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.
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Notes
- 1.
See also Roth (2015) where the continued changes in thinking and writing of mathematical graphs and equations, associated with continued erasure and rewriting, are theorized in the field as the birth of understanding arising from the excess of graphical movements.
References
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.
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.
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.
Boncompagni, A. (2016). Wittgenstein and pragmatism (History of analytic philosophy). London: Macmillan.
de Saussure, F. (1967). Cours de linguistique générale [Course in general linguistics]. Paris: Éditions Payot & Rivages.
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).
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.
Eco, U. (1976). A theory of semiotics. Bloomington: Indiana University Press.
Eco, U. (1984). Semiotics and the philosophy of language. Bloomington: Indiana University Press.
Garfinkel, H. (1967). Studies in ethnomethodology. Englewood Cliffs, NJ: Prentice Hall.
Garfinkel, H. (1996). Ethnomethodology’s program. Social Psychology Quarterly, 59, 5–21.
Hookway, C. (2012). The pragmatic maxim. Essays on Peirce and pragmatism. Oxford: Oxford University Press.
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.
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.
James, W. (1907). Pragmatism: a new name for some old ways of thinking. London, New York: Longmans, Green & Co.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
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.
Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.
Marx, K., & Engels, F. (1962). Werke Band 23 [Works vol. 23]. Berlin: Dietz.
Marx, K., & Engels, F. (1978). Werke Band 3 [Works vol. 3]. Berlin: Dietz.
Peirce, C. S. (1878). How to make our ideas clear. Popular Science Monthly, 12, 286–302.
Peirce, C. S. (1931–1958). Collected papers (CP, Vols. 1–8). Cambridge: Harvard University Press.
Peirce, C. S. (1992). In N. Houser & C. Kloesel (Eds.), The essential Peirce (Vol. 1). Bloomington, IN: Indiana University Press.
Peirce, C. S. (1998). In The Peirce Edition Project (Eds.), The essential Peirce (Vol. 2). Bloomington, IN: Indiana University Press.
Piaget, J., & Inhelder, B. (2013/1958). The growth of logical thinking from childhood to adolescence (A. Parsons & S. Milgram, Trans.). New York: Routledge.
Presmeg, N. C. (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23(6), 595–610.
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.
Presmeg, N. C. (1998). Ethnomathematics in teacher education. Journal of Mathematics Teacher Education, 1(3), 317–339.
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.
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.
Presmeg, N. C. (2006b). Semiotics and the “connections” standard: Significance of semiotics for teachers of mathematics. Educational Studies in Mathematics, 61, 163–182.
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.
Radford, L. (2012). Education and the illusions of emancipation. Educational Studies in Mathematics, 80(1), 101–118.
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.
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.
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.
Roth, W.-M. (2012a). Societal mediation of mathematical cognition and learning. Orbis Scholae, 6(2), 7–22.
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.
Roth, W.-M. (2015). Excess of graphical thinking: Movement, mathematics and flow. For the Learning of Mathematics, 35(1), 2–7.
Roth, W.-M. (2016). Concrete human psychology. New York: Routledge.
Roth, W.-M., & Jornet, A. (2017). Theorizing without “mediators”. Integrative Psychological and Behavioral Science. https://doi.org/10.1007/s12124-016-9376-0.
Roth, W.-M., & McGinn, M. K. (1998). Inscriptions: Toward a theory of representing as social practice. Review of Educational Research, 68, 35–59.
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.
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.
Sáenz-Ludlow, A., & Presmeg, N. (2006). Semiotic perspectives in mathematics education. Educational Studies in Mathematics. Special Issue, 61(1–2).
Snow, R. E. (1992). Aptitude theory: Yesterday, today, and tomorrow. Educational Psychologist, 27, 5–32.
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.
Vygotskij, L. S. (2001). Lekcii po pedologii [Lectures on pedology]. Izhevsk: Udmurdskij University.
Vygotsky, L. S. (1987). The collected works of L. S. Vygotsky, vol. 1: Problems of general psychology. New York: Springer.
Vygotsky, L. S. (1989). Concrete human psychology. Soviet Psychology, 27(2), 53–77.
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.
Wittgenstein, L. (1975/1969). On certainty (revised ed.). New Jersey: Wiley.
Wittgenstein, L. (1997). Philosophical investigations/Philosophische Untersuchungen (2nd ed.). Oxford: Blackwell (First published in 1953).
Wittmann, E. C. (1995). Mathematics education as a “design science”. Educational Studies in Mathematics, 29(4), 355–374.
Yu, P. W. (2004). Prototype development and discourse among middle school students in a dynamic geometry environment. Unpublished Ph.D. dissertation, Illinois State University.
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.
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Presmeg, N., Radford, L., Roth, WM., Kadunz, G. (2018). Discussion and Conclusions. In: Presmeg, N., Radford, L., Roth, WM., Kadunz, G. (eds) Signs of Signification. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70287-2_19
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