Advertisement

Discussion and Conclusions

  • Norma PresmegEmail author
  • Luis Radford
  • Wolff-Michael Roth
  • Gert Kadunz
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

After an introductory section that addresses the nature of semiotics, the editors discuss themes that highlight issues that have arisen from and that illustrate what has been accomplished in the varied chapters of this monograph. The final section provides some suggestions, based on these issues, for further research on the various threads that pertain to the potential significance of semiotics in mathematics education. The editors believe that there is room for both theoretical development and further empirical studies designed in resonance with these theories, in order to address the full potential of semiotics in areas of research that have not yet received widespread attention.

Keywords

Semiotics Signification Iconic and indexical relationships Qualitative methodologies Interactive technology 

References

  1. Bartolini Bussi, M., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artefacts and signs after a Vygotskian perspective. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 746–783). New York: Routledge, Taylor and Francis.Google Scholar
  2. Bikner-Ahsbahs, A., Knipping, C., & Presmeg, N. (Eds.). (2015). Approaches to qualitative research in mathematics education: Examples of methodology and methods. Dordrecht, The Netherlands: Springer.Google Scholar
  3. Boaler, J. (2002). Exploring the nature of mathematical activity: Using theory, research and ‘working hypotheses’ to broaden conceptions of mathematics knowing. Education Studies in Mathematics, 51(1–2), 3–21.CrossRefGoogle Scholar
  4. Boncompagni, A. (2016). Wittgenstein and pragmatism (History of analytic philosophy). London: Macmillan.CrossRefGoogle Scholar
  5. de Saussure, F. (1967). Cours de linguistique générale [Course in general linguistics]. Paris: Éditions Payot & Rivages.Google Scholar
  6. Dewey, J., & Bentley, A. F. (1999). Knowing and the known. In R. Handy & E. E. Hardwood, Useful procedures of inquiry (pp. 97–209). Great Barrington, MA: Behavioral Research Council (First published in 1949).Google Scholar
  7. Dörfler, W. (2016). Signs and their use: Peirce and Wittgenstein. In W. Dörfler, A. Bikner-Ahsbahs, A. Vohns, & R. Bruder (Eds.), Theories in and of mathematics education (pp. 21–31). Berlin, New York: Springer.CrossRefGoogle Scholar
  8. Eco, U. (1976). A theory of semiotics. Bloomington: Indiana University Press.CrossRefGoogle Scholar
  9. Eco, U. (1984). Semiotics and the philosophy of language. Bloomington: Indiana University Press.CrossRefGoogle Scholar
  10. Garfinkel, H. (1967). Studies in ethnomethodology. Englewood Cliffs, NJ: Prentice Hall.Google Scholar
  11. Garfinkel, H. (1996). Ethnomethodology’s program. Social Psychology Quarterly, 59, 5–21.CrossRefGoogle Scholar
  12. Hookway, C. (2012). The pragmatic maxim. Essays on Peirce and pragmatism. Oxford: Oxford University Press.CrossRefGoogle Scholar
  13. Husserl, E. (1913a). Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. Erstes Buch: Allgemeine Einführung in die reine Phänomenologie [Ideas to a pure phenomenology and phenomenological philosophy vol. 1: General introduction to a pure phenomenology]. Halle a.d.S.: Max Niemeyer.Google Scholar
  14. Husserl, E. (1913b). Logische Untersuchungen. Zweiter Band. Untersuchungen zur Phänomenologie und Theorie der Erkenntnis [Logical investigations vol. 2. Investigations of phenomenology and theory of knowledge]. Halle a.d.S: Max Niemeyer.Google Scholar
  15. James, W. (1907). Pragmatism: a new name for some old ways of thinking. London, New York: Longmans, Green & Co.CrossRefGoogle Scholar
  16. Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.Google Scholar
  17. Latour, B. (1993). La clef de Berlin et autres leçons d’un amateur de sciences [The key to Berlin and other lessons of a science lover]. Paris: Éditions la Découverte.Google Scholar
  18. Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  19. Marx, K., & Engels, F. (1962). Werke Band 23 [Works vol. 23]. Berlin: Dietz.Google Scholar
  20. Marx, K., & Engels, F. (1978). Werke Band 3 [Works vol. 3]. Berlin: Dietz.Google Scholar
  21. Peirce, C. S. (1878). How to make our ideas clear. Popular Science Monthly, 12, 286–302.Google Scholar
  22. Peirce, C. S. (1931–1958). Collected papers (CP, Vols. 1–8). Cambridge: Harvard University Press.Google Scholar
  23. Peirce, C. S. (1992). In N. Houser & C. Kloesel (Eds.), The essential Peirce (Vol. 1). Bloomington, IN: Indiana University Press.Google Scholar
  24. Peirce, C. S. (1998). In The Peirce Edition Project (Eds.), The essential Peirce (Vol. 2). Bloomington, IN: Indiana University Press.Google Scholar
  25. Piaget, J., & Inhelder, B. (2013/1958). The growth of logical thinking from childhood to adolescence (A. Parsons & S. Milgram, Trans.). New York: Routledge.Google Scholar
  26. Presmeg, N. C. (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23(6), 595–610.CrossRefGoogle Scholar
  27. Presmeg, N. C. (1997). A semiotic framework for linking cultural practice and classroom mathematics. In J. Dossey, J. Swafford, M. Parmantie, & A. Dossey (Eds.), Proceedings of the 19th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 151–156). Columbus, Ohio.Google Scholar
  28. Presmeg, N. C. (1998). Ethnomathematics in teacher education. Journal of Mathematics Teacher Education, 1(3), 317–339.CrossRefGoogle Scholar
  29. Presmeg, N. C. (2002). A triadic nested lens for viewing teachers’ representations of semiotic chaining. In F. Hitt (Ed.), Representations and mathematics visualization (pp. 263–276). Mexico City: Cinvestav IPN.Google Scholar
  30. Presmeg, N. C. (2006a). A semiotic view of the role of imagery and inscriptions in mathematics teaching and learning. In J. Novotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 19–34). Prague: PME.Google Scholar
  31. Presmeg, N. C. (2006b). Semiotics and the “connections” standard: Significance of semiotics for teachers of mathematics. Educational Studies in Mathematics, 61, 163–182.CrossRefGoogle Scholar
  32. Radford, L. (2008). The ethics of being and knowing: Towards a cultural theory of learning. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom, and culture (pp. 215–234). Rotterdam: Sense Publishers.Google Scholar
  33. Radford, L. (2012). Education and the illusions of emancipation. Educational Studies in Mathematics, 80(1), 101–118.CrossRefGoogle Scholar
  34. Radford, L. (2014). On teachers and students. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the Joint 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the American Chapter (Vol. 1, pp. 1–20). Vancouver, Canada: PME.Google Scholar
  35. Radford, L. (2015). Early algebraic thinking: Epistemological, semiotic, and developmental issues. In S. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 209–227). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-12688-3_15.
  36. Radford, L., & Roth, W.-M. (2011). Intercorporeality and ethical commitment: An activity perspective on classroom interaction. Educational Studies in Mathematics, 77(2–3), 227–245.CrossRefGoogle Scholar
  37. Roth, W.-M. (2012a). Societal mediation of mathematical cognition and learning. Orbis Scholae, 6(2), 7–22.Google Scholar
  38. Roth, W.-M. (2012b). Tracking the origins of signs in mathematical activity: A material phenomenological approach. In M. Bockarova, M. Danesi, & R. Núñez (Eds.), Cognitive science and interdisciplinary approaches to mathematical cognition (pp. 209–247). Munich: LINCOM EUROPA.Google Scholar
  39. Roth, W.-M. (2015). Excess of graphical thinking: Movement, mathematics and flow. For the Learning of Mathematics, 35(1), 2–7.Google Scholar
  40. Roth, W.-M. (2016). Concrete human psychology. New York: Routledge.Google Scholar
  41. Roth, W.-M., & Jornet, A. (2017). Theorizing without “mediators”. Integrative Psychological and Behavioral Science. https://doi.org/10.1007/s12124-016-9376-0.Google Scholar
  42. Roth, W.-M., & McGinn, M. K. (1998). Inscriptions: Toward a theory of representing as social practice. Review of Educational Research, 68, 35–59.CrossRefGoogle Scholar
  43. Sáenz-Ludlow, A., & Kadunz, G. (2016a). Semiotics as a tool for learning mathematics: How to describe the construction, visualisation, and communication of mathematics concepts. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  44. Sáenz-Ludlow, A., & Kadunz, G. (2016b). Constructing knowledge as a semiotic activity. In A. Sáenz-Ludlow & G. Kadunz (Eds.), Semiotics as a tool for learning mathematics (pp. 1–21). Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  45. Sáenz-Ludlow, A., & Presmeg, N. (2006). Semiotic perspectives in mathematics education. Educational Studies in Mathematics. Special Issue, 61(1–2).Google Scholar
  46. Snow, R. E. (1992). Aptitude theory: Yesterday, today, and tomorrow. Educational Psychologist, 27, 5–32.CrossRefGoogle Scholar
  47. Soo, K., Mavin, T. J., & Roth, W.-M. (2016). Mixed-fleet flying in commercial aviation: A joint cognitive systems perspective. Cognition, Technology & Work, 18, 449–463.CrossRefGoogle Scholar
  48. Vygotskij, L. S. (2001). Lekcii po pedologii [Lectures on pedology]. Izhevsk: Udmurdskij University.Google Scholar
  49. Vygotsky, L. S. (1987). The collected works of L. S. Vygotsky, vol. 1: Problems of general psychology. New York: Springer.Google Scholar
  50. Vygotsky, L. S. (1989). Concrete human psychology. Soviet Psychology, 27(2), 53–77.Google Scholar
  51. Vygotsky, L. S. (1997). The collected works of L. S. Vygotsky, vol. 4: The history of the development of higher mental functions. New York: Springer.Google Scholar
  52. Wittgenstein, L. (1975/1969). On certainty (revised ed.). New Jersey: Wiley.Google Scholar
  53. Wittgenstein, L. (1997). Philosophical investigations/Philosophische Untersuchungen (2nd ed.). Oxford: Blackwell (First published in 1953). Google Scholar
  54. Wittmann, E. C. (1995). Mathematics education as a “design science”. Educational Studies in Mathematics, 29(4), 355–374.CrossRefGoogle Scholar
  55. Yu, P. W. (2004). Prototype development and discourse among middle school students in a dynamic geometry environment. Unpublished Ph.D. dissertation, Illinois State University.Google Scholar
  56. Zeyer, A., & Roth, W.-M. (2009). A mirror of society: a discourse analytic study of 14–15-year-old Swiss students’ talk about environment and environmental protection. Cultural Studies of Science Education, 4, 961–998.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Norma Presmeg
    • 1
    Email author
  • Luis Radford
    • 2
  • Wolff-Michael Roth
    • 3
  • Gert Kadunz
    • 4
  1. 1.Mathematics DepartmentIllinois State UniversityMaryvilleUSA
  2. 2.École des sciences de l’éducationUniversité LaurentienneSudburyCanada
  3. 3.Applied Cognitive ScienceUniversity of VictoriaVictoriaCanada
  4. 4.Department of MathematicsAlpen-Adria Universitaet KlagenfurtKlagenfurtAustria

Personalised recommendations