An Interactive Exploration

The Having of
Wonderful Ideas

Eleanor Duckworth's vision of learning—
experienced, not explained.

What follows is not a summary. It's a set of small experiments. Each one embodies an idea from the book. Don't rush. The understanding sneaks in while you play.

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I. Wonderful Ideas

Before anyone asked him to, Kevin picked up the straws.

"The having of wonderful ideas is what I consider the essence of intellectual development. And I consider it the essence of pedagogy to give Kevin the occasion to have his wonderful ideas."

Here are some straws. Nobody's asking you to do anything with them. But you might notice something.

Tap straws to place them in order. Tap again to remove.

Your arrangement:

Kevin wasn't asked to order the straws. He wanted to. The idea was his. That's what made it wonderful—not that it was original to the world, but that it was original to him.

Wonderful ideas build on other ideas. Without previous experience, Kevin couldn't have had this one. The more you know, the more you can think of to do.

II. The Virtue of Not Knowing

The right answer is overrated.

"What you do about what you don't know is, in the final analysis, what determines what you will know."

Inside this box is a hidden circuit. You can test it—but not open it. What's inside?

?

What do you think is inside?

Hank, a fifth grader, figured out what was in his mystery box by burning out the component inside—an act of creative destruction his teacher had to accept. The courage to try, even destructively, matters more than knowing in advance.

III. Time for Confusion

I needed time for my confusion.

"All of us need time for our confusion if we are to build the breadth and depth that give significance to our knowledge."

A ball rolls down a ramp, leaving ink dots as it goes. What do you think the dots look like?

high end low end

The ball picks up speed. As it goes faster, the dots it leaves will be:

Closer together

It's going faster, so more dots per inch

Farther apart

It's going faster, so more distance between dots

Evenly spaced

The rotation stays consistent

I'm not sure

I'd need to see it to know

The dots get farther apart. The ball rotates at the same rate, but covers more ground between each rotation as it speeds up.

About half of adults predict the dots get closer together. One teacher, seeing the result, took a string to measure the gaps, saying: "They don't get closer together as noticeably as I thought they would!" She was still seeing what she expected, even after the evidence was right in front of her.

That confusion is the point. When your prediction is wrong, something interesting is happening in your mind. Don't rush past it.

IV. Keeping It Complex

Twenty-four, forty-two, and I love you.

"If Frost had been able to put what he had to say into a sentence, he would have. So don't worry that you can't."

Four children. Four seats at the movies. How many ways can they sit? Some students say "twenty-four" immediately—they know a formula. But what are the arrangements?

Drag the letters to arrange them. Find as many unique arrangements as you can.

P
L
M
B
0 unique arrangements found

"Twenty-four" is to these arrangements as "forty-two" is to the meaning of life. The formula gives you a number. The exploration gives you understanding.

Every person who does this exercise finds a different system. Some make diagonals. Some fix one letter and rotate the rest. A nine-year-old invented a system of "reversing pairs" that was entirely new to Duckworth. The variety of paths is the point.

V. Many Adequate Ways

Twenty-four divided by eight.

"Imagine a teacher who believes it could mean only one of them. Imagine that teacher explaining a division problem to a child who was thinking about it the other way."

What does 24 ÷ 8 really mean? Pick the one that feels right to you:

📦📦📦📦
📦📦📦📦
Distribute 24 things into 8 piles

Count how many in each pile

🔵🔵🔵🔵🔵🔵🔵🔵
🔵🔵🔵🔵🔵🔵🔵🔵
🔵🔵🔵🔵🔵🔵🔵🔵
Make groups of 8 from 24 things

Count how many groups

Both are completely correct. They're two different mental operations that arrive at the same answer.

In a group discussion Duckworth observed, people were astonished that the other interpretation existed. Each was convinced their way was the only way division could work.

Now imagine a teacher who holds one view, trying to explain division to a child who thinks the other way. The teacher wouldn't even notice the difference. Both would walk away thinking the child can't do math.

"We must find ways to present subject matter that will enable learners to get at their own thoughts about it."

VI. What We Really Learn

Four kinds of belief.

"If we state that our goals include the awakening of interest and the development of confidence, then we must think about teaching these beliefs just as carefully as we think about teaching the-way-things-are beliefs."

Schools focus almost entirely on facts. But Duckworth identified four equally important kinds of learning. Which matters most to you?

In one science study, children who took their magnifiers home every night and ran back if they forgot them—but couldn't state the physics of magnification—scored 95/100 in Duckworth's view. Children who knew the formula but never looked unless told: 5/100.

Teaching "I can figure this out" is not less rigorous than teaching facts. It is more.

VII. Critical Exploration

What do you notice?

"Instead of explaining things to students, try to understand their sense."

This is Duckworth's core teaching method. Read this short poem. Don't look for "the meaning." Just notice things.

— Robert Frost
I found a dimpled spider, fat and white,
Notice: white spider. Spiders aren't usually white. Why white?
On a white heal-all, holding up a moth
A heal-all is usually blue. This one is white. The moth is white. Everything is white.
Like a white piece of rigid satin cloth—
Satin cloth at a funeral? A wedding? "Rigid" = dead.
Assorted characters of death and blight
"Characters" as in a play? "Assorted" = brought together on purpose?
Mixed ready to begin the morning right,
"Morning right" or "morning rite"? Or "mourning"?
Like the ingredients of a witches' broth—
Ingredients = chosen deliberately. Someone (something?) mixed this.
A snow-drop spider, a flower like froth,
"Froth" = temporary, insubstantial. Beauty and death in one image.
And dead wings carried like a paper kite.
"Paper kite" = child's toy. Or a bird (kite)? Play and death.
What had that flower to do with being white,
Now Frost asks: why is everything white? This shouldn't be.
The wayside blue and innocent heal-all?
It should be blue. "Innocent" — was it corrupted?
What brought the kindred spider to that height,
"Kindred" = kin + dread? Related to the flower and moth in whiteness.
Then steered the white moth thither in the night?
"Steered" = someone directing this. Design.
What but design of darkness to appall?—
"Appall" = to make pale (white!). Darkness that creates whiteness. Also: a funeral pall.
If design govern in a thing so small.
The most devastating line. If. Maybe there is no design. Maybe it's all accident. Which is more terrifying?

Tap each line to see what others have noticed. In Duckworth's classes, a group can discuss this poem for over an hour with increasing interest.

"I have always been frightened by being asked: 'What is the meaning of this poem?'" Duckworth writes. "But it is easy for me to point out something I notice."

VIII. What You Know Is Yours

What did you discover?

Look back at what just happened. You ordered straws without being told to. You tested a mystery box. You sat with a wrong prediction. You found arrangements. You noticed things in a poem nobody pointed out to you.

None of these insights came from being told.

That is Duckworth's thesis. And you just experienced it.

"The wonderful ideas that I refer to need not necessarily look wonderful to the outside world. I see no difference in kind between wonderful ideas that many other people have already had, and wonderful ideas that nobody has yet happened upon."

The more ideas you have at your disposal,
the more new ideas occur.

Eleanor Duckworth, The Having of Wonderful Ideas and Other Essays on Teaching and Learning, 3rd edition, Teachers College Press, 2006.