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Articles

Students’ conceptualisations of function revealed through definitions and examples

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Pages 1-19 | Received 20 Sep 2015, Accepted 26 Mar 2016, Published online: 09 Feb 2017

References

  • Ayalon, M., Lerman, S., & Watson, A. (2014a). Progression towards understanding functions: What does spatial generalization contribute? Proceedings of BCME, 8, 17–24.
  • Ayalon, M., Lerman, S., & Watson, A. (2014b). Graph-matching situations: Some insights from a cross year survey in the UK. Research in Mathematics Education, 16(1), 73–74. doi: 10.1080/14794802.2013.849082
  • Ayalon, M., Watson, A., & Lerman, S. (2015). Functions represented as sequential data: Relationships between presentation and student responses. Educational Studies in Mathematics, 90, 321–339.
  • Ayalon, M., Watson, A., & Lerman, S. (2016). Progression towards functions: Identifying variables and relations between them. International Journal of Science and Mathematics Education, 14, 1153–1173.
  • Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23, 247–285. doi: 10.1007/BF02309532
  • Carlson, M., & Oehrtman, M. (2005). Key aspects of knowing and learning the concept of function. Research Sampler Series, 9, The Mathematical Association of America Notes Online. Retrieved from http://www.maa.org/t_and_l/sampler/rs_9.html.
  • Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26, 135–164. doi: 10.1007/BF01273661
  • Confrey, J., & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26(1), 66–86. doi: 10.2307/749228
  • Dreyfus, T., & Eisenberg, T. (1983). The function concept in college students: Linearity smoothness and periodicity. Focus on Learning Problems in Mathematics, 5, 119–132. Ed: 1989, ‘A learning theory approach to calculus’, Proceedings of the St. Olaf.
  • Dubinsky, E. (1989). Using a theory of learning in college mathematics courses. Received from https://www.heacademy.ac.uk/sites/default/files/msor.1.2f.pdf.
  • Dubinsky, E., & Harel, G. (1992). The nature of the process conception of function. In E. Dubinsky & G. Harel (Eds.), The concept of function. Aspects of epistemology and pedagogy (pp. 85–106). Washington, DC: The Mathematical Association of America.
  • Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21, 521–544. doi: 10.1007/BF00315943
  • Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs and graphing: Tasks, learning, and teaching. Review of Educational Research, 60, 1–64. doi: 10.3102/00346543060001001
  • Lincoln, Y. S. (1995). Emerging criteria for quality in qualitative and interpretive research. Qualitative Inquiry, 1(3), 275–289. doi: 10.1177/107780049500100301
  • Markovits, Z., Eylon, B. A., & Bruckheimer, M. (1986). Function today and yesterday. For the Learning of Mathematics, 6(2), 18–28.
  • Meel, D. (1998). Honors students’ calculus understandings: Comparing calculus&mathematica and traditional calculus students. Research in Collegiate Mathematics Education, III, 163–215. doi: 10.1090/cbmath/007/05
  • Ministry of Education. (2009). Mathematics curriculum for grades 7–9. Retrieved from http://meyda.education.gov.il/files/Tochniyot_Limudim/Math/Hatab/Mavo.doc (in Hebrew).
  • Ronda, E. (2009). Growth points in students’ developing understanding of function in equation form. Mathematics Education Research Journal, 21(1), 31–53. doi:10.1007/BF03217537
  • Saldanha, L., & Thompson, P. W. (1998). Re-thinking covariation from a quantitative perspective: Simultaneous continuous variation. In S. B. Berenson, K. R. Dawkins, M. Blanton, W. N. Coloumbe, J. Kolb, K. Norwood, & L. Stiff (Eds.), Proceedings of the 20th annual meeting of the psychology of mathematics education north American chapter (Vol. 1, pp. 298–303). Raleigh, NC: North Carolina State University.
  • Schwarz, B. B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30, 362–389. doi:10.2307/749706
  • Selden, A., & Selden, J. (1992). Research perspectives on conceptions of function: Summary and overview. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 1–16). Washington, DC: Mathematical Association of America.
  • 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, 1–36. doi: 10.1007/BF00302715
  • Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification-the case of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 59–84). Washington, DC: Mathematical Association of America.
  • Sierpinska, A. (1992). On understanding the notion of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 25–28). Washington, DC: Mathematical Association of America.
  • Sinclair, N., Watson, A., Zazkis, R., & Mason, J. (2011). The structuring of personal example spaces. Journal of Mathematical Behavior, 30(4), 291–303. doi: 10.1016/j.jmathb.2011.04.001
  • Slavit, D. (1997). An alternate route to the reification of function. Educational Studies in Mathematics, 33, 259–281. doi: 10.1023/A:1002937032215
  • Spyrou, P., & Zagorianakos, A. (2010). Greek students’understandings of the distinction between function and relation. Research in Mathematics Education, 12(2), 163–164. doi: 10.1080/14794802.2010.496988
  • Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 495–511). New York: Macmillan.
  • Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14, 293–305. doi: 10.1080/0020739830140305
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20, 356–366. doi: 10.2307/749441
  • Vygotsky, L. S. (1986). Thought and language. Cambridge, MA: MIT Press.
  • Watson, A. (2013). Functional relations between variables. In A. Watson, K. Jones, & D. Pratt (Eds.), Key ideas in teaching mathematics: Research-based guidance for ages 9–19 (pp. 172–199). Oxford: Oxford University Press.
  • Watson, A., & Harel, G. (2013). The role of teachers’ knowledge of functions in their teaching: A conceptual approach with illustrations from two cases. Canadian Journal of Science, Mathematics, and Technology Education, 13(2), 154–168. doi: 10.1080/14926156.2013.784826
  • Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Zaslavsky, O., & Peled, I. (1996). Inhibiting factors in generating examples by mathematics teachers and student-teachers: The case of binary operation. Journal for Research in Mathematics Education, 27(1), 67–78. doi: 10.2307/749198
  • Zaslavsky, O., & Ron, G. (1998). Student’s understanding of the role of counter-examples. In A. Oliver & K. Newstead (Eds.), Proceedings of the 22nd conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 225–232). Stellenbosch, South Africa: PME.
  • Zinchenko, V. P. (2007). Thought and word: The approaches of L.S. Vygotsky and G.G. Shpet. In H. Daniels, M. Cole, & J. V. Wertsch (Eds.), The Cambridge companion to Vygotsky (pp. 212–245). New York: Cambridge University Press.

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