The Way We Teach Math, Sciences, and Languages Is Wrong
A few years after I learned German, I got the chance to learn French. That experience gave me lots of ideas for why our teaching of many subjects, especially science and mathematics, is so unsuccessful—and for how we can improve our learning.
I studied French in school for five years. However, when I went to France after college, I could barely buy a train ticket. The impetus to try again came a few years later, in the summer of 1993. Our whole family was going to spend two months in Lyon while my father took a sabbatical. The rest of us enrolled in a four-week language course at the Alliance Française.
While still in America, to get more benefit from the language course, I started relearning French. On the recommendation of a friend who is a linguist and mathematician, I got the self-study French course made by Assimil entitled Le Nouveau Français sans Peine (New French With Ease). (Many other self-study courses should also work well. I have not tried them, so I do not have the knowledge to draw out lessons for learning other subjects, which is my main interest here. But to learn about language programs, I recommend the excellent “How to learn any language” site.)
I did one French lesson daily starting from Lesson 1. I read a short, idiomatic dialogue out loud using the pronunciation key, then listened to it on the tape, repeating it sentence by sentence. The lesson finished with 2 minutes of fill-in-the-word exercises using the vocabulary from the dialogue. Each lesson took about 30 minutes. After three months of this preparation, when I landed in France I could converse with random French people on the train. Read More »
How to Learn (Not Just) a Language Quickly
I was never good at languages. Although my first language was Punjabi, I grew up as a monolingual English speaker. In grade school, I took French for many years with grades of mostly Bs and a few Cs. However, I managed to learn fairly fluent German in just a few months. As I look back on it, I realize that I applied methods that help in learning any subject, which is my reason for telling you what I did.
It was 20 years ago in the eight-week language course at the Goethe Institute in Prien am Chiemsee, a beautiful resort town in the foothills of the Bavarian Alps (sadly, that school has since closed its doors). Upon arrival, we took placement tests to determine a suitable class. The instructors offered me the choice of starting in the highest of the three beginning levels or in the lowest of the three intermediate levels. (In college I had studied a year of German, which I estimate as comparable to four weeks of immersion in language school.)
I chose the intermediate class. For the first five weeks, I understood almost nothing that the teacher or the other students said. However, in the sixth week of the course, something amazing happened. Each day in that week I understood more. Read More »
How Are Sharks Less Dangerous than Vending Machines? An Exercise in Conditional Risk
Did you know that vending machines, not a major danger in most of our minds, are twice as likely to kill you as a shark? I heard this statistic at the new shark-and-ray touch tank of the New England Aquarium, which I try to visit weekly with my daughters. You stand at a large, shallow tank with plexiglass walls and can lay your hand in the water, gently feeling the sharks and sting rays swimming by.
The aquarium probably wants to convince visitors that sharks are not the fierce predators of Jaws fame, and thereby help protect sharks from hunting and extinction. Although I could admire this motive, the comparison always surprised me. My number sense complained that sharks simply must be more dangerous than vending machines.
However, upon looking up the risks, I found that the comparison was correct. The yearly risk (in the United States) of dying from a shark attack is roughly 1 in 250 million. In contrast, the yearly risk of dying from a vending machine accident is roughly 1 in 112 million. The vending machine is indeed roughly twice as lethal as the shark!
Why then was I still troubled by the comparison? Maybe my number sense needed a tune up, and I should just accept the statistical facts of life. I then started thinking about it using the method of easy cases. Read More »
Were Colonial Americans More Literate than Americans Today?
In 1776, one book, written in complex language, sold over 120,000 copies in Colonial America. That number does seem large on its own. However, to give it even more meaning, I like to convert it to an equivalent number today.
This conversion is a task for proportional reasoning—one of my favorite tools for finding meaning in the numbers that surround us. First convert 120,000 into a fraction of the U.S. population in 1776: compared to the population at the time of 2.5 million, 120,000 is roughly 1 in 20, or 5%. Today’s U.S. population is about 300 million—of which 5% is 15 million.
Fifteen million copies today! More surprisingly, Common Sense by Thomas Paine sold this equivalent in just three months. In its first year, it sold 500,000 copies, or 20% of the colonial population. Today’s equivalent is 60 million copies. On Wikipedia’s list of bestselling books, all books that have sold that many or more copies have done so over a much longer time. The shortest time is 8 years, for The Da Vinci Code; several others, such as Heidi, were published in the 19th century.
Another surprise arrives upon opening Common Sense: the sophistication of the writing and reasoning. Read More »
Planned Obsolescence: A Lament for Quality Amid a World of Junk
Our family recently camped for a week in a nearby state forest where our most trusted item was a cast-iron frying pan. Its thickness distributes heat evenly. Nothing can harm it. The wrong kind of spatula won’t scratch some special non-stick coating.With simple care, it will last for a thousand years. Which reminded me how rare that combination of high quality and durability is today.
Most everything else I own is junk and seems to be designed that way. Here are several anecdotal examples:
In the old days, most Americans rented phones from the phone company (“Ma Bell”). My parents still own one, now over 30 years old, that survived raising three boys. These phones lasted forever. Meanwhile, Ma Bell was broken up in the 1980s. One engineer who worked for the phone company before and after the breakup told me of how the engineers were gathered together and given new ground rules: “It was all well and good in the old days to make phones with gold-plated contacts. But now it’s different. Here’s how to make the newer phones…” I think back on this comment as I watch one phone after another die, often after a few months. Read More »
A Stack of Bills Reaching to the Moon: How to Quantify Our National Debt
Now that the U.S. national debt is in the headlines, the media is awash in astronomical numbers such as $14.3 trillion (the current debt). Everyone realizes that this number is incomprehensible. Even back in 1981, when the national debt was only about $1 trillion, the debt was still incomprehensible. Thus, speechwriters for Ronald Reagan created, or at least popularized, a widely used attempt to give it meaning. Speaking to Congress in February 1981, Reagan said:
A few weeks ago I called such a figure, a trillion dollars, incomprehensible, and I’ve been trying ever since to think of a way to illustrate how big a trillion really is. And the best I could come up with is that if you had a stack of thousand-dollar bills in your hand only 4 inches high, you’d be a millionaire. A trillion dollars would be a stack of thousand-dollar bills 67 miles high.
This comparison is often quoted as a stack of one-dollar bills 67,000 miles high (perhaps because thousand-dollar bills don’t exist). No matter which denomination you use, I give the explanation an A for effort, but an F for performance. For I have little idea of how far 67,000 miles is. I know it’s way too far to walk and even too far to fly (jumbo jets have a maximum range of around 7,000 miles). But is it large as a national debt? I have no idea. Perhaps a large national debt would reach all the way to Mars. The connection to a height has merely replaced one meaningless idea ($1 trillion) with another meaningless idea (a stack 67,000 miles high). Read More »
Another Salvo in the Tenure Debate
Should professors have tenure? The question, debated recently on this blog, misses the mark—as do the usual answers, whether “yes,” “no,” or “maybe.”
On the “no” side, it is argued that tenure protects incompetent spongers. A very reliable (tenured) colleague, at a university that shall remain nameless, tells me of professors whose interests are no longer intellectual and who spend their time playing the real estate market. Their research productivity, measured in grant dollars or papers, is low; thus, the university is angry. Their teaching is also substandard, yet not quite abysmal enough to get them fired. To urge them to resign, the department punishes them… by assigning extra teaching!
On the “yes” side, it is argued that tenure protects academic freedom. That point is made by my colleague on this blog Dan Hamermesh. Ten years ago I agreed with him. I would not have imagined my future self happy as an associate professor at Olin College of Engineering: Olin offers six-year renewable contracts instead of tenure. Now I see Olin’s system as a reasonable alternative to tenure, for I no longer believe that tenure supports academic freedom. Read More »
L.A.’s Carmageddon: Would Building a Train Be Smarter Than Widening the 405?
The “mother of all traffic jams,” in the words of L.A. County supervisor Zev Yaroslavsky, is coming to Los Angeles. On the weekend of July 16/17, an 11-mile segment of Interstate 405 will be closed as part of a $1 billion widening project. Reading of the expected traffic jams, and having recently returned from western Europe, where I traveled mostly by train, I was reminded of an earlier traffic nightmare.
This example I learned from Robert Caro’s 1974 masterpiece The Power Broker: Robert Moses and the Fall of New York. Robert Moses was New York City’s “master builder” in the mid-20th century, and famously hated public transportation. Read More »
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