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Research papers

The role of symbols in mathematical communication: the case of the limit notation

References

  • Alcock, L. J. (2008). Mathematicians' perspectives on the teaching and learning of proof. In F. Hitt, D. A. Holton, & P. Thompson (Eds.), Research in collegiate mathematics education VII (pp. 73–100). Providence, RI: American Mathematical Society.
  • Bagni, G. T. (2005). The historical roots of the limit notation: Cognitive development and development of representation registers. Canadian Journal of Science, Mathematics and Technology Education, 5, 453–468. doi:10.1080/14926150509556675
  • Bezuidenhout, J. (2001). Limits and continuity: Some conceptions of first-year students. International Journal of Mathematical Education in Science and Technology, 32, 487–500. doi:10.1080/00207390010022590
  • Cobb, P. (2000). From representations to symbolizing: Introductory comments on semiotics and mathematical learning. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 17–36). Mahwah, NJ: Lawrence Erlbaum.
  • Cornu, B. (1991). Limits. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 153–166). Dordrecht: Kluwer.
  • Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 95–123). Dordrecht: Kluwer.
  • Dubinsky, E. (2000). Meaning and formalism in mathematics. International Journal of Computers for Mathematical Learning, 5, 211–240. doi:10.1023/A:1009806206292
  • Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM-The International Journal on Mathematics Education, 39(1–2), 127–135. doi:10.1007/s11858-006-0004-1
  • Goldin, G. A. (1997). Observing mathematical problem solving through task-based interviews. Journal for Research in Mathematics Education. Monograph: Qualitative Research Methods in Mathematics Education, 9, 40–177. doi:10.2307/749946
  • Gray, E. M., & Tall, D. O. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 26, 115–141.
  • Gray, E. M., & Tall, D. O. (2001). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 65–72). Utrecht: Freudenthal Institute, Utrecht University.
  • Güçler, B. (2012). Limitless ways to talk about limits: Communicating mathematical ideas in the classroom. Mathematics Teacher, 105, 697–701. doi:10.5951/mathteacher.105.9.0697
  • Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Educational Studies in Mathematics, 82, 439–453. doi:10.1007/s10649-012-9438-2
  • Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.
  • Parameswaran, R. (2007). On understanding the notion of limits and infinitesimal quantities. International Journal of Science and Mathematics Education, 5, 193–216. doi:10.1007/s10763-006-9050-y
  • Radford, L., & Puig, L. (2007). Syntax and meaning as sensuous, visual, historical forms of algebraic thinking. Educational Studies in Mathematics, 66, 145–164. doi:10.1007/s10649-006-9024-6
  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36. doi:10.1007/BF00302715
  • Sfard, A. (1992). Operational origin of mathematical objects and the quandary of reification – the case of function. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 59–84). Washington, DC: Mathematical Association of America.
  • Sfard, A. (2000). Symbolizing mathematical reality into being: How mathematical discourse and mathematical objects create each other. In P. Cobb, K. E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on mathematical discourse, tools, and instructional design (pp. 37–98). Mahwah, NJ: Erlbaum.
  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses and mathematizing. New York, NY: Cambridge University Press.
  • Tall, D. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal, 20(2), 5–24. doi:10.1007/BF03217474
  • Tall, D., & Schwarzenberger, R. (1978). Conflicts in the learning of real numbers and limits. Mathematics Teaching, 82, 44–49.
  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169. doi:10.1007/BF00305619
  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
  • Williams, S. R. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22, 219–236. doi:10.2307/749075

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