Education

Derek Sivers tells how a mentor was able to teach him a semester’s worth of music theory in three hours. His mentor also prepared him to place out of four more classes in four sessions. He gives the details in his blog post There’s no speed limit. It’s an inspiring story.

However, Sivers didn’t go through his entire education this way. He finished his degree in 2.5 years, but at the rate he started he could have finished in under a semester. Obviously he wasn’t able to blow through everything as fast as music theory.

Some classes compress better than others. Theoretical classes condense better than others. A highly motivated student could learn a semester of music theory or physics in a short amount of time. But it would take longer to learn a semester of French or biology no matter how motivated you are because these courses can’t be summarized by a small number of general principles. And while Sivers learned basic music theory in three hours, he says it took him 15 years to learn how to sing.

Did Sivers’ mentor expose him to everything students taking music theory classes are exposed to? Probably not. But apparently Sivers did learn the most important material, both in the opinion of his mentor and in the opinion of the people who created the placement exams. His mentor not only taught him a lot of ideas in a short amount of time, he also told him when it was time to move on to something else.

It’s hard to say when you’ve learned something. Any subject can be explored in infinite detail. But there comes a point when you’ve learned a subject well enough. Maybe you’ve learned it to your personal satisfaction or you’ve learned it well enough for an exam. Maybe you’ve reached diminishing return on your efforts or you’ve learned as much as you need to for now.

One way to greatly speed up learning is to realize when you’ve learned enough. A mentor can say something like “You don’t know everything, but you’ve learned about as much as you’re going to until you get more experience.”

Occasionally I’ll go from feeling I don’t understand something to feeling I do understand it in a moment, and not because I’ve learned anything new. I just realize that maybe I do understand it after all. It’s a feeling like eating a meal quickly and stopping before you feel full. A few minutes later you feel full, not because you’ve eaten any more, but only because your body realizes you’re full.

Related posts:

Just-in-case versus just-in-time
Learners versus the learned
Feed the stars, milk the cows, and shoot the dogs
Evaluate people at their best or at their worst?

Math Fun Facts is a large collection of very short mathematical articles, each less than a page, maintained by my friend Francis Su. These articles are a great resource for teachers looking for interesting examples to spice up a class.

I just found out that Francis has made an iPhone app for Math Fun Facts. It is available for free from the iTunes store.

“In times of change, learners will inherit the earth while the learned will find themselves beautifully equipped to deal with a world that no longer exists.” — Eric Hoffer

American creativity is declining according to a recent Newsweek article. The article says that America is embracing rote learning just as China is embracing creativity.

In China there has been widespread education reform to extinguish the drill-and-kill teaching style. … When faculty of a major Chinese university asked [Jonathan] Plucker to identify trends in American education, he described our focus on standardized curriculum, rote memorization, and nationalized testing. “After my answer was translated, they just started laughing out loud,” Plucker says. “They said, ‘You’re racing toward our old model. But we’re racing toward your model, as fast as we can.’ ”

Ken Robinson argues in his TED Talk that rather than encourage creativity, schools kill it.

Related posts:

Preparing for innovation
Evaluate people at their best or at their worst?

In his book Made by Hand, Mark Frauenfelder quotes Peter Gray on what’s wrong with contemporary education. Gray says that school is about

always preparing for some future time when you will know enough to actually do something, instead of doing things now. And that’s such a tedious approach for anybody to take to life — always preparing.

Related post:

“Just in case” versus “just in time”

“The university’s ‘hidden curriculum’ … has always been teaching its own importance.” — Anya Kamenetz

Thoughts from Tom Green on preparing students for innovation.

Today, many critics lament the lack of innovation in our society and draw the conclusion that more emphasis on teaching mathematics and science will lead to innovation. That will probably fail. Innovation comes from repeated successes in innovating. Innovation means trying ideas outside the accepted patterns. It means providing the opportunity to fail as a learning experience rather than as an embarrassment. … the traditional school powerfully suppresses any tendency toward being innovative. Both teachers and students are driven to conform.

From Bright Boys: The Making of Information Technology.

Related posts:

Don’t standardize education, personalize it
Evaluate people at their best or at their worst?

What do you learn just in case you’ll need it in the future, and what do you learn just in time when you do need it?

In general, you learn things in school just in case you’ll need them later. Then once you get a job, you learn more things just as you need them.

When you learn just-in-time, you’re highly motivated. There’s no need to imagine whether you might apply what you’re learning since the application came first. But you can’t learn everything just-in-time. You have to learn some things before you can imagine using them. You need to have certain patterns in your head before you can recognize them in the wild.

Years ago someone told me that he never learned algebra and has never had a need for it. But I’ve learned algebra and use it constantly. It’s a lucky thing I was the one who learned algebra since I ended up needing it. But of course it’s not lucky. I would not have had any use for it either if I’d not learned it.

The difference between just-in-case and just-in-time is like the difference between training and trying. You can’t run a marathon by trying hard. The first person who tried that died. You have to train for it. You can’t just say that you’ll run 26 miles when you need to and do nothing until then.

Software developers prefer just-in-time learning. There’s so much out there that you aren’t going to need. You can’t learn every detail of every operating system, every programming language, every library etc. before you do any real work. You can only remember so much arbitrary information without a specific need for it. Even if you could learn it all in the abstract, you’d be decades into your career without having produced anything. On top of that, technological information has a short shelf life, so it’s not worthwhile to learn too much that you’re not sure you have a need for.

On the other hand, you need to know what’s available, even if you’re only going to learn the details just-in-time. You can’t say “I need to learn about version control system now” if you don’t even know what version control is. You need to have a survey knowledge of technology just in case. You can learn APIs just-in-time. But there’s a big gray area in between where it’s hard to know what is worthwhile to learn and when.

Update: Here is a Chinese translation of this post.

Related posts:

Software that gets used
Why programmers write unneeded code
Don’t standardize education, personalize it
Worthless technical books

This is one of my favorite quotes from Starbucks’ coffee cups:

When I was young I was mislead by flash cards into believing that xylophones and zebras were much more common.

Alphabet books treat every letter as equally important even though letters like X and Z are far less common than letters like E and T. Children need to learn the entire alphabet eventually, and there are only 26 letters, so teaching all the letters at once is not bad. But uniform emphasis doesn’t scale well. Learning a foreign language, or a computer language, by learning words without regard to frequency is absurd. The most common words are far more common than the less common words, and so it makes sense to learn the most common words first.

John Miles White has applied this idea to learning R. He did a keyword frequency analysis for R and showed that the frequency of the keywords follows Zipf’s law or something similar. I’d like to see someone do a similar study for other programming languages.

It would be interesting to write a programming language tutorial that introduces the keywords in the approximately the order of their frequency. Such a book might be quite unorthodox, and quite useful.

White points out that when teaching human languages in a classroom, “the usefulness of a word tends to be confounded with its respectability.” I imagine something similar happens with programming languages. Programs that produce lists of Fibonacci numbers or prime numbers are the xylophones and zebras of the software world.

Related posts:

Zebras and xylophones part II: learning Spanish
Rate of regularizing English verbs
Four reasons we don’t apply the 80-20 rule
R, the good parts

The blog Confessions of a Community College Dean had a post on Monday entitled Cash Cows that talks candidly about the financial operations of a community college.

It’s a commonplace of for-profit management that units can be characterized in one of three ways: rising stars, cash cows, and dogs. The savvy manager is supposed to feed the stars, milk the cows, and shoot the dogs. … We milk the cows precisely so we don’t have to shoot the dogs.

The “cows” are the profitable courses and the “dogs” are the unprofitable courses. Popular belief has it that English classes are cash cows because they require fewer resources than, say, chemistry classes. However, this blog says that English classes only break even because they also have smaller classes. The real cash cows are the social sciences. The biggest dog is nursing. The profit from teaching history, for example, makes it possible to train nurses.

Near the end of her course on classical mythology, Elizabeth Vandiver speculates on why people find Shakespeare hard to read. She says that, contrary to popular opinion, the difficulty is not the language per se. Elizabethan English is not that foreign to modern readers. The difficulty in reading Shakespeare comes from the literary allusions, particularly the allusions to classical mythology.

Her explanation matches my experience. I can easily read the King James version of the Bible, produced during Shakespeare’s lifetime, but I find it hard to slog through Shakespeare. (To be fair, I must say I grew up with far more exposure to the King James Bible than to Shakespeare.)

Vandiver when on to say that the primary source of classical mythology for Shakespeare and his audience was Ovid’s Metamorphoses. Studying this one book would make the Bard much more approachable.

I ran across a blog post this morning that makes some excellent points about timed exams. Here are three points from Jon Dron’s blog post What exams have taught me:

• that slow, steady, careful work is not worth the hassle — a bit of cramming (typically one-three days seemed to work for me) in a mad rush just before the event works much more effectively and saves a lot of time
• the corollary — adrenalin is necessary to achieve anything worth achieving
• that the most important things in life generally take around three hours to complete

As Marshal McLuhan said, the medium is the message. That is, the context of a message may speak louder than its content. Still, I’d like to defend timed exams in a limited context. You need to have quick recall of some facts. There are some skills you need to practice to the point that they are second nature. Not because these things are ultimately important but so you don’t have to think about them and can move on to other things.

Joel Spolsky gave an example along these lines in his recent podcast. He said that Serge Lang once began a calculus class with an algebra quiz, one expression to simplify. Thirty seconds into the quiz, it made everyone stop and turn in their work. At the end of the year, he compared the final grades to the grades on his algebra quiz. The students who got A’s in freshman calculus were almost exactly the same as those who were able to simply the algebra expression quickly. (The story begins around 8:12 in the audio file. It’s also on the transcript wiki.)

There are a couple ways to interpret this anecdote. One is that Lang’s exams measured quick reaction time and that students who were able to do algebra quickly were also able to do calculus quickly and thus succeed on Lang’s exams. There may be some truth to that. But I think more fundamentally, those who had mastered algebra were able to pay attention to the new material. Because algebra was second nature to these students, they could think about calculus.

I agree that typical hour-long exams are artificial and create some perverse incentives. I see a place for leisurely evaluation: take-home exams, projects, portfolios, etc. But I also see a place for timed evaluation, even quiz show-like rapid recall, though such evaluation need not factor into assigning grades.  I think Jon Dron’s criticism is that timed exams are usually not created deliberately. I don’t think he would necessarily find fault with someone explicitly identifying a list of fundamental skills and explaining that these need to be performed quickly. I believe his criticism is that everything is evaluated in a rush by default.

Thanks to Daniel Lemire for pointing out Jon Dron’s post. Read Daniel’s commentary here.

Related posts:

Evaluate people at their best or at their worst?
Don’t standardize education, personalize it

I just finished reading Ken Robinson’s book The Element. The title comes from the idiom of someone being in his or her “element.” The book is filled with stories of people who have discovered and followed their passions.

Here are a couple quotes from the book regarding standardized education.

The fact is that given the challenges we face, education doesn’t need to be reformed — it needs to be transformed. The key to this transformation is not to standardize education but to personalize it, to build achievement on discovering the individual talents of each child, to put students in an environment where they want to learn and where they can naturally discover their true passions.

Learning happens in the minds and souls of individuals — not in the databases of multiple-choice tests. I doubt there are many children who leap out of bed in the morning wondering what they can do to raise the reading score for their state. Learning is a personal process …

Here is a talk Ken Robinson gave at TED in 2006 that led to his writing The Element. The video is entertaining as well as thought-provoking.

Related posts:

Success in eight words
The Medici Effect
Evaluate people at their best or at their worst?

Here are three ways to evaluate a person’s performance.

1. How good are they at their worst?
2. How good are they on average?
3. How good are they at their best?

Schools use the first two criteria, but the market uses the third.

Schools evaluate people at their worst

Teachers average grades to come up with semester grades, and semester grades feed into a grade point average. So in some sense schools evaluate average performance.

But in more subtle ways schools evaluate students by how good they are at their worst. To graduate, your lowest course grade in all your required courses must be passing. No amount of brilliance in one area can compensate for a failing grade in another area. Your creative writing grades are excellent, Mr. Shakespeare, but we cannot let you graduate until you pass physics.

How do you get on the honor roll? Your lowest grade has to be above a certain level. Again, what matters is how good you are at your worst.

How do you get to be valedictorian? Be good enough at every class to get an A. You have to be pretty good at everything, but you don’t have to be truly exceptional at anything.

Schools encourage perfectionism, not excellence. They encourage people to avoid mistakes, not to be creative.

Markets evaluate people at their best

Markets often evaluate people and products at their best.

If you write 100 obscure novels and one best-seller, you’re a best-selling author. If you consistently write moderately popular novels, you’re not. If you write one really good novel, you might get a Nobel prize. Imagine the Nobel committee evaluating a writer saying “Yeah, these two novels were brilliant, world-changing. But he also wrote this one novel that was mediocre. Let’s give the prize to someone whose books are consistently pretty good.”

The Ford F150 did poorly in focus groups. The average rating wasn’t good. But the people who liked it really liked it. And the F150 went on to be the most popular truck in history. All that matters in business is people who like your product enough to buy it. You don’t make any money by being everyone’s second choice.

If a company has one product that is a runaway success, the company is a success. If it has two or three runaway successes, even better. But a company can produce a few dismal failures (think Microsoft Bob or the Apple Newton) and still do quite well if their flagship products succeed.The same is true of the people behind these products. Someone can make a successful career with one big win even if they have a number of failures.

We all want others to see the best in us. There are ethical and economic reasons to look for the best in others. But years of education can incline us to look for the worst in others and in ourselves.

Related posts:

Quantity and quality
Four reasons we don’t apply the 80/20 rule
Gerald Weinberg’s law of twins