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Discussion I of Part II

Representing and Meaning-Making: The Transformation of Transformation
  • Falk Seeger
Chapter

Abstract

This commentary simultaneously offers a broad and a narrow perspective. It is narrow in that it does not attempt to synthesize or digest the chapters in this section. It can be called broad as it attempts to sketch some salient features of the future development of and learning geometry, of the transformation of transformation. Four such strands of reasoning are discussed: the paramount significance of meaning-making, the role of artefacts as socially and culturally embedded, embodiment and enactment, and, finally, emotions, meaning-making, and triangulation.

Keywords

Mathematics Education Technical Artefact Personal Sense Identical Learning Educational Situation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman.Google Scholar
  2. Bandura, A. (2001). Social cognitive theory: An agentic perspective. Annual Review of Psychology, 52, 1–26.Google Scholar
  3. Baron-Cohen, S., Bolton, P., Wheelwright, S., Scahill, V., Short, L., Mead, G., & Smith, A. (1998). Autism occurs more often in families of physicists, engineers, and mathematicians. Autism, 2, 296–301.Google Scholar
  4. Baron-Cohen, S., Wheelwright, S., Burtenshaw, A., & Hobson, E. (2007). Mathematical talent is linked to autism. Human Nature, 18, 125–131.Google Scholar
  5. Bullowa, M. (Ed.) (1979). Before speech: The beginnings of human communication. Cambridge: Cambridge University Press.Google Scholar
  6. Campbell, S. R. (2010). Embodied minds and dancing brains: New opportunities for research in mathematics education. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 309–331). Heidelberg: SpringerGoogle Scholar
  7. Cole, M. (1996). Cultural psychology. A once and future discipline. Cambridge, MA: Harvard University Press.Google Scholar
  8. Daniels, H., Cole, M., & Wertsch, J. V. (2007). The Cambridge companion to Vygotsky. New York: Cambridge University Press.Google Scholar
  9. Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–40.Google Scholar
  10. Dehaene, S. (1997). The number sense. How the mind creates mathematics. New York: Oxford University Press.Google Scholar
  11. Di Paolo, E., & De Jaegher, H. (2012). The interactive brain hypothesis. Frontiers in Human Neuroscience, 6, Article 163 (doi: 10.3389/fnhum.2012.00163)Google Scholar
  12. Dornes, M. (1993). Der kompetente Säugling. [The competent infant]. Frankfurt/Main. Fischer.Google Scholar
  13. Dornes, M. (2005). Die emotionalen Ursprünge des Denkens [The emotional origins of thinking]. West-End. Neue Zeitschrift für Sozialforschung, 2(1), 3–48Google Scholar
  14. Dyson, G. (2010). Kayaks vs. canoes http://www.edge.org/q2010/q10_2.html
  15. Elias, N. (1994). The Civilizing process. Oxford: Blackwell (original 1934)Google Scholar
  16. Engeström, Y., & Escalante, V. (1995). Mundane tool or object of affection? The rise and fall of the postal buddy. In B. Nardi (Ed.), Context and consciousness: activity theory and human-computer interaction (pp. 325–373). Cambridge: The MIT Press.Google Scholar
  17. Fonagy, P,. Gergely, G., Jurist, E., & Target, M. (2002). Affect regulation, mentalization, and the development of the self. New York: Other Press.Google Scholar
  18. Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement: Potential of the concept, state of the evidence. Review of Educational Research, 74(1), 59–109.Google Scholar
  19. Goldin, G. A., Epstein, Y. M., Schorr, R. Y., & Warner, L. B. (2011). Beliefs and engagement structures: Behind the affective dimension of mathematical learning. ZDM-The International Journal on Mathematics Education, 43, 547–560.Google Scholar
  20. Goldin-Meadow, S. (2003). Hearing gesture-How our hands help us think. Cambridge, MA: Harvard University Press.Google Scholar
  21. Hegel, G. W. F. (1801). „Habilitationsthesen“. In: Georg Willhelm Friedrich Hegel, Werke in Zwanzig Bänden. Band 2. Jenaer Schriften 1801-1807 (S. 533). Frankfurt am Main: Suhrkamp.Google Scholar
  22. Hobson, R. P. (1993). Autism and the development of mind. Hillsdale: Lawrence Erlbaum.Google Scholar
  23. Hobson, R. P. (2002). The cradle of thought. Exploring the origins of thinking. London: Macmillan.Google Scholar
  24. Holodynski, M. (2006). Die Entwicklung der Emotionen. Berlin: Springer.Google Scholar
  25. Honneth, A. (1995). The Struggle for recognition. The moral grammar of social conflicts. 1995. Cambridge: Polity Press.Google Scholar
  26. Hutchins, E. (2010). Enaction, imagination, and insight. In J. Stewart, O. Gapenne, & E. A. Di Paolo (Eds.), Enaction. Toward a new paradigm for cognitive science (pp. 425-450). Cambridge, MA: MIT Press.Google Scholar
  27. Latour, B. (1993). Aramis, or the love of technology. Cambridge, MA: Harvard University Press.Google Scholar
  28. Lave, J. (1988). Cognition in practice. Mind mathematics and culture in everyday life. Cambridge: Cambridge University Press.Google Scholar
  29. Lave, J., & Wenger, E. (1991). Situated learning - Legitimate peripheral participation. Cambridge: Cambridge University Press.Google Scholar
  30. Leder, G. C., Pehkonen, E., & Törner, G. (Eds.) (2002). Beliefs: A hidden variable in mathematics education? Dordrecht: Kluwer.Google Scholar
  31. Leont’ev, A. N. (1981). Problems of the development of the mind. Moscow: Progress Publishers.Google Scholar
  32. Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, N.J.: Prentice-HallGoogle Scholar
  33. Maschietto, M., & Bartolini Bussi, M. G. (2009). Working with artefacts: gestures, drawings and speech in the construction of the mathematical meaning of the visual pyramid. Educational Studies in Mathematics, 70, 143–157.Google Scholar
  34. Maass, J., & Schlöglmann, W. (Eds.) (2009). Beliefs and attitudes in mathematics education: New research results. Rotterdam: Sense.Google Scholar
  35. Meltzoff, A. N. (2002). Elements of a developmental theory of imitation. In A. N. Meltzoff &W. Prinz (Eds.), The imitative mind (pp. 19-41). Cambridge: Cambridge University Press.Google Scholar
  36. Meltzoff, A. N. (2007). ‘Like me’: A foundation for social cognition. Developmental Science, 10(1), 126–134.Google Scholar
  37. Meltzoff, A. N., Kuhl, P. K., Movellan, J., & Sejnowski, T. J. (2009). Foundations for a new science of learning. Science, 325, 284–288.Google Scholar
  38. Meltzoff, A. N., & Moore, M. K. (1977). Imitation of facial and manual gestures by human neonates. Science, 198, 75–78.Google Scholar
  39. Ogden, C. K., & Richards, I. A. (1923). The meaning of meaning: A study of the influence of language upon thought and of the science of symbolism. London: Routledge & Kegan Paul.Google Scholar
  40. Otte, M. F. (2011). Evolution, learning, and semiotics from a Peircean point of view. Educational Studies in Mathematics, 77, 313–329.Google Scholar
  41. Papousek, H., & Papousek, M. (1974). Mirror image and self-recognition in young infants. Developmental Psychology, 7, 149–157.Google Scholar
  42. Papousek, H., & Papousek, M. (1977). Cognitive aspects of preverbal social interaction between human infants and adults. In R. Porter & M. O’Connor (Eds.), Ciba Foundation Symposium 33: Parent-infant interaction (pp. 241–269). New York: WileyGoogle Scholar
  43. Papousek, H., & Papousek, M. (1981). How human is the human newborn, and what else is to be done. In K. Bloom (Ed.), Prospective issues in infancy research (pp. 137–155). Hillsdale: Erlbaum.Google Scholar
  44. Rachman, G. (2011). Zero-sum future-American power in an age of anxiety. New York: Simon & Schuster.Google Scholar
  45. Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic‐cultural approach to students’ types of generalization. Mathematical Thinking and Learning 5(1), 37–70Google Scholar
  46. Radford, L., Bardini, C., Sabena, C., Diallo, P., & Simbagoye, A. (2005). On embodiment, artefacts, and signs: A semiotic-cultural perspective on mathematical thinking. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th International Group for the Psychology of Mathematics Education (vol. 4, pp. 113–122). Melbourne, AustraliaGoogle Scholar
  47. Robutti, O. (2006). Motion, technology, gesture in interpreting graphs. International Journal of Computer Algebra in Mathematics Education, 13, 117–126.Google Scholar
  48. Roth, W.-M. (2001). Gestures: Their role in teaching and learning. Review of Educational Research, 71(3), 365–392.Google Scholar
  49. Roth, W.-M., & Welzel, M. (2001). From activity to gestures and scientific language. Journal of Research in Science Teaching, 38(1), 103–136.Google Scholar
  50. Sabena, C. (2007). Body and signs: A multimodal semiotic approach to teaching-learning processes in early calculus. Unpublished Doctoral Dissertation, Università degli Studi di Torino, TorinoGoogle Scholar
  51. Sacks, O. (1989). Seeing voices - A journey into the world of the deaf. Berkeley: University of California Press.Google Scholar
  52. Sinclair, N. (2010). Knowing more that we can tell. In B. Sriraman & L. English (Eds.), Theories of mathematical education: Seeking new frontiers (pp. 595–612). Heidelberg: SpringerGoogle Scholar
  53. Sriraman, B., & English, L. (2010) (Eds.), Theories of mathematical education: Seeking new frontiers. Heidelberg: SpringerGoogle Scholar
  54. Steinbring, H. (2005). Do mathematical symbols serve to describe or to construct reality? In M. Hoffmann, J. Lenhard, & F. Seeger (Eds.), Activity and sign (pp. 91–104). New York: Springer.Google Scholar
  55. Stern, D. (1971). A microanalysis of mother-infant interaction. Journal of the American Academy of Child Psychiatry, 10, 501–517Google Scholar
  56. Stern, D. (1985). The interpersonal world of the infant: A view from psychoanalysis and developmental psychology. New York: Basic Books.Google Scholar
  57. Stewart, J. (2010). Foundational issues in enaction as a paradigm for cognitive science: From the origin of life to consciousness and writing. In J. Stewart, O. Gapenne, & E. A. Di Paolo (Eds.), Enaction. Toward a New Paradigm for Cognitive Science (pp. 1-31). Cambridge: MIT Press.Google Scholar
  58. Stone, L. J., Smith, H. T., & Murphy, L. B. (Eds.) (1973). The Competent Infant. New York: Basic Books.Google Scholar
  59. Thom, A. (1973), Modern mathematics: Does it exist? In A. G. Howson (Ed.), Developments in mathematical education. Proceedings of the 2nd International Congress on Mathematical Education (pp.  194–210). Cambridge: Cambridge University PressGoogle Scholar
  60. Tomasello, M. (1999). The cultural origins of human cognition. Cambridge, MA: Harvard University Press.Google Scholar
  61. Tomasello, M. (2005). Constructing a language: A usage-based theory of language acquisition. Cambridge, MA: Harvard University Press.Google Scholar
  62. Tomasello, M. (2008). Origins of human communication. Cambridge, MA: MIT Press.Google Scholar
  63. Tomasello, M. (2006). Why don’t apes point? In N. J. Enfield & S. C. Levinson (Eds.), Roots of human sociality: Culture, cognition and interaction (pp. 506-524). Oxford: Berg.Google Scholar
  64. Trevarthen, C. (1979). Communication and cooperation in early infancy: A description of primary intersubjectivity. In M. Bullowa (Ed.), Before Speech: The Beginnings of human communication (pp. 321-347). Cambridge: Cambridge University Press.Google Scholar
  65. Trevarthen, C. (1980). The foundations of intersubjectivity: Development of interpersonal and cooperative understanding in infants. In D. Olson (Ed.), The social foundations of language and thought: Essays in honor of J. S. Bruner (pp. 316–342). New York: Norton.Google Scholar
  66. Trevarthen, C. (1994). Infant semiosis. In W. Nöth (Ed.), Origins of semiosis: Sign evolution in nature and culture (pp. 219–252). Berlin: Mouton de Gruyter.Google Scholar
  67. Trevarthen, C., & Hubley, P. (1978). Secondary intersubjectivity: Confidence, confiding and acts of meaningin the first year. In A. Lock (Ed.), Action, gesture, and symbol: The emergence of language (pp. 183–230). London: Academic.Google Scholar
  68. Van der Veer, R., & Valsiner, J. (1991). Understanding Vygotsky: A quest for synthesis. Oxford: Blackwell.Google Scholar
  69. Van der Veer, R., & Valsiner, J. (Eds.) (1994). The Vygotsky reader. Oxford: Blackwell.Google Scholar
  70. Varela, F. J., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA: MIT.Google Scholar
  71. Von Holst, E., & Mittelstaedt, H. (1950).  Das Reafferenzprinzip. Wechselwirkungen zwischen Zentralnervensystem und Peripherie. Die Naturwissenschaften, 37, Heft 20, 464–476.Google Scholar
  72. Von Uexküll, J. (2010). A foray into the worlds of animals and humans; with a theory of meaning. Minneapolis: University of Minnesota Press (original work published 1934).Google Scholar
  73. Vygotsky, L.S. (1994). The problem of the environment. In van der Veer, R. & Valsiner, J. (Eds.), The Vygotsky reader (pp. 338–354). Oxford: Blackwell. (Original work 1934).Google Scholar
  74. Vygotsky, L. S. (1997). The history of the development of higher mental functions. In R. W. Rieber (Ed.), The collected works of L. S. Vygotsky, Vol. 4 New York: Plenum. (Original work 1931).Google Scholar
  75. Vygotsky, L. S. (1999). Tool and sign in the development of the child. In R. W. Rieber (Ed.), The collected works of L. S. Vygotsky, Vol. 6 (pp. 1–68). New York: Kluwer. (Original work 1930).Google Scholar
  76. Wing, L. (1996). The autistic spectrum: A guide for parents and professionals. London: Constable.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2014

Authors and Affiliations

  • Falk Seeger
    • 1
  1. 1.the Institut für Didaktik der MathematikUniversität BielefeldSteinhagenGermany

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