:

Mult by 11

Try multiplying 942 x 11  and you’ll quickly get the hang of it.

Do it once more, this time with a much larger number: 8,562,320 x 11. It goes quickly, as you’ll see.

Multiplying by 12 is just as easy, but the rule changes to: “double the number, add the neighbor.” Here, my explanation includes specific numbers.

Mult by 12

In fact, there is a similar rule for multiplication by any number (1-12). And there are rules for quickly adding long, complicated columns of numbers, as there are for division, square roots and more.

These rules were developed by a man facing his own demise in the Nazi camps during the Second World War. Danger was nothing new to him…this is the story and the enduring legacy of Jakow Trachtenberg, who first escaped the wrath of the Communists as he escaped his native Russia, then became a leading academic voice for world peace. His book, Das Friedensministerium (The Ministry of Peace), was read by FDR and other world leaders. His profile was high; capture was inevitable. He made it out of Austria, got caught in Yugoslavia, and was sentenced to death at a concentration camp. To maintain his sanity, Trachtenberg developed a new system for mathematical calculation. Paper was scarce, so he used it mostly for proofs. The rest, he kept in his head.

Madame Trachtenberg stayed nearby, in safety. She bribed officials, pulled strings, and managed to get Jakow moved to Dresden, which was a mess, allowing him to escape. Then, he was caught again, and was moved to Trieste. More bribes and coercion from Madame. He escaped. The couple maneuvered into a more normal existence beginning at refugee camp in Switzerland. By 1950, they were running the Mathematical Institute in Zurich, teaching young students a new way to think about numbers. A system without multiplication tables. A system based upon logic. A system that somehow survived.

A system that, against all odds, made it into my elementary classroom. One classroom in the New York City school district. For one year. The parents were certain that the teacher was making a terrible mistake, that the people in my class, myself included, would never be able to do math in the conventional way again. Of course, we learned a lot more than an alternative from of arithmetic.

And now, after decades out of print, in an era when arithmetic hardly matters because of calculators and computers, the original book is back in print. The brilliance of system remains awesome, and the book is worth reading just to understand how Trachtenberg conceived an entirely fresh approach under the most extraordinary circumstances.

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