Place a tiny mirror flat against a wall and guess where two people must stand so each can see the other's reflection. Then explain why.

** or this:** walk into a room full of helium balloons weighted with yarn and snip off or tie on yarn to make all float at the same height.
**these puzzles** seem simple enuff. But solving them took two HS boys and 20 adults several hours crawling on floors, craning necks, gasping with surprise and dissolving in laughter.
**this is** what learning means to **Eleanor Duckworth, Professor at the Harvard Graduate School of Education**, teacher of teachers and leading interpreter of the early childhood scholar Jean Piaget.

Before they can teach, she says, teacher must learn how it feels not to have the right answer, and learn how to follow children's struggles toward understanding.

**her unconventional** methods grew from her own experience of **"feeling
dumb" **as a graduate student. Accordingly, she dropped out of a
Harvard Ph.D. program to spend l7 years developing the ideas that
made her reputation: applying Piaget's pioneering observations of
how young children learn to the art of teaching. She is one theorist whose notions can apply directly to the classroom.

digging into a problem two shy teenagers on loan from a local HS stood facing 50 student observers as Duckworth presented them with the **mirror puzzle.** Self-conscious at first, their embarrassment disappeared as they were drawn into the problem, with the professor egging them on at every turn. Soon they aligned so they could see each other in the small mirror, and they glanced at her, thinking they have solved the puzzle. "What were you thinking about when you decided that was where you would stand" she asked. "It was a guess," replied John.

**"i'll bet** it was based on something," she pressed, and asked them to test every possible place they could stand and still see each other in the mirror. When they did so, she made the problem even more difficult. "Do you think you could try to explain to somebody how it works ?"

**for the** next two hours, the two boys walked back and forth, dropping to the ground to measure the angles at which they stood with lengths of string. Every time they came close to what they thought was the answer, she asked another question, trying to chart for her 50 student observers
**how the** teenagers were moving toward understanding and deliberately
throwing out wrong answers to test just how deep their understanding
lay.

gradually, the boys grew more certain of their responses. "The angles have to be equal," they said. By the end of the class they had discovered for themselves the physics formula that the professor never stated:

** **

**
**
**this is** the kind of teaching and learning that she endorses, a painstaking, time-consuming exploration that enables pupils to be confident they really know something and are not just parroting back facts the teacher told them.

**real learning**, she says, is **"the having of wonderful ideas,"**

** Leyden note:**

where are students going to get **'wonderful ideas'** unless they come to class every day --

take copious notes -- go home an re-write the notes ( constructivism ) -- for an hour or so **every nite. Learning is NOT FUN. It is very interesting. Life is not Disney World.**

and children will not have them unless teachers are willing to take the time to lead them thru the same torturous path the two boys had trod. Hers is a classroom where groping toward understanding is an important as achieving it, where teachers used to having the right answer rediscovered the terror and excitement of uncertainty.

**"learning is messy," **

she said, in class I put off 'why' question and turn them into a "what."

The 'why' usually pushes people to use words without knowing what the meanings are.

**If someone** says 'why,' I say, 'see if you can do it again,' or 'can you still do it if you do it like that? By the time you are pretty familiar with what you become very good at presenting the whys.'

**she explained** that she built her method on two foundations. First, she drew on her work with Piaget as a student in the late l950's, and then as the English interpreter during his N. American lectures until is death in l980. Piaget was the first scholar to systematically study the ways young children learn and from the publication of his first book, Language and Thought of the Child, in l924, he created and dominated a new area of inquiry.

** tracking how children learn**

**from piaget** she learned how to analyze how children gradually acquire understanding, and how to elicit from them what they do and do not understand. She applied these methods to teaching; training
teachers to track how children learn.

**she then** turned to the ESS curriculum development program (l960's) and helped create teaching children with natural materials: batteries, bulbs, bones, etc.

**from ESS** she drew the techniques she uses to impart and test understanding: having adults and children work with materials like balloons and mirrors, a technique that does not allow them to mask confusion behind memorized rules or formulas.

**she requires** students to watch the moon, a project that starts with students' assuming they understanding the moon and discovering they cannot explain by conventional book learning why the moon changes shape and position in the sky. She hopes adults will find her passion to keep learning infections ... and indeed, she is part of one moon watching group that has persisted for 11 years.
**the classes** are as informal as herself. She talks to her students with her shoes off and knees up, or sits down on the he floor along with other adults trying to understand why balloons are not behaving as they should. She is direct and unaffected ... and she took her own path to Harvard, by way of Montreal and Paris and Geneva and Africa.

**born in** Montreal in l935, she found her way to Paris as a graduate student and attended Piaget's lectures sitting in front to help her then-shaky Parisian French. After several months, Piaget approached her saying he had noticed she laughed at his jokes and saying that is were he put his most important ideas. After studying him ... she entered PhD program at Harvard and then dropped out in frustration.

**"i felt dumb,"** she said, and spent the next l7 years working on ESS; teaching 3rd grade in Montreal; evaluating science curricula in Africa and developing educational program in Nova Scotia.

**importance of feeling dumb**
**she got** her doctorate in Geneva in **l977**, but feeling dumb had a profound effect on her thinking. "it made me very aware of when I don't understand, I am very skeptical about whether anybody understands anything. I have to work hard to find some way for people who thought they know something to understand they know less than they thought.

**her students** say this process can be enthralling, infuriating and terrifying. It also runs counter to the current emphasis on using standardized tests results to evaluate what children learn. Professor Duckworth contends that conventional teaching and testing methods do not really convey knowledge to children or measure the breadth of their understanding. Her way takes much more time. To fully carry it out would require an ideal classroom, where teachers could work with pupils individually to unearth what they know and wherea typical test might be to put students in a room with a box of
materials and see what they make of it.

in the far from ideal world of the Boston schools, Lisa Schneier is putting Duckworth's ideas to work. She was able to teach fractions to a remedial HS class only after a slow patient assessment of just how her students perceived fractions.

**she presented** a student with a drawing of a circle cut into five equal pieces. She took away one piece and asked what that represented: l/4, the student told her, because there are four pieces there. It took weeks to wean the student from failing to take account of the part that had been removed and thereby reaching the correct answer, l/5.

**yet Duckworth's** students understand that teachers may not have the luxury of time and that failure to score well on tests can label students for the future.

**"she is **re-conceptualizing the kinds of structures schools should have. But most school are not like that. It's like a balancing act. There is a certain curriculum you have to be responsible for. Sometimes you have to say, 'OK , you're not going to understand this in the way I want you to, but learn it, pass it, and then we'll go back to what we're doing."

6/18s/95 -- 11/12sn/95 -- 4/15m/96