Abstract
A challenging task when doing research in mathematics education is the comprehensible description of activity shown by students and their construction of new knowledge when doing mathematics. The semiotics of Charles S. Peirce seems to be a promising tool for fulfilling this task.
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References
Anderson, M., Sáenz-Ludlow, A., Zellweger, S., & Cifarelli, V. V. (Eds.). (2003). Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing. New York, NY & Ottawa, ON: Legas.
Arzarello, F., Olivero, F., Domingo, D., & Robutti, O. (2002). A cognitive analysis of dragging practices in cabri environments. Zentralblatt für Didaktik der Mathematik, 34(3), 66–72.
Bakker, A., & Hoffmann, M. H. G. (2005). Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students’ learning about statistical distribution. Educational Studies in Mathematics, 60(3), 333–358.
Boehm, G. (1994). Die Wiederkehr der Bilder. In G. Boehm (Ed.), Was ist ein Bild? (pp. 11–38). München, Germany: Wilhelm Fink Verlag.
Cobb, P., Yackel, E., & McClain, K. (Eds.). (2000). Symbolizing and communication in mathematics classrooms: Perspectives on discourse, tools, and instructional design. Mahwah, NJ: Lawrence Erlbaum.
Dörfler, W. (2005). Diagrammatic thinking: Affordances and constraints. In M. Hoffmann, J. Lenhard, & F. Seeger (Eds.), Activity and sign: Grounding mathematics education (pp. 57–66). New York, NY: Springer.
Goldin, G. (1998a). Representational systems, learning and problem solving in mathematics. Journal of Mathematical Behavior, 17(2), 137–165.
Goldin, G. (1998b). The PME working group on representations. Journal of Mathematical Behavior, 17(2), 283–299.
Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. P. Steffe & P. Nesher (Eds.), Theories of mathematical learning. Mahwah, NJ: Lawrence Erlbaum.
Goodman, N. (1976). Languages of art: An approach to a theory of symbols. Indianapolis, IN: Hackett Publishing Company.
Hoffmann, M. H. G. (Ed.). (2003). Mathematik verstehen: Semiotische Perspektiven. Hildesheim, Germany & Berlin, Germany: Franzbecker.
Hoffmann, M. H. G. (2005a). Signs as means for discoveries: Peirce and his concepts of “diagrammatic reasoning”, “theorematic deduction”, “hypostatic abstraction”, and “theoric transformation.” In M. Hoffmann, J. Lenhard, & F. Seeger (Eds.), Activity and sign: Grounding mathematics education (pp. 45–56). New York, NY: Springer.
Hoffmann, M. H. G. (2005b). Erkenntnisentwicklung. Frankfurt am Main, Germany: Vittorio Klostermann.
Hoffmann, M. H. G. (2006). What is a “semiotic perspective”, and what could it be? Some comments on the contributions to this special issue. Educational Studies in Mathematics, 61(1), 279–291.
Latour, B. (1987). Science in action: How to follow scientists and engineers through society. Cambridge, MA: Harvard University Press.
Mitchell, W. J. T. (1994). Picture theory. Chicago, IL: The University of Chicago Press.
Nöth, W. (1995). Handbook of semiotics. Bloomington, IN: Indiana University Press.
Oliveri, G. (1997). Mathematics, a science of patterns? Synthese, 112(3), 379–402.
Peirce, C. S. (1976). The new elements of mathematics (NEM) (Vols. I–IV). The Hague-Paris/Atlantic highlands, NJ: Mouton/Humanities.
Presmeg, N. (2006). Semiotics and the “connections” standard: Significance of semiotics for teacher of mathematics. Educational Studies in Mathematics, 61(1), 163–182.
Sáenz-Ludlow, A. (2006). Classroom interpreting games with an illustration. Educational Studies in Mathematics, 61(1), 183–218.
Sáenz-Ludlow, A., & Presmeg, N. (2006a). Guest editorial semiotic perspectives on learning mathematics and communicating mathematically. Educational Studies in Mathematics, 61(1), 1–10.
Seeger, F. (2000). Lernen mit grafischen Repräsentationen: Psychologische und semiotische Überlegungen. Semiotik, 22(1), 51–79.
Stjernfelt, F. (2000). Diagrams as centerpiece of a Peircian epistemoloy. Transactions of Charles S. Peirce Society, XXXVI(3), 357–384.
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Kadunz, G. (2016). Diagrams as Means for Learning. In: Sáenz-Ludlow, A., Kadunz, G. (eds) Semiotics as a Tool for Learning Mathematics. Semiotic Perspectives in the Teaching and Learning of Mathematics Series. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-337-7_6
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DOI: https://doi.org/10.1007/978-94-6300-337-7_6
Publisher Name: SensePublishers, Rotterdam
Online ISBN: 978-94-6300-337-7
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