Volume 9 · Number 3 · Pages 302–310
Constructing Constructivism

Hugh Gash

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Context: The paper is a selective survey of radical constructivist (RC) research that relates to education. Problem: Over the past 40 years there have been developments in the research reviewed. Earlier work was often concerned with conceptual clarification and showing different ways children and teachers think, whereas recent work is more systemic and applied. Method: Research with educational implications done by the author and colleagues is surveyed. This survey shows how RC influenced research in a variety of psychological domains including attitudes to different others, science education, and teacher professional development. Results: While initial work by the author in this area focussed on conceptual clarification, the more recent work is classroom-based, with implications for educational practice in schools. The final part of the paper on research by colleagues emphasises how teachers might work together in schools and the broader school system. Implications: RC plays a significant role in national curricula as a theoretical approach to facilitating diversity in schools and empowering children in their education. There is an urgent need to focus on student learning. The work on educational applications cited provides important insights into the resolvable problems of enabling genuine learning communities. Constructivist Content: The paper addresses theoretical clarification, variations in children’s concepts about different others, inclusion, and implementation of educational programmes that use RC frameworks.

Key words: Dewey, Piaget, process, certainty, education, facilitating learning.


Gash H. (2014) Constructing constructivism. Constructivist Foundations 9(3): 302–310. http://constructivist.info/9/3/302

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Ackermann E. (1991) From de-contextualized to situated knowledge: Revisiting Piaget’s water-level experiment. In: Harel I. & Papert S. (eds.) Constructionism: Research reports and essays, 1985–1990. Ablex, New Jersey: 367–377. ▸︎ Google︎ Scholar
Arons A. B. & Karplus R. (1976) Implications of accumulating data on levels of intellectual development. American Journal of Physics 44(4): 396. ▸︎ Google︎ Scholar
Ashby W. R. (1947) Principles of the self-organizing dynamic system. Journal of General Psychology 37: 125–128. ▸︎ Google︎ Scholar
Bell B. F. (1991) A constructivist view of learning and the draft forms 1–5 Science Syllabus. SAME Papers: 154–180. ▸︎ Google︎ Scholar
Bell M. A. & Deater-Deckard K. (2007) Biological systems and the development of self-regulation: Integrating behavior, genetics, and psychophysiology. Journal of Developmental and Behavioural Pediatrics 28(5): 409–420. ▸︎ Google︎ Scholar
Berkeley G. (1975) Philosophical works, including the works on vision. Edited by Michael R. Ayers. Everyman edition. J. M. Dent, London. Originally published in 1709. ▸︎ Google︎ Scholar
Bickhard M. (1995) World mirroring versus world making: There’s gotta be a better way. In: Steffe L. P. & Gale J. (eds.) Constructivism in education. Lawrence Erlbaum, Hillsdale NJ: 229–267. ▸︎ Google︎ Scholar
Bigler R. S. (1995) The role of classification skill in moderating environmental influences on children’s gender stereotyping. Child Development 66(4): 1072–1087. ▸︎ Google︎ Scholar
Bonabeau E., Dorigo M. & Theraulaz G. (1999) Swarm intelligence: From natural to artificial systems. Oxford University Press, Oxford. ▸︎ Google︎ Scholar
Boxer P. & Kenny V. (1990) The economy of discourses: A third-order cybernetics? Human Systems Management 9(4): 205–224. ▸︎ Google︎ Scholar
Bringuier J.-C. (1980) Conversations with Jean Piaget. University of Chicago Press, Chicago. ▸︎ Google︎ Scholar
Brown J. S., Collins A. & Duguid P. (1989) Situated cognition and the culture of learning. Educational Researcher 18(1): 32–41. ▸︎ Google︎ Scholar
Bruner J. (1960) The process of education. Vintage Books, New York. ▸︎ Google︎ Scholar
Butler D. & Gash H. (2003) Creative learning and spiritual moments. In: Lasker G. E. (ed.) Advances in sociocybernetics and human development. Volume XI. International Institute for Advanced Studies, Windsor: 41–46. ▸︎ Google︎ Scholar
Butler D. (2004) Self-determined teacher learning in a digital context: Fundamental change in thinking and practice. Unpublished doctoral dissertation, Dublin City University, Ireland. ▸︎ Google︎ Scholar
Campbell R. L. & Bickhard M. H. (1986) Knowing levels and developmental stages. Karger, Basel. ▸︎ Google︎ Scholar
Ceccato S. (1961) The machine which observes and describes. University of Milan (Mimeo), Milan. ▸︎ Google︎ Scholar
Chapman M. (1986) The structure of exchange: Piaget’s sociological theory. Human Development 29: 181–194. ▸︎ Google︎ Scholar
Chapman M. (1988) Constructive evolution. Origins and development of Piaget’s thought. Cambridge University Press, New York. ▸︎ Google︎ Scholar
Chomsky N. (1957) Syntactic structures. Mouton, The Hague. ▸︎ Google︎ Scholar
Cobb P. & Bowers J. (1999) Cognitive and situated perspectives in theory and practice. Educational Researcher 28(2): 4–15. ▸︎ Google︎ Scholar
Cobb P. (2002) Theories of knowledge and instructional design: A response to Colliver. Teaching and Learning in Medicine 14(1): 52–55. ▸︎ Google︎ Scholar
Confrey J. & Kazak S. (2006) A thirty-year reflection on constructivism in mathematics education in PME. In: Gutièrrez A. & Boero P. (eds.) Handbook of research on the psychology of mathematics education: Past, present and future. Sense, Rotterdam: 305–345. ▸︎ Google︎ Scholar
Confrey J. (1995) How compatible are radical constructivism, sociocultural approaches, and social constructivism? In: Steffe L. P. & Gale J. E. (eds.) Constructivism in education. Lawrence Erlbaum Associates, Hillsdale NJ: 185–225. ▸︎ Google︎ Scholar
Corcoran D. (2008) Developing mathematical knowledge for teaching: A three-tiered study of Irish pre-service primary teachers. Unpublished doctoral thesis, University of Cambridge UK. ▸︎ Google︎ Scholar
Damerow P. (1996) Abstraction and representation. Essays on the cultural evolution of thinking. Kluwer, Dordrecht. ▸︎ Google︎ Scholar
Davis B. & Sumara D. (2002) Constructivist discourses and the field of education. Educational Theory 52(4): 409–428. ▸︎ Google︎ Scholar
de Laguna G. A. (1962) The role of teleonomy in evolution. Philosophy of Science 29(2): 117–131. ▸︎ Google︎ Scholar
Dewey J. (1960) The quest for certainty. Capricorn, New York. Originally published 1929. ▸︎ Google︎ Scholar
Dooley T. (2010) The construction of mathematical insight by pupils in whole-class conversation. Unpublished doctoral dissertation. University of Cambridge UK. ▸︎ Google︎ Scholar
Drudy S., Gash H., Lynch K., Lavin P., Moles, Lane C., Ganly M., Forgarty C., O’Flynn G. & Dunne A. (1991) Integrating equal opportunities in the curriculum of teacher education 1988–1991: TENET Programme Dissemination Phase. Irish Educational Studies 10(1): 271–289. ▸︎ Google︎ Scholar
Dunne J. (1996) Beyond sovereignty and deconstruction: The storied self. In: Kearney R. (ed.) Paul Ricoeur: The hermeneutics of action. Sage, London: 137–154. ▸︎ Google︎ Scholar
Dwyer B. (2010) Scaffolding internet reading: A study of a disadvantaged school community in Ireland. Unpublished doctoral dissertation. University of Nottingham UK. ▸︎ Google︎ Scholar
Dykstra D. I. Jr. (2005) Against realist instruction: Superficial success masking catastrophic failure and an alternative. Constructivist Foundations 1(1): 49–60. http://www.univie.ac.at/constructivism/journal/1/1/049.dykstra
Dykstra D. I. Jr. (2009) Theoretical foundations for college learning – Piaget and Vygotski: Sorting fact from fiction. In: Fuller R. G., Campbell T. C., Dykstra D. I. Jr. & Stevens S. M. (eds.) College teaching and the development of reasoning. Information Age Publishers: Charlotte NC: 183–202. ▸︎ Google︎ Scholar
English translation: Glasersfeld E. von (2007) Aspects of constructivism: Vico, Berkeley, Piaget. In: Key works in radical constructivism. Edited by Marie Larochelle. Sense, Rotterdam: 91–99. http://www.vonglasersfeld.com/139.2
Floridi L. (2011) A defence of constructionism: Philosophy as conceptual engineering. Metaphilosophy 42(3): 282–304. ▸︎ Google︎ Scholar
Gash H. & Bajd B. (2005) Young people’s heroes in Ireland and Slovenia. Irish Journal of Psychology 26: 137–148. ▸︎ Google︎ Scholar
Gash H. & Chocholouskova Z. (2013) A model for promoting constructivist education. In: Lasker G. E., Hiwaki K. & Aydin A. (eds.) Life-long integral education for a viable human future. International Institute for Advanced Studies, Tecumseh Ontario: 39–43. ▸︎ Google︎ Scholar
Gash H. & Conway P. (1997) Images of heroes and heroines: How stable? Journal of Applied Developmental Psychology 18: 349–372. ▸︎ Google︎ Scholar
Gash H. & Domínguez Rodríguez P. (2009) Young people’s heroes in France and Spain. Spanish Journal of Psychology 12: 246–257. ▸︎ Google︎ Scholar
Gash H. & Glasersfeld E. von (1978) Vico (1668–1744): An early anticipator of radical constructivism. Irish Journal of Psychology 4(1): 22–32. ▸︎ Google︎ Scholar
Gash H. & Morgan M. (1993) School-based modifications of children’s gender-related beliefs. Journal of Applied Developmental Psychology 14: 277–287. ▸︎ Google︎ Scholar
Gash H. (1974) The constructivist epistemology in John Dewey, Jean Piaget, and Cognitive developmental psychology. In: Smock C. D. & Glasersfeld E. von (eds.) Epistemology and education. Follow Through Publications, Athens GA: 27–44. ▸︎ Google︎ Scholar
Gash H. (1982) Associated structures: Class inclusion and role-taking. Journal of Genetic Psychology 141: 155–166. ▸︎ Google︎ Scholar
Gash H. (1995) Attitudes of Irish primary school children to European and Third World children. In: Hackett M. (ed.) Intercultural education – celebrating diversity. Drumcondra Education Centre, Dublin: 44–65. ▸︎ Google︎ Scholar
Gash H. (2009) What you always wanted to know about constructivist education… Review of “Constructivist Instruction: Success or Failure?” edited by Sigmund Tobias & Thomas M. Duffy. Constructivist Foundations 5(1): 64–65. http://www.univie.ac.at/constructivism/journal/5/1/064.gash
Gash H. (2010) Remembering Ernst von Glasersfeld. Constructivist Foundations 6(2): 164–168. http://www.univie.ac.at/constructivism/journal/6/2/168.gash
Gash H. (ed.) (2006) Beginning teachers and diversity in school: A European Study. Instituto Politéchnica de Braganca, Braganca Portugal. ▸︎ Google︎ Scholar
Gash H., Guardia Gonzales S., Pires M. & Rault C. (2000) Attitudes towards Down Syndrome: A national comparative study: France, Ireland, Portugal, and Spain. Irish Journal of Psychology 21: 203–214. ▸︎ Google︎ Scholar
Gash M.-A. (1988) Learning French with a communicative approach. Unpublished doctoral dissertation. Trinity College, Dublin, Ireland. ▸︎ Google︎ Scholar
Gil-Pérez D., Guisasola J., Moreno A., Cachapuz A., Pessoa De Carvalho A.-M., Martínez Torregrosa J., Salinas J., Valdés P., González E., Gené D., A., Dumas-Carré A., Tricárico H. & Gallego R. (2002) Defending constructivism in science education. Science & Education 12(1): 557–571. ▸︎ Google︎ Scholar
Glasersfeld E. von (1974) Piaget and the radical constructivist epistemology. In: Smock C. D. & Glasersfeld E. von (eds.) Epistemology and education. Follow Through Publications, Athens GA: 1–24. http://www.vonglasersfeld.com/034
Glasersfeld E. von (1983) Learning as a constructive activity. In: Bergeron J. C. & Herscovics N. (eds.) Proceedings of the 5th Annual Meeting of the North American Group of Psychology in Mathematics Education, Volume 1. PME-NA, Montreal: 41–101. http://www.vonglasersfeld.com/083
Glasersfeld E. von (1987) The construction of knowledge. Intersystems Publications, Seaside CA. ▸︎ Google︎ Scholar
Glasersfeld E. von (1989) Constructivism in education. In: Husen T. & Postlethwaite T. N. (eds.) International encyclopedia of education. Supplement Volume 1. Pergamon Press, Oxford: 162–163. http://www.vonglasersfeld.com/114
Glasersfeld E. von (1992) Aspekte des Konstruk-tivismus: Vico, Berkely, Piaget. In: Rusch G. & Schmidt S. J. (eds.) Konstruktivismus: Geschichte und Anwendung. DELFIN 1992. Suhrkamp, Frankfurt am Main: 20–33. ▸︎ Google︎ Scholar
Glasersfeld E. von (1995) A constructivist approach to teaching. In: Steffe L. P. & Gale J. (eds.) Constructivism in education. Lawrence Erlbaum, Hillsdale NJ: 3–15. ▸︎ Google︎ Scholar
Glasersfeld E. von (1995) Radical constructivism. Falmer Press, London. ▸︎ Google︎ Scholar
Glasersfeld E. von (1997) Homage to Jean Piaget (1896–1980) Irish Journal of Psychology 18(3): 293–306. http://www.vonglasersfeld.com/204
Glasersfeld E. von (2010) Why people dislike radical constructivism. Constructivist Foundations 6(1): 19–21. http://www.univie.ac.at/constructivism/journal/6/1/019.glasersfeld
Glasser W. (1986) Control theory in the classroom. Harper and Row, New York. ▸︎ Google︎ Scholar
Good T., Mulryan C. & McCaslin M. (1992) Grouping for instruction in mathematics. In: Grouws D. (ed.) Handbook of research on mathematics teaching and learning. Macmillan, New York: 165–196. ▸︎ Google︎ Scholar
Gopnik A., Glymour C., Sobel D., Schulz L., Kushnir T. & Danks D. (2004) A theory of causal learning in children: Causal maps and Bayes nets. Psychological Review 111(1): 1–31. ▸︎ Google︎ Scholar
Gresalfi M. S. & Lester F. (2009) What’s worth knowing in mathematics? In: Tobias S. & Duffy T. M. (eds.) Constructivist Instruction: Success or Failure. Routledge, London: 264–290. ▸︎ Google︎ Scholar
Habermas J. (1981) Theorie des kommunikativen Handelns. Band 1–2. Suhrkamp, Frankfurt am Main. ▸︎ Google︎ Scholar
Hall E. (1970) A conversation with Jean Piaget and Bärbel Inhelder. Psychology Today 3(12): 25–32, 54–56. ▸︎ Google︎ Scholar
Harri-Augstein E. S. & Thomas L. F. (1983) Developing self-organized learners: A reflective technology. New Directions for Adult and Continuing Education 19: 39–48. ▸︎ Google︎ Scholar
Harris P. L. & Koenig M. (2006) Trust in testimony: How children learn about science and religion. Child Development 77: 505–524. ▸︎ Google︎ Scholar
Hersh R. (2008) Skeptical Mathematics? Constructivist Foundations 3(2): 72. http://www.univie.ac.at/constructivism/journal/3/2/072.hersh
Hershkowitz R., Schwartz B. B. & Dreyfus T. (2001) Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education 32(2): 195–222. ▸︎ Google︎ Scholar
Heyting F. G. (1997) Konstruktivistische Erziehungswissenschaft. In: Hierdeis H. & Hug T. (eds.) Taschenbuch der Pädagogik. Schneider-Verlag Hohengehren, Baltmannsweiler: 400–408. ▸︎ Google︎ Scholar
Hsueh Y. (2004) “He sees the development of children’s concepts upon a background of sociology”: Jean Piaget’s honorary degree at Harvard University in 1936. History of Psychology 7(1): 20–44. ▸︎ Google︎ Scholar
Hug T. (2010) Radical constructivism mainstreaming: A desirable endeavor? Critical considerations using examples from educational studies and learning theory. Constructivist Foundations 6(1): 58–64. http://www.univie.ac.at/constructivism/journal/6/1/058.hug
Hug T. (2011) Die Paradoxie der Erziehung. Theo Hug über den Konstruktivismus in der Pädagogik. In: Pörksen B. (ed.) Schlüsselwerke des Konstruktivismus. VS, Wiesbaden: 463–483. ▸︎ Google︎ Scholar
Hug T. (2012) Media competence and visual literacy – Towards considerations beyond literacies. Periodica Polytechnica: Social and Management Sciences 20/2: 115–125. http://www.pp.bme.hu/so/article/view/1574
Hug T. (2012) Microlearning. In: Seel N. M. (ed.) Encyclopedia of the sciences of learning. Volume 5. Springer, New York: 2268–2271. ▸︎ Google︎ Scholar
Hunter D. J. (2005) Gene–environment interactions in human disease. Nature Reviews Genetics 6: 287–298. ▸︎ Google︎ Scholar
Jaworski B. (1988) “Is” versus “seeing as”: Constructivism and mathematics classroom. In: Pimm D. (ed.) Mathematics, teachers and children. Hodder & Stoughton, London. ▸︎ Google︎ Scholar
Kant I. (1787) Kritik der reinen Vernunft. Second edition. Akademieausgabe Volume III. http://gutenberg.spiegel.de/kant/krvb/krvb.htm
Kennedy E. (2010) Improving literacy achievement in a disadvantaged primary school: Empowering classroom teachers through professional development. Unpublished doctoral dissertation. Dublin City University, Ireland. ▸︎ Google︎ Scholar
Kilpatrick J. (1987) What constructivism might be in mathematics education. In: Bergeron J. C., Herscovics N. & Kieran C. (eds.) Psychology of mathematics education. Proceedings of the 11th International Conference for the Psychology of Mathematics Education. Volume 1. International Group for the Psychology of Mathematics Education, Montreal: 3–27. ▸︎ Google︎ Scholar
Klafki W. (1976) Aspekte kritisch-konstruktiver Erziehungswissenschaft. Gesammelte Beiträge zur Theorie-Praxis-Diskussion. Beltz, Weinheim. Originally published in 1971. ▸︎ Google︎ Scholar
Kohlberg L. (1969) Stage and sequence: The cognitive-developmental approach to socialization. In: Goslin D. (ed.) Handbook of socialization theory and research. Rand McNally, New York. ▸︎ Google︎ Scholar
Krippendorff K. (1993) Major metaphors of communication and some constructivist reflections on their use. Cybernetics & Human Knowing 2(1): 3–25. ▸︎ Google︎ Scholar
Krippendorff K. (2006) The semantic turn: A new foundation for design. CRC Press, Boca Raton FL. ▸︎ Google︎ Scholar
Larochelle M., Bednarz N. & Garrison J. (eds.) (1998) Constructivism and education. Cambridge University Press, Cambridge. ▸︎ Google︎ Scholar
Lave J. & Wenger E. (1991) Situated learning: Legitimate peripheral participation. Cambridge University Press, Cambridge. ▸︎ Google︎ Scholar
Lourenço O. & Machado A. (1996) In defense of Piaget’s theory: A reply to 10 common criticisms. Psychological Review 103(1): 143–164. ▸︎ Google︎ Scholar
Mason J. (2008) Making use of children’s powers to produce algebraic thinking. In: Kaput J. J., Carraher D. W. & Blandon M. L. (eds.) Algebra in the early years. Lawrence Erlbaum, New York: 57–94. ▸︎ Google︎ Scholar
Matthews M. R. (1993) Constructivism and science education: Some epistemological problems. Journal of Science Education and Technology 2(1) 359–370. ▸︎ Google︎ Scholar
Matthews M. R. (1994) Science teaching: The role of history and philosophy of science. Routledge, London. ▸︎ Google︎ Scholar
Matthews M. R. (1995) Challenging New Zealand science education. Dunmore Press, Palmerston North. ▸︎ Google︎ Scholar
Maturana H. R. (1988) Reality: The search for objectivity or the quest for a compelling argument. Irish Journal of Psychology 9(1): 25–82. http://www.enolagaia.com/M88Reality.html
Müller U., Carpendale J. I. M. & Smith L. (2009) Introduction: Overview. In: Müller U., Carpendale J. I. M. & Smith L. (eds.) The Cambridge companion to Piaget. Cambridge University Press, New York: 1–44. ▸︎ Google︎ Scholar
McEwan B. S. (2004) How sex and stress hormones regulate the structural and functional plasticity of the hippocampus. In: Gazzaniga M. S. (ed.) Cognitive neurosciences. MIT Press, Cambridge MA: 171–182. ▸︎ Google︎ Scholar
National Governors Association Center for Best Practices & Council of Chief State School Officers (NGAC) (2010) Common core state standards. NGAC, Washington DC. ▸︎ Google︎ Scholar
Noddings N. (1990) Constructivism in mathematics education. In: Davis R. B., Maher C. A. & Noddings N. (eds.) Constructivist views on the teaching and learning of mathematics. JRME Monograph no. 4. NCTM, Reston VA: 7–18. ▸︎ Google︎ Scholar
Piaget J. (1954) The construction of reality in the child. Routledge & Kegan Paul, London. Originally published as: Piaget J. (1937) La construction du réel chez l’enfant. Delachaux et Niestlé, Neuchâtel. ▸︎ Google︎ Scholar
Piaget J. (1964) Cognitive development in children: development and learning. Journal of Research in Science Teaching 2: 170–186. ▸︎ Google︎ Scholar
Piaget J. (1967) Logique et connaissance scientifique. Édition sous la direction de Jean Piaget. Encyclopédie de la Pléiade 22. Gallimard, Paris. ▸︎ Google︎ Scholar
Piaget J. (1970) Piaget’s theory. In: Mussen P. H. (ed.) Carmichael’s manual of child psychology. Wiley, New York: 703–732. ▸︎ Google︎ Scholar
Piaget J. (1970) Science of education and the psychology of the child. New York, Orion. ▸︎ Google︎ Scholar
Piaget J. (1972) Problems of equilibration. In: Nodine C. F., Gallagher J. M. & Humphreys R. H. (eds.) Piaget and Inhelder: On equilibration. Proceedings of the First Annual Symposium of the Jean Piaget Society. The Jean Piaget Society, Philadelphia: 1–20. ▸︎ Google︎ Scholar
Piaget J. (1995) Sociological studies. Routledge, London. Originally published in French as: Piaget J. (1965) Ètudes sociologiques. Droz, Geneva. ▸︎ Google︎ Scholar
Piatelli-Palmarini M. (1994) Ever since language and learning: Afterthoughts on the Piaget–Chomsky debate. Cognition 50(1–3): 315–346. ▸︎ Google︎ Scholar
Pittendrigh C. S. (1958) Adaptation, natural selection, and behavior. In: Roe A. & Simpson G. G. (eds.) Behavior and evolution. Yale University Press, New Haven: 390–416. ▸︎ Google︎ Scholar
Polanyi M. (1958) Personal knowledge: Towards a post-critical philosophy. University of Chicago Press, Chicago. ▸︎ Google︎ Scholar
Rault C., Molina Garcia S. & Gash H. (2001) Learning difficulties: What types of help? Harmattan, Paris. ▸︎ Google︎ Scholar
Reich K. (2010) Systemisch-konstruktivistische Pädagogik. Sixth Edition. Beltz, Weinheim. The first edition was published in 1996. ▸︎ Google︎ Scholar
Ridley M. (2003) Nature via nurture: Genes, experience, & what makes us human. Harper Collins, New York. ▸︎ Google︎ Scholar
Robert S., Gash H., McCloughlin T., Bajd B., Krnel D., Chocholouskova Z., Dolenska M. & Valanides N. (2009) Formation des enseignants: Un exemple de recherche-action. Review Internationale D’éducation de Sèvres 51: 47–58. http://ries.revues.org/660
Rowland T. & Turner F. (2007) Developing and using the “Knowledge Quartet”: A framework for the observation of mathematics teaching. The Mathematics Educator 10(1): 107–124. ▸︎ Google︎ Scholar
Rowland T. (1992) Pointing with pronouns. For the Learning of Mathematics 12(2): 44–48. ▸︎ Google︎ Scholar
Rowland T. (1995) Hedges in mathematics talk: Linguistic pointers to uncertainty. Eductional Studies in Mathematics 29: 327–353. ▸︎ Google︎ Scholar
Rutter M. (2006) Genes and behavior: Nature–nurture interplay explained. Blackwell, Oxford. ▸︎ Google︎ Scholar
Schmidt S. J. (2012) Lehren der Kontingenz. Eine Erinnerung an 40 Jahre Doppelleben. LIT, Münster. ▸︎ Google︎ Scholar
Serres M. (2013) Petite pousette. Pommier, Paris. ▸︎ Google︎ Scholar
Sfard A. (2008) Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press, Cambridge. ▸︎ Google︎ Scholar
Sfard A., Nesher P., Streefland L., Cobb P. & Mason J. (1998) Learning mathematics through conversation: Is it as good as they say? For the Learning of Mathematics 18(1): 41–51. ▸︎ Google︎ Scholar
Simon M. A. (1995) Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education 26(2): 114–145. ▸︎ Google︎ Scholar
Smith J. P., diSessa A. & Roschelle J. (1993) Misconceptions reconceived: A constructivist analysis of knowledge in transition. Journal of the Learning Sciences 3(2): 115–163. ▸︎ Google︎ Scholar
Smith L. (1993) Necessary knowledge. Piagetian perspectives on constructivism. Lawrence Erlbaum, Hove UK. ▸︎ Google︎ Scholar
Smith L. (1999) What exactly is constructivism in education? Studies in Science Education 33(1): 149–160. ▸︎ Google︎ Scholar
Steffe L. P. & Thompson P. W. (2000) Radical constructivism in action. Routledge & Falmer, London. ▸︎ Google︎ Scholar
Steffe L. P., Cobb P. & Glasersfeld E. von (1988) Construction of arithmetical meanings and strategies. Springer, New York. ▸︎ Google︎ Scholar
Thompson P. W. (1994) Images of rate and operational understanding of the Fundamental Theorem of Calculus. Educational Studies in Mathematics 26: 229–274. ▸︎ Google︎ Scholar
Tobias S. & Duffy T. M. (2009) Constructivist instruction: Success or failure. Routledge, London. ▸︎ Google︎ Scholar
Wohlwill J. (1973) The concept of experience: S or R? Human Development 16: 90–107. ▸︎ Google︎ Scholar

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