1. The work of Jean Piaget and Bärbel Inhelder. Duckworth was a student and colleague in the late 1950s and she acted as the English translator and interpreter of Piaget during his American lectures, until his death in 1980. Two aspects in the work of Piaget and Inhelder were especially important for Duckworth (2005b, p. 258—259): First, the basic idea of assimilation, that is, every person creates meaning on her own, while taking any experience into her own schemes, structures, previous understanding. Second, the clinical interviewing or clinical method, that is, engaging children in talking about their ideas with a researcher.
2. Her experience with the Elementary Science Study (ESS) curriculum development program. This program is consistent with the work of Piaget and Inhelder in psychology and it is considered to be a milestone in the history of science education. The Elementary Science Study tackled the following main question: "So how do we present material 'from without' so that the activity that 'the mind itself undergoes' is valuable?" (Duckworth, 2005a, p. 142)

The main ideas of the teaching/learning research

• Students bring their prior expectations, interests and knowledge to the learning experience: The students' experience and insights are of high value as the development of their personal intelligence emerges through actions and the having of wonderful ideas. To reach deep understanding, students need to start from their own sets of ideas, be engaged in the subject matter and make a connection from the actual problem or subject matter to what they already understand. Consequently, the students do the talking as they explain the sense they are making, while the teacher listens. However, this requires a learning culture that accommodates students in feeling free and safe to say what their emerging ideas are, and that what they say is valued (Duckworth in Meek, 1991). "[B]y opening up to children the many fascinating aspects of the ordinary world and by enabling them to feel that their ideas are worthwhile having and following through, their tendency to have wonderful ideas can be affected in significant ways" (Duckworth, 2006, p. 12).
• Students need something complex that challenges them to explore: Students need to engage with the phenomena of study, not schematic substitutes. It is in struggling with complex problems that every learner undergoes the process of constructing their own knowledge. As learners experience internal cognitive conflicts in what they believe about the subject matter, their minds become more deeply engaged with the problem at hand. Learners' efforts in figuring out questions and puzzles are more productive than knowing the right answer because higher order thinking processes are involved. Therefore, teachers of critical exploration value the diverse efforts that students make during their explorations even where these efforts do not arrive at expected answers. In facilitating this investigative work, the questions that are asked over and over again by students and teachers alike are, for example: "What do you notice?" What do you mean?" "How you are thinking about it?" "Why do you think that?" "Is that the same as what (someone else) thought they saw?" "How did you figure that?" "How did you do that?" "How does that fit with what she just said?" "Could you give an example?" The responses that teachers and students give to each other might have the form of: "I don't quite get it." "It doesn't make sense (to me)." "I don't really get that; could you explain it another way?" Hence, most important: It is the students who make sense and understand by trying out their ideas, explaining them to others, and seeing how this holds up in other people's and their own eyes and in the light of the phenomena itself (Duckworth, 2002).
• Teacher as facilitator with a researcher mind-set: The teacher creates situations and selects environmental resources that get students excited and engaged in learning that is meaningful to them. The teacher is sensitive to the thoughts and feelings of learners, puts students at ease, engages learners, invites them to talk about their ideas, waits for learners to think and listens and then, reacts to the substance of their answers without judging them. The teacher takes a neutral researcher's stance. Instead of lecturing, the teacher creates situations that put learners into confronting their thinking processes, where they are responsible for their own learning. The teachers' role then, is asking questions like “When you say x, what do you mean by it?" "How would that work if applied to this situation?" "Am I right in understanding your idea, if I say it this way?” to reveal students' thinking and take their own thoughts further. That way, the teacher refrains from signaling to the students what he might expect them to say. Instead, the teacher provides opportunities for learners to reveal their own understanding. The thoughts that learners have become visible through the responses they make including: actions, drawings, gestures, constructions, dialogues and sound, for example. Guiding questions for the teacher himself might be as follows (Duckworth, 2005b, p. 261): "What lies behind this response? How may the other children be responding to it? What question shall I ask next, or what experience to offer next, or where to direct their attention next?" The students' work is to make sense of the phenomena of study. The teachers' work is to ensure safe and supportive conditions in the classroom so that the students can take intellectual risks and do their work investigatively.

Some learning/teaching examples

(1) Learning science with mirrors (Chira, 1989, para. 6)

Two shy teenagers, Dan and John, on loan from a local high school, stood facing 50 student observers as Professor 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 themselves 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? she asked.

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 told her. By the end of the class, they had discovered for themselves the physics formula that Professor Duckworth never stated: The angle of incidence equals the angle of reflection.

(2) Moonwatching - the moon project (Pettigrew, 2007, p. 43—44)

Our most dramatic assignment required that we watch the moon for an entire semester. Every day we recorded our sightings and shaped questions. It was astonishing to discover how pitifully little most of us knew about the moon. At first our questions were simple: When does the moon rise? Where does it rise? Wait, does it rise in a different place sometimes? Why was it still in the sky this morning at 8:45? How does that happen? We drew pictures in our journals; we reflected in writing on what we saw. And then we brought our jottings to class, sharing observations, sharing information, and sharing our confusions. We worked together. Eleanor listened. Her utterances were invariably inquisitive and open-ended and completely nonjudgmental; she was singularly focused on understanding the meaning we were making. Her focus seemed to be on how we were building our understanding rather than on what we understood. I wonder if you could say more about that, she might say. Or, I’m curious about what you see happening here. Over the course of our first semester, my classmates and I experienced a change: our observations of the moon became more subtle and our questions became very much more complicated, more sophisticated. One night, late into our second term, I came into class with a question about the rotations of the moon as it revolves around the Earth. Eleanor brought me - and my question - to the front of the room. She let me explain the problem. I drew pictures on the board, thinking out loud. She and the class listened hard; I could feel them listening. I can’t tell you how affirming such listening is. And then, when I seemed to hit a wall, a dead-end in my process, Eleanor asked, Would it help if you used this flashlight and this orange, and before long, I was the sun and a classmate was the Earth, and another classmate rotated the orange as he revolved around the “Earth.” I was directing the action out of my own body of understanding, and I could feel myself moving toward a solution. It took time. It felt like a few minutes to me, but it must have been much longer because Eleanor, sensing that I was on the brink and knowing that learning is a series of “flights and perchings,” put her hand on my shoulder and asked me if I’d like to let it rest a little. I went back to my desk in the far rear of the darkened room and pulled out a notebook in which I began to draw, still noodling the problem. I could feel that my solution was imminent; I could feel it. One of my classmates, sitting in the dark on the floor next to me, whispered urgently that he knew the answer to my question. He could tell me. And he began to explain. He wanted to be helpful, but resentment and self-protection rushed up inside me: here was a robber entering my house. He would steal from me an understanding that in a minute or two, by my own efforts, would be mine. I was desperate. I leaned down and hissed into his face: “Shut up!” And he did. I began then, for the first time in my life, to solve a problem by laying out an algebraic formula (I don’t know where that impulse came from), and as I constructed the formula, the pieces fell, breathtakingly, into place. It was an “aha” moment. I knew, perhaps, for the first time, the euphoria of discovery. I walked home that night with the knowledge that there would be a fundamental change in my teaching.

(3) Teaching commas (Stewart, 1995, p. 1—2 cited in Duckworth, 2005a, p. 146—147)

On Friday, I taught the lesson on commas that I had been working on. It went superbly well. The students were engaged in the lesson throughout the period and really seemed to both enjoy and learn the material (and we’re talking about commas here). I also felt confident and knowledgeable about the purposes and pedagogy, especially after discussing my plans with [fellow students of teaching and learning].

I introduced the lesson by asking if any of the students felt comfortable using commas. None did. I then spoke about the wonderful ideas I had seen in many of their papers and how important it was to polish their papers by using commas correctly, for, if they don't, their brilliant ideas will be lost in the world's judgment of their mechanics. I handed out the materials: sheets of comma-less sentences from the students' writing, sheets of correct comma usage in the students' writing for them to refer to, and newspaper clippings. After I had arranged the students to work in pairs, one student called me over. She wanted to tell me that I was 'doing it wrong,' that I was supposed to give them all the rules regarding commas and then they were supposed to fill out the worksheets demonstrating what they had learned.

After the pairs of students worked together on the passages that needed commas, the class as a whole worked on them with an overhead projection that allowed them to share a single conversation. When students disagreed on comma placement, much of the class would get involved in the debate. I would move the commas to different places on the transparency according to their thinking. During this time, the students were completely engaged in the class. Together we developed a few basic rules of comma usage...I...was impressed with how much more engaged the students were when they had a chance to 'figure things out.' ...One student came up after class and thanked me for the class, saying that she had always felt unsure of herself and her writing because of commas.

Implications for teacher education: Teaching teachers to understand understanding

1. Films and/or (life) demonstrations with one or two children or adolescents. In this way teacher education students can observe children/adults learning while instructors are teaching by engaging those learners and by listening and understanding the explanations of those learners;
2. Teacher education students carry out a similar inquiry outside of classtime, where they meet with one or two people who are their practice learners. In this way, each teacher education student creates, on his own, a trial critical exploration for learners and then reflects on it in writing;
3. Teacher education students learn as a group about a particular subject other than teaching and learning. Through this exploratory study by the group, the teacher education students are learning in the same way that the children in their classes will be learning. This subject could be from any area of study such as: pendulums, mathematical permutations, history, arts and poems.

• "My way of teaching was an extension of finding out what the kids did and didn't understand, and I had fun extending my discussions with kids. The more they told me about their explorations, the more their understanding developed; they also heard and responded to each other's ideas" (Duckworth in Meek, 1991, p. 30).
• "In all of my formal schooling, I have only three memorable learning experiences. And they were all where I was called upon to have some ideas of my own... All these were examples of times when teachers gave me the opportunity to think on my own" (Duckworth, 1999, p. 29).
• "[Y]ou can't assume people have understood something because you've led them through it very carefully. Nowadays that is absolutely critical to everything I do... Taking them through my sequence fails on two counts - one, it's boring to the learner and, two, it doesn't correspond to the ways their minds are taking on the subject. So it misses the boat" (Duckworth, 1999, p. 29).
• "Real learning, attentive, real learning, deep learning, is playful and frustrating and joyful and discouraging and exciting and sociable and private all the time, which is what makes it great" (Duckworth, 1999, p. 30).
• "Knowing the right answer requires no decisions, carries no risks, and makes no demands. It is automatic. It is thoughtless" (Duckworth, 2006, p. 63).
• "The virtues involved in not knowing are the ones that really count in the long run. What you do about what you don't know is, in the final analysis, what determines what you will know" (Duckworth, 2006, p. 67).
• "For Piaget the question is not how fast you go but how far you go" (Duckworth, 2006, p. 69).
• "Our challenge as curriculum developers is to find the ways to engage learners, young or old, in the complexities of the areas we think it is important for them to know about. As researchers who are interested in how ideas actually develop, I think we have exactly the same challenge. I hope I have made clear how intertwined these challenges are" (Duckworth, 2006, p. 154).
• "Teaching is helping people learn, and you have not taught if people have not learned. Teaching is not telling" (Duckworth in Bobilya & Daniel, 2009, p. 115).
• "When I'm working well, I speak maybe four times in a 50-minute period - and I try to make those remarks brief. Such teaching requires continual self-discipline: I will admit that my own enthusiasms are sometimes hard to contain. My interests and interpretations - my understanding - continually threaten to burst into the open. Put another way: my ego is always ready to get between the students and their explorations - 'like a robber breaking in upon their thoughts.' I must be vigilant. To practice a pedagogy of critical exploration, a listening pedagogy, the teacher must be ready to stand out of the way" (Pettigrew, 2007, p. 45).
• "Becoming a critical explorer, a creative teacher, or a thoughtful citizen all require a willingness to forgo the comfort of certainty and engage with the discomfort of ambiguity and uncertainty" (Shorr, 2007, p. 371).

• Inaugural Barbara K. Lipman Award for Advances in Early Childhood Education given annually to a researcher, writer or program designer who has significantly influenced early childhood education or child growth and development, University of Memphis (2008).
• Doctor of the University, Honoris Causa, University of Ottawa (1993).
• The book "The having of wonderful ideas" and other essays on teaching and learning won the American Educational Association Award for writing on teaching and teacher education (1987).
• Invited to give Catherine Molony Memorial Lecture at City College School of Education, Workshop Center for Open Education (1979).
• Doctor of Humane Letters, Honoris Causa, Lesley University (1977).

• Duckworth, E.R. (1964a). Piaget rediscovered. Journal of Research in Science Teaching, 2(3), 172—175.
• Duckworth, E.R. (1964b). Floating color tubes. Nature and Children, 1(2), 6—7.
• Duckworth, E.R. (1973a). Language and Thought. In M. Schwebel & J. Raph (Eds.), Piaget in the classroom (pp. 132—154). New York: Basic Books.
• Duckworth, E.R. (1973b). The having of wonderful ideas. In M. Schwebel & J. Raph (Eds.), Piaget in the classroom (pp. 258—277). New York: Basic Books.
• Duckworth, E.R. (1973c). Piaget takes a teacher's look. An interview with Jean Piaget. Learning: The magazine for Creative Teaching, 22—27.
• Duckworth, E.R. (1978). The African primary science program: An evaluation and extended thoughts. Grand Forks: North Dakota Study Group on Evaluation.
• Duckworth, E.R. (1979). An introductory note about Piaget. Journal of Education, 161, 5—12.
• Duckworth, E.R. (1983). Teachers as learners. Archives de Psychologie, 51, 171—175.
• Duckworth, E.R. (1987). Some depths and perplexities of elementary arithmetic. Journal of Mathematical Behavior, 6, 43—94.
• Duckworth, E.R. (1990). Opening the world. In E. Duckworth, J. Easley, D. Hawkins & A. Henriques (Eds.), Science education: A minds-on approach for the elementary years (pp. 21—59). Hillsdale, NJ: Erlbaum.
• Duckworth, E.R. (1999). Engaging learners with their own ideas: An interview with Eleanor Duckworth. The Active Learner, 4(1), 28—30.
• Duckworth, E.R. (2001a). Inventing density. In E. Duckworth (Ed.), "Tell me more": Listening to learners explain (pp. 1—41). New York: Teachers College Press. Original publication 1986.
• Duckworth, E.R. (2001b). "Tell me more": Listening to learners explain. New York: Teachers College Press. Booknote retrieved, April 12, 2009 at http://www.hepg.org/her/booknote/79 Book review retrieved, April 12, 2009 at http://www.nicholasmeier.com/Articles/2005-04_duckworth.htm
• Duckworth, E.R. (2002). "The having of wonderful ideas" and other essays on teaching and learning. Fieldwork - Notes from expeditionary learning classrooms, X(2), 11—12. Book review retrieved, April 12, 2009 at http://thunder1.cudenver.edu/cye_journal/review.pl?n=66
• Duckworth, E.R. (2005a). A reality to which each belongs. In B.S. Engel (Ed.), Holding values: What we mean by progressive education (pp. 142—147). Portsmouth, NH: Heinemann.
• Duckworth, E.R. (2005b). Critical exploration in the classroom. New Educator, 1 (4), 257—272.
• Duckworth, E.R. (2006). "The having of wonderful ideas" and other essays on teaching and learning. Third edition. New York: Teachers College Press.
• Duckworth, E.R. (2008). Teaching as research. In A. Miletta & M. Miletta (Eds.), Classroom conversations. A collection of classics for parents and teachers (pp. 119—144). New York: The New Press.
• Duckworth, E.R. (2009a). Helping students get to where ideas can find them. The New Educator 5(3), 185-188.
• Duckworth, E.R. (2009b). Critical exploration in the classroom. Harvard Graduate School of Education - Usable Knowledge.
• Duckworth, E.R. and the Experienced Teachers Group (1997). Teacher to teacher: Learning from each other. New York: Teachers College Press.Book review retrieved, April 12, 2009 at http://edrev.asu.edu/reviews/rev42.htm
• Duckworth, E.R. & Julyan, C. (2005). A constructivist perspective on teaching and learning science. In C.T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice (pp. 61—79). 2nd edition. New York: Teachers College Press.
• Duckworth, E.R., Easley, J., Hawkins, D. & Henriques, A. (Eds.) (1990). Science education: A minds-on approach for the elementary years. Hillsdale, NJ: Erlbaum.

• Annenberg Media (w.d.). Tune in to the moon. Materials, activities and resources regarding learning about the moon.
• Duckworth, E.R. (1973). Learning about thinking and vice versa (videorecording, 32 min.), Films Inc., Ford Foundation. Educator Eleanor Duckworth demonstrates children's thinking processes (and developmental differences in children's learning) through classic Piaget-type interviews held during a workshop for teachers, teacher aides, and principals of two inner-city Philadelphia schools.
• Duckworth, E.R. (2009a). Faculty profile, Harvard University School of Education.
• Duckworth, E.R. (2009b). Critical thinking through learner-centred teaching. An interview with Eleanor Duckworth conducted by Anis Haffar.
• Evans, R.I. (1973). Jean Piaget. The man and his ideas. New York: E.P. Dutton & Co., Inc.; Translated by Eleanor Duckworth.
• Falk, B. (Ed.) (2009). Critical explorations: The road to understanding. Theme issue in The New Educator 5(3).
• Mayer, S.J. (2009). Critical exploration - website online.
• Piaget, J. (1968, lecture one). Genetic Epistemology. A series of lectures delivered by Piaget at Columbia University. Published by Columbia University Press; translated by Eleanor Duckworth.