You Are Smarter than You Think

Originally published in

Northland Reader
now the
Reader Weekly
Duluth, Minnesota
February 3, 2000

 

Do you think in the same way all the time?  Or, do you look at things in different ways?  This article is a little test of your willingness to think creatively and to try different things.

I recently attended a dinner at which a speaker gave this exercise.

Pick any number from 1 to 9.  Multiply it by 9.  If the result is a two-digit number, add the two digits together.  Subtract 5 from the result.

Think of each letter of the alphabet as a number; that is A is 1, B is 2, and so on.  Match the number you had after subtracting 5 with the corresponding letter of the alphabet.

Think of a country name beginning with that letter.
Think of an animal name beginning with the last letter of the country’s name.
Think of a color name beginning with the last letter of the animal’s name.

Let me take out my magic wand, tap you on the head three times, and say that you thought of Denmark, kangaroo, and orange.

Now, let’s test your creativity.

First, did you ask yourself why the number part of the trick works?  Did you start juggling numbers in your head to prove it should work?  If you didn’t, your first lesson in creativity is to demonstrate why it works.  It may take several minutes of effort, but you can do it if you are willing to apply a little elementary arithmetic, a bit of abstraction to symbols, and a some small changes in viewpoint.

Secondly, did you ask yourself why I thought you would answer Denmark, kangaroo, and orange?  Are these the only country, animal, and color that begin with these letters?  Or are these more readily known than other examples?  If these aren’t the only country, animal, and color beginning with these letters, did you search your memory for any others?

Why not put the Northland Reader down right now, get out a piece of scratch paper and a pen, and work on these two problems?  First, prove that the number part of the exercise will work.  Second, list some other sequences of countries, animals, and colors in which the country name begins with D, the animal name begins with the last letter of the country name, and the color name begins with the last letter of the animal name.

OK, did you get anywhere?

The easy answer for the number question is the “rule of nine”.  Because we multiplied the original number by 9, then the second number is divisible by 9.  We will come back to 9 as our next result by applying the rule of nine.  That is, to see if any number is divisible by 9, add its digits together.  If the result is two or more digits long, add those digits together.  Repeat until you have a single digit.  If that digit is 9, then the number you applied the rule to is divisible by 9.  Since we started adding the digits together in the trick after we multiplied by 9, then the result of our addition has to be 9.

This method also applies to numbers divisible by 3, but the single digit may be 3, 6, or 9.  For now, we’ll stick with 9.

The harder part is now to explain why the rule of nine works.  Our first step is to introduce a bit of symbolism; let good old X stand for our original number.  Our first step is to multiply by 9, giving us 9X.  Now we have to make a little jump in viewpoint; 9 is 10-1, and so we have (10-1)X.  We can rewrite this as 10X - X.

That doesn’t look very promising.  Let’s try another jump in viewpoint; let Y be X - 1 or conversely, let X be Y+1.  We now have 10(Y+1) - X.  Why not replace both X’s with Y+1?  Because we need another jump in viewpoint.  First, rewrite our formula as 10Y + 10 - X.  Now let’s replace 10 - X with Z giving 10Y + Z.  If we add Y and Z using their equivalents expressed with X, we should get 9.  Here we go!  Y + Z is X - 1 + 10 - X which we can reorder as X - X + 10 - 1 which is 9!  Finally, subtracting 5 gets us 4, and D is the fourth letter of the alphabet.

To see it better, let’s put it in the compact but excruciating form we had to do in junior high algebra:

Assume we have a number 9X where X is any number from 1 to 9.

 9X = (10-1)X
 (10-1)X = 10X - X
 Let Y = X - 1
 X = Y + 1
 10X - X = 10(Y + 1) - X
 10(Y + 1) - X = 10Y + 10 - X
 Let Z = 10 - X
 10Y + 10 - X = 10Y + Z
 Y + Z = (X -1) + (10 - X)
 (X - 1) + (10 - X) = X - X - 1 + 10
 X - X - 1 + 10 = 9

Did you have difficulty following this?  Guess what?  I had difficulty coming up with it.  It took me several minutes of trial and error, spread over two days, to get all the steps right.  But Thomas Edison said that creativity is one percent inspiration and ninety-nine percent perspiration, and he went through a lot of glass to be the first to create a useful light bulb!

The second problem is a bit easier if you read a lot.  Did you also come with koala bear and red?  How about Dhubai, ibex, and hmm!  Oops!  Dubayy is a city in the United Arab Emirates.  Creativity can make errors.  How about Deutschland, deer, and red?  These were my thoughts at the dinner.

Curiosity, an important part of creativity, led me to the dictionary and atlas.  For colors other than orange we have olive and ochre.  Starting with countries, we have Dahomey, yak, and hmm?  Or, Dominican Republic, cat, and teal, or cougar and red, or chimpanzee and emerald, or …

Space doesn’t allow me to fill in my “hmm”s.

If you got this far, you know creativity is not that hard.  Unleash yours!  If you have a dull job, creativity may not get you a better job,  but it may make your job a bit more interesting.  If you have some tough fix-it problems at home, a fresh look at them may lead you to a solution or at least a workaround.  Finally, by looking past the figures and ideas in sound bites and headlines, you may gain a better perspective on many of the problems that confront us as a society.

Short-sighted politicians or visionaries

The Duluth News Tribune editorial board asked for questions to ask candidates. I was fortunate to have two of mine be selected. For city councilors it was, "Is it more important to attract businesses or people to Duluth?" For school board members it was, "Is it more important to have students pass reading tests or read and discuss?

I didn't see all the responses because I didn't read much about candidates whom I could not vote for. What I did see is competing school board candidates answer, "Read and discuss." Hurray! Long term thinking. I was really disappointed to see competing council candidates answer "Business". How short sighted?

Don't they remember all the fiascos of businesses that were attracted with big fanfare and they were going to provide jobs? Far too many of these businesses never provided all they promised, and too many left town or folded.

The "correct" answer is people because people create businesses but businesses don't create people.

I saw some vindication of this in "That used to be us" by Thomas Friedman and Michael Mandelbaum.

Attracting a big plant is harder because there are fewer and fewer because of robotics. "What a town needs to thrive today is a hundred people starting companies that employ twenty-five people each, and twenty people starting companies that employ fifty each, and five people starting companies that employ three hundred people each."

Taking a different tack, how are you even going to attract businesses or people to Minnesota when many people don't want to move here because they think it is too cold? On the other hand, many people in Minnesota don't want to live anywhere else.

Many people forget that Minnesota once was a hot bed of creativity and still has many large corporations that are designing and manufacturing a wide range of innovative products. But given the political dominance of "no new taxes" and "cut spending" people, we have cut way back on our investment in creating and educating people who will carry on this tradition.

And if Minnesota regains its image as an innovative place to be, it will attract both people and businesses. The computer business in Minnesota and canoeing in the Boundary Waters attracted me forty-eight years ago.

Why do we expect more from kids than adults?

Every day all across the country, we make kids sit still in classes of dozens for 40-45 minutes at a time, sometimes listening, sometimes participating.  They are supposed to do this every weekday for over 30 weeks a year.

Now, go to any lecture or concert.  Look around you about a half hour into the event.  How many adults do you see (or hear) nodding off?  How often do you yourself stay awake through a lecture without a cup of coffee in front of you?  And we went because we were interested in the lecture or concert!

This little diatribe was inspired by "Apple co-founder Wozniak: computers can teach kids", Reuters, 2011-05-03.  My favorite quote is:

"School in itself is pretty much a restrictive force on creativity," he said. "When you come to class, you do the exact same pages in the book, the same hours as everyone else in the class. You don't go off in your own little directions."

BTW, he secretly taught elementary school for eight years.

The conspiracy against children and the public education system

1984 has arrived with more newspeak than we can keep track of.  No Child Left Behind (NCLB) is one of the diversions supposedly to promote improved education while actually destroying public education.

What are the reasons for NLCB: Lower taxes? Lowering the ability to think critically?  Pretending to do something productive without having to do anything substantive?  Destroying the public education system?

Supposedly one of the benchmarks is improved reading scores, no matter how good or poor previous scores were.  One improves reading scores by providing lots of reading material.  However, the budgets of the most accessible sources of reading materials are being cut, especially in schools with already low scores.  See "ALA Report: Poor Middle, High School Libraries Suffer the Most Budget Cuts".

But standardized tests are not the measure of critical thinking and creativity.  They measure the ability to give correct answers to tests.  It's like supposedly being skilled in a foreign language by knowing many details of grammar and having a large vocabulary.  Passing tests based on these two aspects mean nothing without lots and lots of practice in reading, writing, speaking, and listening.

For example, I have spent many classroom hours on German and French and practically none on Swedish and Italian.  I read French OK because I've read dozens of books in French, but speaking French and German is difficult.  Speaking Italian comes easier to me because I lived in Italy and spoke it more than I ever spoke French or German.  Swedish comes even more easily to me because I spoke it at work for three years; sometimes I even think in Swedish.  Even then, these two languages are still a struggle because I don't practice.

What is really a pity on public education is that much research has been done by educators on better methods.  Politicians don't want to follow through on these ideas because they cost money, and politicians are better scientists and educators than scientists and educators.

An excellent view of what's really needed has been presented in many ways be Ken Robinson.  See an animation of his lecture, "Changing Education Paradigms".

One of his key points is "divergent thinking is an essential ingredient of creativity."  Divergent thinking is the ability to see many ideas at once rather than regurgitate the one "correct" idea.  He cites a longitudinal study of children in kindergarten scoring an average of 98% on divergent thinking and dropping dramatically as they grow older.

See also "Do Schools Destroy Creativity".  Ken Robinson says that George Harrison and Paul McCartney were not recognized as musicians by the music teacher!!

He also says that there is more money to be made by large corporations in the correction system of California than in the schools of California.  That is, short-term corporate profits are more important than long-term investment in people.

Now I know why some creative types go crazy

Many of us know of the problems of Robert Schuman, Vincent Van Gogh, and Virginia Woolf.  I know now why they could have problems.  Either a creator gets depressed when the ideas run dry or frustrated when the ideas come faster than they can put them on paper or canvas.

You can see from today's postings that I have lots of ideas, whether you agree with them or not.  Beyond that are files for each month with notes for possible amplification, a two-inch pile of 1/4 sheets of scribbled notes, and about two dozen record books of notes, some in a shorthand.

And I keep generating more ideas as I read newspapers, magazines, and books, both paper and online.

Grading teachers, there you go again!

See "Method to Grade Teachers Provokes Battles", Sam Dillon, New York Times, 2010-08-31.

Supposedly somebody's come up with a way to accurately grade teacher performance, but others find many flaws in applying the measures.

However, the major flaw is that teacher performance can be measured on how students perform on standardized tests.  Passing tests is not what made this country great; it was learning to be creative.

Furthermore, if you look back at your own education, which teachers do you think were most effective.  Those who prepared you for tests or those who put a dream in your head?  Who do you remember best?  Miss Grumpy who made you an expert on parsing sentences?  Or Frank McCourt who taught you how to tell your own story?

Let's stop letting ideologues drive the debate

Two of the great mantras of our time are the need to improve test scores and the need for performance pay to satisfy the first.

One article that seemed to make sense was "The Uncertain Impact of Merit Pay for Teachers", Edwin Glaeser, New York Times, 2010-06-08.   Even though some studies were not solid on merit pay, Prof. Glaeser still supported merit pay for teachers.

In trying to retrieve this article, I stumbled on "Let's Have Merit Pay for Economists Who Muck Around in Education Issues",  Jim Horn, School Matters, 2010-06-08.  Horn counters with other studies that showed performance pay doesn't work, including a study presented at the conference that Glaeser wrote about.

See also Horn's "More Research on Teacher Performance Pay for Duncan to Ignore".

What all this clamor for performance pay misses is that schools aren't really about test taking and getting good scores.  They are about learning to learn and learning to be creative.  I read that East Asian kids may be much better at passing tests than American kids, but they don't seem to have the innovative skills that are far more abundant in the U.S.

A refreshing antidote is "History for Dollars", David Brooks, New York Times, 2010-06-07.  He wrote that many students are opting for college degrees in "practical matters" like accounting and that the portion of humanities majors has dropped as much as 50 percent in a generation.  He argues that humanities gives communication skills, "a wealth of analogies", and the ability to think in different ways.

Ah!  Think in different ways!  That certainly beats thinking in differing ways.

Jobs: The Times They Are A-changin'

As I drove up Central Entrance in Duluth I was struck by how many billboards were LED billboards. Those that weren't were often a set of big panels screwed to the supports.

What are all those who pasted up great rolls of paper doing now? The panels are probably placed up in a fraction of the time needed for the rolls of paper. "As for changing [an LED billboard], it's as easy as clicking with a mouse button, rather than sending out a crew to pull down and replace a billboard message." - LED Billboards: Outdoor Advertising in the Video Age

But this kind of change is happening throughout many businesses; jobs are going away because of changes of business practices and technology. They won't be coming back and those who think they will are deluded. We have to change our whole education system to train people to adapt to change.

I don't hold out much hope for this. It was in 1963 that Bob Dylan's "The Times They Are A-changin'" was introduced. In the same era Pete Seeger wrote "Where Have All the Flowers Gone" with the line "When will they ever learn".

The times are are still a-changin' and we still haven't learned.

Little things can save our empire

I saved a few articles about education that take a different tack from all the grandiose schemes that are current and was going to write a summary. Then today's Star Tribune had several op-ed pieces that stressed some of the same old, same old ideology: blame the teacher's unions or put the schools under control of mayors.

As usual, I keep reading new stuff that takes time from writing about old stuff I had read. As I went through the list of articles for today's Yahoo! Finance, I was struck by the title "Collapse of the American Empire: Swift, Silent, Certain".

I think our national arrogance ("leader of the free world"), military overreach, and short-term ideological thinking do contribute to the possibility of our soon being surpassed by the likes of China, India, and Brazil.

One thing that can keep us going for a long time is our history of innovation, innovation that is often falling victim to ideology. As long as we run our schools on ideological principles like "No Child Left Behind" and control from larger and more remote political entities, innovation may be stifled.

To get more innovation, we have to educate children for creativity, not passing tests.

I finally finished Eric Booth's "The Music Teaching Artist's Bible: Becoming a Virtuoso Educator". The more I read, the more I understood he was talking about education in general. If we don't engage students in creativity, all the rote learning in the world will only turn out automatons. See "Teaching: putting in or drawing out?"

Then I read three revolutionary articles on education: "Scholar's School Reform U-Turn", "Building a Better Teacher", and "Why you should read Diane Ravitch's new book".

The first is how Diane Ravitch, a respected education historian who was in the first Bush's Department of Education, has changed her mind on some of the conservative standard views on education, including No Child Left Behind. If you want to get some idea of her independence, read her "The Language Police".

The second is a long New York Times Magazine article centered on a charter school founder who learned that teachers aren't being trained in the little things that really matter. The most striking paragraph was:

"When Doug Lemov conducted his own search for those magical ingredients, he noticed something about most successful teachers that he hadn’t expected to find: what looked like natural-born genius was often deliberate technique in disguise. “Stand still when you’re giving directions,” a teacher at a Boston school told him. In other words, don’t do two things at once. Lemov tried it, and suddenly, he had to ask students to take out their homework only once."

The third is a short review of Diane Ravitch's "The Death and Life of the Great American School System". The review gives a good summary of the ferment that is going on in education circles, a ferment that could give us a truly Great American School System.

Teaching: putting in or drawing out?

"A teaching artist is an artist who actively engages learners in consciously developing the aesthetics of their own processes of learning."

- Arnold Aprill, Chicago Arts Participation in Education (CAPE)

Quoted in "The Music Teaching Artist's Bible: Becoming a Virtuoso Educator", Eric Booth, p. 16.

See the same section for other incisive quotes on what a teaching artist is.

When I read the above to my wife, she said that's what most teachers strive for. I replied that that's not what politicians want. She replied, "Unfortunately!"

One of the other quotes mentioned education as drawing out rather than putting in. It was this idea that led me to make the remark about politicians. "No child left behind" rewards schools for "putting in" and makes no provision for drawing out.

More on the changing economy

David Brooks wrote an interesting column on how we are changing from making stuff to creating ideas or protocols, ways of doing things. See "The Protocol Society", New York Times, 2009-12-22.

I checked on the local availability of the books Brooks recommended: "From Poverty to Prosperity" and "Smart World". Neither the Duluth Public Library nor the UMD Library has either book.

Are we changing fast enough? Are we too concerned about jobs for doing the same old things few want to pay for? Shouldn't we be more concerned about opportunities to bring forth new ideas? Is "No Child Left Behind" more about training kids to make stuff rather than to create ideas? Are our politicians more interested about protecting companies and industries that make stuff rather than encouraging companies and industries that make protocols?

Sometimes I think we have more of the prerequisites than any other country to move to a protocol society, and sometimes I think by we are going to let other countries get there first.

Misuse of statistics?

Stephen J. Schroeder-Davis wrote a generally good article about "gifted students" being "left behind", "Federal rules leave gifted kids behind", but I have a few bones to pick.

He wrote:

"There are no provisions in NCLB to support gifted students, and these student receive less than 3 cents of every $100 in federal education dollars."

First, are federal dollars the only available money for education? I hope not.

Second, does every student need the same amount of resources to get a good education? For example, advanced students can often be given an assignment and go off by themselves to do it. I would hope that teachers would still be available to answer questions. On the other hand, "average" students would need more attention and help. "Slow" students might need one-on-one assistance.

Third, he assumes that all students should make the same amount of progress throughout their education. He cites a study that low achieving students "were progressing in reading at five times the rate of high-achieving students". Is progress in reading unlimited? If the low-achieving students move from 100 words per minute to 500 wpm, does it follow that the high-achieving students should move from 800 wpm to more than 4000 wpm? Few schools have ever been equipped to teach the techniques to read at that rate.

Fourth, we overuse the word "gifted". Advanced students may have very supportive parents who encourage them to learn. OK, good parents are a "gift". These advanced students may have worked harder earlier and have a good base to learn at faster rates later. Sort of the more you learn, the easier it is to learn more.

I do agree with the author that advanced students could be given many more opportunities to learn as much as they can. It is no fun to sit in a high-school class with people who stumble over book reports. We have cut off many classes that not only would give advanced students more opportunities for learning, but that would give many other students opportunities to expand their interests and abilities. In the interest of low taxes we have considered libraries, foreign languages, music, arts, and other creative subjects as frills. These have been touted by many as keeping young minds more active and receptive to other learning experiences.

Oh, well! I guess we get what we pay for.

The importance of creativity in education

When I started working for Univac in the 1960s, I met a few musicians who had become computer programmers. I think I thought of it as the ability to manipulate symbols.

Decades later, I codified it as mathematics is the science of relationships and music is the art of relationships.

I was delighted to read the following in Ed Raymond's column in the Reader Weekly last week:

"Some day we will even find out why musicians make the best mathematicians."

He was decrying how arts and music have been cut from too many schools because of budget cuts. If you missed his column in the Reader Weekly, you can find it online in the High Plains Reader, "Cherry Wood and the Golden Gopher Jockstrap".

Libraries in schools, frill or necessity

As I rode up the chair lift with an 8-year-old ski student, I asked her what books she's been reading. She said Judy B Jones. I asked her what the books were about. "She does things." "Does she solve problems or get in trouble?" "Gets in trouble." "Does she figure out how to fix things up?" "Generally."

I asked her if she gets Judy B Jones books at the public library or the school library. "School library". "Which do you prefer, the library or the classroom?" "The library." "Why?" "There are so many books."

There is a whole kid world out there that many adults are unaware of. First, I never heard of Judy B Jones until I talked to this girl about her interests. Second, my own expectation of what names sound like led me to assume the wrong name. The heroine of the books is Junie B Jones!

I found this out by a search of the web. Check http://www.randomhouse.com/kids/junieb/books/books.html
For another series that is exciting kids, see Captain Underpants.

Maybe we have schools organized all wrong. Instead of classrooms where children sit in rows or circles, maybe we should have libraries, labs, workshops, and other activity centers. They would be staffed with teachers who would make suggestions and answer questions. On certain days children would move from one activity center to another. On other days they would choose which they wanted to use and when.

Yes, there should be benchmark tests, but they should be written or oral presentations or they should be demonstrations of skills. The demonstrations could be musical or theatrical performances, an art work, or construction of an object.

In other words, schools should be places where kids imaginations and creativity are allowed to soar. Tests should be something that take advantage of kids' desire to show off.

There is no standardized kid; why should they take standardized tests?