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“At Sea”: Reversibility in Teaching and Learning

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Abstract

An equal-armed balance at equilibrium—the bar is horizontal—tips into disequilibrium upon displacing a weight. Equilibrium is restored by reversing that move—putting the weight back where it was, or doing the same on the other side. Piaget adopted the idea of equilibration to describe how the intellect, in relating to the world, develops. Equilibrium arises as: our mind adjusts its structures in response to the outer world (accommodation), so our internalized views can take in this outer world (assimilation). That is the process Piaget calls equilibration. Upon undergoing disequilibrium, the intellect employs these equilibrating moves, changing its structures in the process. When the intellect resolves a disturbing problem no matter how it is encountered, the intellect tries to reverse the disturbing feature: how did the familiar situation get to this disturbing one; how might that change be reversed? These equilibrating processes are encouraged as means of teaching and learning in this paper’s math and science examples. The clinical interviewing methodology of Piaget and Inhelder, as adapted by Eleanor Duckworth in the research pedagogy of clinical exploration in the classroom, provides the neutral, safe conditions requisite for these learners and teachers in undergoing disequilibrium, struggling with uncertainty, and constructing new understandings. In beginning to teach through exploration, the author and an undergraduate experimented with free fall motion. Experiencing disequilibrium, the student reconstructed her understanding of time as concurrently continuous and divisible. Seeking to enact methods of Piaget and Duckworth while engaging her, the teacher also experienced disequilibrium.

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References

  • Abrahams, I., & Reiss, M. J. (2012). Practical work: Its effectiveness in primary and secondary schools in England. Journal of Research in Science Teaching, 48(8), 1035–1055.

    Article  Google Scholar 

  • Baker, R. M. (1970). A study of the effects of a selected set of science teaching materials (Elementary Science Study) on classroom instructional behaviors. Unpublished doctoral dissertation. Rochester, NY: University of Rochester.

  • Bamberger, J. (2013). The laboratory of making things: Developing multiple representations of knowledge. In W. Shorr, S. Hoidn, C. Lowry, & Author (Eds.), Always Wondering A Mélange of Eleanor Duckworth and Critical Exploration, pp. 175–200. Critical Exploration Press: Cambridge, MA.

  • Baptiste, H. P., & Turner, J. (1972). A study of the implimentation of the elementary science study program on a system-wide basis in the Penn-Harris-Madison Schools. ED 064107.

  • Bonawitz, E., Shafto, P., Gweon, H., Goodman, N., Spelke, E., & Schulz, L. (2011). The double-edged sword of pedagogy: Instruction limits spontaneous exploration and discovery. Cognition, 120, 322–330.

    Article  Google Scholar 

  • Breddermen, T. (1982). The effects of activity-based elementary science programs on student outcomes and classroom practices: A meta analysis of controlled studies. Albany, NY: New York State University, ED216870.

  • Cavicchi, E. (1993). Observation notes, S510. Cambridge, MA: Harvard Graduate School of Education.

    Google Scholar 

  • Cavicchi, E. (1994a). Words, symbols, patterns: Student talk about (and in) algebra. S510 Final Paper January 14, 1994, Harvard Graduate School of Education, Cambridge, MA.

  • Cavicchi, E. (1994b). Transcripts. T150, Harvard Graduate School of Education, Cambridge, MA.

  • Cavicchi, E. (1994c). Fieldworks. T150, Harvard Graduate School of Education, Cambridge, MA.

  • Cavicchi, E. (1994d). Halfway through the darkness. T150 Final Paper May 1994, Harvard Graduate School of Education, Cambridge, MA.

  • Cavicchi (1994e). Summer meetings. Harvard Graduate School of Education, Cambridge, MA

  • Cavicchi, E. (1996). Watching Galileo’s learning. In L. Kime & J. Clark (Eds.), Explorations in college algebra (pp. 581–595). New York: Wiley.

    Google Scholar 

  • Cavicchi, E. (1997). Experimenting with magnetism: Ways of learning of Joann and Faraday. American Journal of Physics, 65, 867–882.

    Article  Google Scholar 

  • Cavicchi, E. (1999). Experimenting with wires, batteries, bulbs and the induction coil: Narratives of teaching and learning physics in the electrical investigations of Laura, David, Jamie, Myself and the Nineteenth Century Experimenters—Our Developments and Instruments. Unpublished dissertation, Harvard University, Cambridge, MA.

  • Cavicchi, E. (2006). Faraday and Piaget: Experimenting in Relation with the World. Perspectives on Science, 14(1), 66–96.

    Article  Google Scholar 

  • Cavicchi, E. (2007). Mirrors, swinging weights, lightbulbs…: Simple experiments and history help a class become a community. In P. Heering & D. Osewold (Eds.) Constructing scientific understanding through contextual teaching, Frank & Timme, Berlin, pp. 47–63.

  • Cavicchi, E. (2008a). Opening possibilities in experimental science and its history: Critical explorations with pendulums and singing tubes. Interchange, 39, 415–442.

    Article  Google Scholar 

  • Cavicchi, E. (2008b). Historical experiments in students’ hands: Unfragmenting science through action and history. Science & Education, 17(7), 717–749.

    Article  Google Scholar 

  • Cavicchi, E. (2009). Exploring mirrors, recreating science and history, becoming a class community. New Educator, 5(3), 249–273.

    Article  Google Scholar 

  • Cavicchi, E. (2011). Classroom explorations: Pendulums. Mirrors and Galileo’s Drama. Interchange, 42(1), 21–50.

    Article  Google Scholar 

  • Cavicchi, E. (2012). Explorando Péndulos en el Salón de Clases. In Z. Monroy-Nasr, G. Alvarez, & R. León (Eds.), Enseñanza de la Ciencia (pp. 27–50). México City, Mexico: Facultad de Psicología y DGAPA, UNAM.

    Google Scholar 

  • Cavicchi, E. (2013a). Transcripts and notes. Edgerton Center.050, MIT, Cambridge, MA.

  • Cavicchi, E. (2013b). Shadows of light and history in explorative teaching and learning. In C. C. Silva & M. E. B. Prestes (Eds.), Learning science and about science through history and philosophy. Sao Paulo: Editora da Livraria da Física/FAPESP.

    Google Scholar 

  • Cavicchi, E. (2014). Learning science as explorers: Historical resonances, inventive instruments, evolving community. Interchange, 45(3), 185–204.

    Article  Google Scholar 

  • Cavicchi, E. (2017). Shaping and being shaped by environments for learning science: continuities with the space and democratic vision of a century ago. Science & Education, 26, 529–556.

    Article  Google Scholar 

  • Cavicchi, E. (2018). Syllabus, EC.050/090: Recreate historical experiments: Inform the future with the past. Cambridge, MA: MIT.

    Google Scholar 

  • Cavicchi, E., Chiu, S.-M., & McDonnell, F. (2009). Introductory paper on critical explorations in teaching art, science and teacher education. New Educator, 5(3), 189–204.

    Article  Google Scholar 

  • Chiu, S.-M. (2009). The ancient master painted like me. New Educator, 5(3), 229–248.

    Article  Google Scholar 

  • Cifone, M. (2001). A study of children’s spontaneous questioning and its relationship to their learning. Unpublished doctoral dissertation, Harvard University, Cambridge, MA.

  • Cifone, M. (2013). Questioning and learning: How do we recognize children’s questions? Curriculum and Teaching Dialogue, 15(1), 41–55.

    Google Scholar 

  • Cirino, H. (2001). Journal journeys: An exploration with young writers. In E. Duckworth (Ed.), “Tell Me More”: Listening to learners explain (pp. 79–92). New York: Teachers College Press.

    Google Scholar 

  • Critical Explorers Inc. (2010). Critical Explorers website. Retrieved January 2, 2018, from https://www.criticalexplorers.org/.

  • Colombe, L. (1612). Discorso Apologetico… Florence Italy: Pignoni. In Edizione digitale delle opera complete di Galileo Galilei, iv. Retrieved January 1, 2018, from https://bibdig.museogalileo.it/Teca/Viewer?an=961715.

  • Dean, D., & Kuhn, D. (2006). Direct instruction vs. discovery: The long view. Science Education, 91(3), 384–397.

    Article  Google Scholar 

  • DeBoer, G. (1991). A history of ideas in science education: Implications for practice. New York: Teacher’s College Press.

    Google Scholar 

  • Delaney, M. K. (2001). Understanding the Presidency. In E. Duckworth (Ed.), “Tell me more”: Listening to learners explain (pp. 125–146). New York: Teacher’s College Press.

    Google Scholar 

  • Di Stefano, R. (1996). The IUPP evaluation: What we were trying to learn and how we were trying to learn it. American Journal of Physics, 64, 49–57.

    Article  Google Scholar 

  • Duckworth, E. (2001a). Inventing density. In: E. Duckworth (Ed.), “Tell me more”: Listening to learners explain (pp. 1–41). New York: Teacher’s College Press. (Original essay published in 1986).

  • Duckworth, E. (2001b). Teaching/learning research. In E. Duckworth (Ed.), “Tell me more”: Listening to learners explain (pp. 181–187). New York: Teacher’s College Press.

    Google Scholar 

  • Duckworth, E. (2006a). The having of wonderful ideas. In E. Duckworth (3rd ed.), “The having of wonderful ideas” and other essays on teaching and learning (pp. 1–14). New York: Teacher’s College Press. (Original essay published in 1973).

  • Duckworth, E. (2006b). The virtues of Not-Knowing. In E. Duckworth (3rd ed.), “The having of wonderful ideas” and other essays on teaching and learning (pp. 63-68). New York: Teacher’s College Press. (Original essay published in 1975).

  • Duckworth, E. (2006c). Teaching as research. In E. Duckworth (3rd ed.), “The having of wonderful ideas” and other essays on teaching and learning (pp. 173–192). New York: Teacher’s College Press. (Original essay published in 1987).

  • Duckworth, E. (2006d). Twenty-four, forty-two and I love you: Keeping it complex. In E. Duckworth (3rd ed.), “The having of wonderful ideas” and other essays on teaching and learning (pp. 125-155). New York: Teacher’s College Press. (Original essay published in 1991).

  • Duckworth, E. (2006e). Critical exploration in the classroom. In E. Duckworth (3rd ed.), “The having of wonderful ideas” and other essays on teaching and learning (pp. 157–172). New York: Teacher’s College Press. (Original essay published in 2005, New Educator, 1, 257–272).

  • Ecsher, M. C. (n.d.) Picture gallery symmetry. Retrieved January 1, 2018 from http://www.mcescher.com/Gallery/gallery-symmetry.htm.

  • ESS. (1970). The ESS reader. Newton MA: Educational Development Center.

    Google Scholar 

  • ESS (Elementary Science Study). (1965). The faithful eye of Robert Hooke. Newton MA: Educational Development Center.

    Google Scholar 

  • ESS (Elementary Science Study). (1966a). Clay Boats; developmental teaching edition. Newton, MA: Educational Development Center.

    Google Scholar 

  • ESS (Elementary Science Study). (1966b). Melting ice cubes. Newton, MA: Educational Development Center.

    Google Scholar 

  • ESS (Elementary Science Study). (1968). Sink or float; teacher’s guide. Newton, MA: Educational Development Center.

    Google Scholar 

  • ESS (Elementary Science Study). (1969a). Balancing; teacher’s guide. Newton, MA: Educational Development Center.

    Google Scholar 

  • ESS (Elementary Science Study). (1969b). Teacher’s guide for Pendulums: [a study unit]. St. Louis: Webster Division, McGraw-Hill.

    Google Scholar 

  • ESS (Elementary Science Study). (1969c). Earthworms: A working paper. Newton, MA: Educational Development Center.

  • ESS (Elementary Science Study). (1969d). Children printing. Newton, MA: Educational Development Center.

    Google Scholar 

  • Faraday, M. (1932). In T Martin (Ed.), Faraday’s diary: Being the various philosophical notes of experimental investigation. London: G. Bell and Sons LTD.

  • Galilei, G. (1957). Discoveries and Opinions of Galileo, S. Drake, trans, notes, Garden City NY: Doubleday.

  • Galilei, G. (1967). Dialogue Concerning the Two World Systems, S. Drake, (trans.), Berkeley CA: University of California Press. (Original work published in 1632).

  • Galilei, G. (1978). Operations of the Geometrical and Military Compass, S. Drake, trans., Washington DC: Smithsonian. (Original work published in 1606). Retrieved January 1, 2018, from, http://brunelleschi.imss.fi.it/esplora/compasso/dswmedia/simula/esimula2.html.

  • Galilei, G. (1989). Sidereus Nuncius, A. Van Helden, trans., Chicago IL: University of Chicago Press. (Original work published in 1610).

  • Gill, K. (2004). At Cézanne’s table: Exploring content-based instruction in the English language in an art museum. Unpublished qualifying paper, Harvard University, Cambridge, MA

  • Goldstein, J. (1992). A different sort of time: The life of Jerrold R. Zacharias, Scientist, Engineer, Educator. Cambridge, MA: MIT Press.

  • Gooding, D. (1990). Experiment and the making of meaning. Dordrecht: Kluwer.

    Book  Google Scholar 

  • Gooding, D. (2006). From phenomenology to field theory: Faraday’s visual reasoning. Perspectives on Science, 14(1), 40–65.

    Article  Google Scholar 

  • Griffith, J., & Morrison, P. (1971). Reflections on a decade of grade-school science. Physics Today, 25(6), 29–34.

    Article  Google Scholar 

  • Hammer, D. (2000). Teacher Inquiry. In J. Minstrell & E. van Zee (Eds.), Inquiring into inquiry learning and teaching in science (pp. 184–215). Washington, DC: American Association for the Advancement of Science.

    Google Scholar 

  • Hammer, D., & van Zee, E. H. (2006). Seeing the science in children’s thinking: Case studies of student inquiry in physical science. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Harouni, H. (2013). The risking of observations in the classroom: Teacher as cultural critic. In: W. Shorr, S. Hoidn, C. Lowry, Author, (Eds.), Always Wondering… A Mélange of Eleanor Duckworth and Critical Exploration (pp. 130–142). Critical Exploration Press: Cambridge, MA.

  • Harouni, H. (2015). Purpose and education: The case of mathematics. Unpublished doctoral dissertation, Harvard University, Cambridge, MA.

  • Hausknecht, A. O., & Kowalczyk, R. E. (2000–2011). Temath. University of Massachusetts Dartmouth.Retrieved January 1, 2018, from, http://www.faculty.umassd.edu/adam.hausknecht/temath/.

  • Hawkins, D. (2002). I, thou and it. In D. Hawkins (2nd ed.), The informed vision: Essays on learning and human nature (pp. 51–64). New York: Algora. (Original work published in 1967).

  • Hughes-McDonnell, F. J. (2000). Circuits and pathways of understanding: “I can’t believe we’re actually figuring out some of this stuff”. Unpublished doctoral dissertation, Harvard University, Cambridge, MA.

  • Hughes-McDonnell, F. (2009). “I wonder how this little seed can have so much potential”: Critical exploration supports preservice teacher's development as science researchers and teachers. The New Educator, 5, 205–228.

    Article  Google Scholar 

  • Inhelder, B., & Piaget, J. (1958). The Growth of Logical Thinking: From Childhood to Adolescence (A. Parsons and S. Milgram, Trans.). NY NY: Basic Books. (Original Work published in 1955).

  • Inhelder, B., Sinclair, H., & Bovet, M. (1974). Learning and the development of cognition (S. Wedgwood, Trans.). Harvard University Press, Cambridge, MA.

  • Julyan, C. (1988). Understanding trees: five case studies. Unpublished doctoral dissertation, Harvard University, Cambridge. MA.

  • Kime, L., & Clark, J. (1993). Free fall experiment. Math 110 Part II, Day 3, November 18, 1993.

  • Kime, L., & Clark, J. (1996). Explorations in college algebra: Discovering algebra from data based applications. New York: Wiley.

    Google Scholar 

  • Kline, M. (1967). Mathematics for the nonmathematician. Reading, MA: Addison Wesley.

    Google Scholar 

  • Knox, I. (2001). Newborn Developments. In E. Duckworth (Ed.), “Tell Me More”: Listening to learners explain (pp. 147–165). New York: Teachers College Press.

    Google Scholar 

  • Kuhn, T. (1970). Structure of scientific revolutions. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Kuhn, T. (1977). The essential tension: Selected studies in scientific tradition and change. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Learning Progressions Project (2013). Responsive Teaching in Science. Retrieved January 1, 2018, from, http://cipstrends.sdsu.edu/responsiveteaching/index.html.

  • Lowry, C. (2006). Six mothers in search of a Swiss author: A critical exploration into Piaget’s ideas of learning. Unpublished doctoral dissertation, Harvard University, Cambridge, MA.

  • Magau, N. (2001). Looking at learning to understand teaching: A South African case study. In E. Duckworth (Ed.), “Tell Me More”: Listening to learners explain (pp. 166–180). New York: Teachers College Press.

    Google Scholar 

  • Maskiewicz, A., & Winters, V. (2012). Understanding the co-construction of inquiry practices: A case study of a responsive teaching environment. Journal of Research in Science Teaching, 49(4), 429–464.

    Article  Google Scholar 

  • McKinney, A. W. (2004). Shaping history: Five students, three artifacts, and the material, social and economic lives of late nineteenth-century butter-makers. Unpublished doctoral dissertation, Harvard University, Cambridge, MA.

  • Melville, H. (2008). Moby Dick, or The Whale. (Original work published in 1851). Retrieved January 1, 2018, from https://www.gutenberg.org/files/2701/2701-h/2701-h.html.

  • Millar, R., & Driver, R. (1987). Beyond processes. Studies in Science Education, 14(1), 33–62.

    Article  Google Scholar 

  • NGSS. (2013). Model Course Mapping, Appendix K, Next Generation Science Standards. Retrieved January 1, 2018 from http://www.nextgenscience.org/sites/ngss/files/Appendix%20K_Revised%208.30.13.pdf.

  • NSES. (1996). National Science Education Standards. Washington DC: National Academy Press. Retrieved January 1, 2018 from http://www.nap.edu/openbook.php?record_id=4962.

  • NSTA. (2004a). Science Teacher Preparation, NSTA Position Statement. Retrieved January 1, 2018, from http://www.nsta.org/about/positions/preparation.aspx.

  • NSTA. (2004b). Scientific Inquiry, NSTA Position Statement. Retrieved January 1, 2018 from http://www.nsta.org/about/positions/inquiry.aspx.

  • Piaget, J. (1952). The origins of intelligence in children (M. Cook, Trans.). New York: International Universities Press. (Original work published in 1936). Retrieved January 1, 2018, from https://archive.org/details/originsofintelli017921mbp.

  • Piaget, J. (1954). The construction of reality in the child (M. Cook, Trans.). New York: Basic Books. (Original work published in 1936).

  • Piaget, J. (1955). The Language and Thought of the Child (M. Gabain, Trans.). New York: Meridian Books. (Original work published in 1926).

  • Piaget, J. (1960). The child’s conception of the world (J. & A. Tomlinson, Trans.). Totowa, NJ: Littlefield, Adams. (Original work published in 1926).

  • Piaget, J. (1965a). The moral judgment of the child (M. Gabain, Trans.). New York: Free Press. (Original work published in 1932) http://www.archive.org/details/moraljudgmentoft005613mbp

  • Piaget, J. (1965b). The child’s conception of number, (C. Gattegno & F. M. Hodgson, Trans.). New York: W. W. Norton & Co. (Original work published in 1941).

  • Piaget, J. (1969). The child’s conception of time (A.J. Pomerans, Trans.). New York: Ballantine Books. (Original work published in 1927).

  • Piaget, J. (1981). The Psychology of Intelligence (M. Piercy and D. E. Berlyne, Trans.). Totowa, NJ: Littlefield Adams. (Original work published in 1947).

  • Piaget, J. (1987a). Possibility and necessity: Volume 1; The role of possibility in cognitive development (H. Feider, Trans.). Minneapolis MN: University of Minnesota Press. (Original work published in 1981).

  • Piaget, J. (1987b). Possibility and necessity: Volume 2; The role of necessity in cognitive development (H. Feider, Trans.). Minneapolis MN: University of Minnesota Press. (Original work published in 1981).

  • Piaget, J., & Garcia, R. (1989). Psychogenesis and the History of Science (H. Feider, Trans.). NY: Columbia University Press. (Original work published in 1983).

  • Piaget, J., & Inhelder, B. (1958). The Growth of Logical Thinking: From Childhood to Adolescence (A. Parsons and S. Milgram, Trans.). New York: Basic Books. (Original work published in 1955).

  • Piaget, J., & Inhelder, B. (1967). The child’s conception of space (F. J. Langdon & J. L. Lunzer Trans.). New York: Norton. (Original work published in 1948).

  • Piaget, J., & Inhelder, B. (1969). The Psychology of the Child (H. Weaver, Trans.). New York: Basic Books. (Original work published in 1966).

  • Piaget, J., & Inhelder, B. (1975). The Origin of the Idea of Chance in Children (L. Lake Jr., P. Burrell, H. D. Fishbein, Trans.) New York: Norton. (Original work published in 1951).

  • Piaget, J., Inhelder, B., & Szeminska, A. (1981). The child’s conception of geometry (E.A. Lunzer, Trans.). New York: Norton. (Original work published in 1960).

  • PSSC (Physical Science Study Committee). (1960). Physics. Boston, MA: Heath.

    Google Scholar 

  • Quintero, I. (2001). Children map their neighborhoods. In E. Duckworth (Ed.), “Tell Me More”: Listening to learners explain (pp. 93–124). New York: Teachers College Press.

    Google Scholar 

  • Rauchwerk, S. (2005). Incubating knowledge: A critical exploration with teachers studying live chickens. Unpublished doctoral dissertation, Harvard University, Cambridge MA.

  • Rogers, R., & Voekler, A. (1970). Programs for Improving Science Instruction in the Elementary School, Part 1, ESS. Columbus OH: Ohio State University, ED 039128.

  • Romney, E., & Neuendorffer, M. J. (1973). The Elementary Science Study: A history. Newton, MA: Elementary Science Study of Education Development Center.

    Google Scholar 

  • Rowe, T. (1987). Using introspective methods to investigate the learning strategies of adult foreign-language learners: four case studies. Unpublished doctoral dissertation, Harvard University, Cambridge, MA.

  • Rudolph, J. (2002). Scientists in the classroom: The cold war reconstruction of American science education. New York: Palgrave.

    Book  Google Scholar 

  • Schneier, L. (2001). Apprehending poetry. In E. Duckworth (Ed.), “Tell Me More”: Listening to learners explain (pp. 42–78). New York: Teachers College Press.

    Google Scholar 

  • Schneier, L. (2018). Dancing in the Hall. Interchange, this issue.

  • Science a Process Approach (SAPA). 1965. Science: A process approach, Commentary for Teachers. Washington, DC: American Association for the Advancement of Science.

  • Sconiers, Z., & Rosiek, J. (2000). Historical perspective as an important element of teachers’ knowledge: A Sonata-Form case study of equity issues in a chemistry classroom. Harvard Educational Review., 70(3), 370–405.

    Article  Google Scholar 

  • Shorr, W. (2006). Coordinating conceptions of peace: A critical exploration in social studies curriculum development. Unpublished doctoral dissertation, Harvard University, Cambridge MA.

  • Shorr, W., Hoidn, S., Lowry, C., & Cavicchi, E. (Eds.). (2013). Always wondering… A Mélange of Eleanor Duckworth and critical exploration. Cambridge, MA: Critical Exploration Press.

    Google Scholar 

  • Stefanich, G. (1976). Comparison of the treatment of electricity in the SAPA, SCIS and ESS elementary science curricula. American Journal of Physics, 44(4), 384–386.

    Article  Google Scholar 

  • Steinle, F. (2002). Experiments in history and philosophy of science. Perspectives on Science, 10(4), 408–432.

    Article  Google Scholar 

  • Tierney, C. (1988). Construction of fraction knowledge: two case studies. Unpublished doctoral dissertation, Harvard University, Cambridge, MA.

  • Tweney, R. (2001). Scientific thinking: A cognitive-historical approach. In K. Crowley, C. D. Schunn, & T. Okada (Eds.), Designing for science: Implications from everyday, classroom, and professional settings (pp. 141–173). Mahwah, NJ: Erlbaum Associates.

    Google Scholar 

  • Tweney, R. (2006). Discovering discovery: How Faraday found the first metallic colloid. Perspectives on Science, 14(1), 97–121.

    Article  Google Scholar 

  • Yang, Y. (2013). Unrelenting curiosity. Final Paper EC.090, MIT, Cambridge MA.

  • Yang, Y. (2014). Finding roots: a learner’s voyage. Unpublished qualifying paper, Harvard University, Cambridge, MA.

  • Yang, Y. (2018). A learner’s voyage: my moon exploration in 2009. Interchange, this issue.

  • Zion, M., & Slezak, M. (2005). It takes two to tango: In dynamic inquiry, the self-directed student acts in association with the facilitating teacher. Teaching and Teacher Education, 21, 875–894.

    Article  Google Scholar 

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Acknowledgements

I am happy to thank students who have joined me in classes and studies, including: the 1993 college algebra class, Hazel Garland, Sarah Alexander, Lydia Anzures, Yang Yan, Madhu Anantharajan, Houman Harouni. James Bales, Ed Moriarty and the MIT Edgerton Center support my exploratory teaching. Linda Kime, Judy Clark and colleagues encouraged my study in their algebra class; Paul Foster provided access to the free fall apparatus. I thank my teachers and teaching fellows: Joseph Maxwell and Stephen Sherblom; Eleanor Duckworth and Susan Rauckwerk. Contributors to these educational studies include: Jeanne Bamberger, Alva Couch, Eleanor Duckworth, Philip and Phylis Morrison I am grateful for provocative discussions with: Peter Heering, Fiona Hughes-McDonnell, Lisa Schneier, Bonnie Tai, Ryan Tweney, Yang Yan. This paper was improved by thoughtful comments of Judy Clark, Alva Couch, Houman Harouni, Bonnie Tai, Ryan Tweney, Chris Lowry, William Shorr, and the journal’s reviewers, and discussion with: Jasleen Anand, Son-Mey Chiu, Eleanor Duckworth, Tim Johnson, Lisa Schneier, and Yang Yan. I wrote this account from my researches at the request of Yang Yan.  This work holds in memory: Yang Yan, Philip Morrison, Alanna Connors and my father.

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    Elizabeth Mary Cavicchi

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Cavicchi, E.M. “At Sea”: Reversibility in Teaching and Learning. Interchange 49, 25–68 (2018). https://doi.org/10.1007/s10780-018-9314-9

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