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Articles

Eliciting the coordination of preservice secondary mathematics teachers’ definitions and concept images of function

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Pages 1387-1412 | Received 21 Dec 2018, Published online: 07 Oct 2020

References

  • Akkoc, H. (2008). Pre-service mathematics teachers’ concept images of radian. International Journal of Mathematical Education in Science and Technology, 39(7), 857–878. https://doi.org/10.1080/00207390802054458
  • Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. http://www.amte.net/standards.
  • Attorps, I. (2003, February 28–March 3). Teachers’ images of the ‘equation’ concept. CERME 3: Third Conference of the European Society for research in mathematics education, Bellaria, Italy.
  • Australian Curriculum Assessment and Reporting Authority (ACARA). (2020, April 20). The Australian curriculum: Mathematics, all curriculum elements. http://www.australiancurriculum.edu.au/download/f10.
  • Ayalon, M., Watson, A., & Lerman, S. (2017). Students’ conceptualisations of function revealed through definitions and examples. Research in Mathematics Education, 19(1), 1–19. https://doi.org/10.1080/14794802.2016.1249397
  • Bardini, C., Pierce, R., Vincent, J., & King, D. (2014). Undergraduate mathematics students’ understanding of the concept of function. Indonesian Mathematical Society Journal on Mathematics Education, 5(2), 85–107. https://doi.org/10.22342/jme.5.2.1495.85-107
  • Bannister, V. R. P. (2014). Flexible conceptions of perspectives and representations: An examination of pre-service mathematics teachers’ knowledge. International Journal of Education in Mathematics, Science and Technology, 2(3), 223–233. https://doi.org/10.184040/ijemst.23592
  • Carlson, M. P. (1998). A cross-sectional investigation of the development of the function concept. Research in Collegiate Mathematics Education, III, Issues in Mathematics Education, 7(1), 115–162. https://doi.org/10.1090/cbmath/007/04
  • Carlson, M. P., Smith, N., & Persson, J. (2003). Developing and connecting Calculus students’ Notions of Rate-of change and Accumulation: The Fundamental Theorem of Calculus. International Group for the Psychology of Mathematics Education, 2, 165–172. https://doi.org/10.1201/9780203417867.ch8
  • Chesler, J. (2012). Pre-service secondary mathematics teachers making sense of definitions of functions. Mathematics Teacher Education and Development, 14(1), 27–40.
  • Conference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II. American Mathematical Society and Mathematical Association of America. https://doi.org/10.1090/cbmath/017.
  • Cooney, T. J., Beckman, S., & Lloyd, G. M. (2010). Developing essential understanding of functions for teaching mathematics in grades 9-12. National Council of Teachers of Mathematics.
  • Cooney, T. J., & Wilson, M. R. (1993). Teachers’ thinking about functions: Historical and research perspectives. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.), Integrating research on the graphical representation of functions (pp. 131–158). Erlbaum.
  • Creswell, J. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). SAGE Publications.
  • Cunningham, R. F., & Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. Issues in Undergraduate Mathematics Preparation of School Teachers: The Journal, 1, 1–17.
  • DeCuir-Gunby, J.P., Marshall, P.L., & McCulloch, A.W. (2011). Developing and using a codebook for the analysis of interview data: An example from a professional development research project. Field Methods, 23(2), 136–155.
  • Dede, Y., & Soybas, D. (2011a). Preservice mathematics teachers’ experiences about function and equation concepts. Eurasia Journal of Mathematics, Science & Technology Education, 7(2), 89–102. https://doi.org/10.12973/ejmste/75183
  • Dede, Y., & Soybas, D. (2011b). Preservice mathematics teachers’ concept images of polynomials. Quality and Quantity, 45(2), 391–402. https://doi.org/10.1007/s11135-009-9303-2
  • Department for Education. (2014). The national curriculum in England: complete framework for key stages 1 to 4. Retrieved April 20, 2020, from https://www.gov.uk/government/publications/national-curriculum-in-england-framework-for-key-stages-1-to-4.
  • Doerr, H. M. (2004). Teachers’ knowledge and the teaching of algebra. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 267–290). Kluwer Academic.
  • Dubinsky, E., & Harel, G. (1992). The concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America.
  • Dubinsky, E., & Wilson, R. T. (2013). High school students’ understanding of the function concept. Journal of Mathematical Behavior, 32(1), 83–101. https://doi.org/10.1016/j.jmathb.2012.12.001
  • Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21(6), 521–544. https://doi.org/10.1007/BF00315943
  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94–116. https://doi.org/10.5951/jresematheduc.24.2.0094
  • Hatisaru, V., & Erbas, A. K. (2017). Mathematical knowledge for teaching the function concept and student learning outcomes. International Journal of Science and Mathematics Education, 15(4), 703–722. https://doi.org/10.1007/s10763-015-9707-5
  • Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64. https://doi.org/10.3102/00346543060001001
  • Lloyd, G. M., & Wilson, M. (1998). Supporting innovation: The impact of a teacher’s conceptions of function on his implementation of a reform curriculum. Journal for Research in Mathematics Education, 29(3), 248–274. https://doi.org/10.5951/jresematheduc.29.3.0248
  • Martinez-Planell, R., & Trigueros Gaisman, M. (2012). Students’ understanding of the general notion of function of two variables. Educational Studies in Mathematics, 81(3), 365–384. https://doi.org/10.1007/s10649-012-9408-8
  • McCulloch, A.W., Lovett, J.N., & Edgington, C. (2019). Transforming preservice teachers' understanding of function using a vending machine applet. Contemporary Issues in Technology and Teacher Education 19(1). Retrieved from https://www.citejournal.org/volume-19/issue-1-19/mathematics/designing-to-provoke-disorienting-dilemmas-transforming-preservice-teachers-understanding-of-function-using-a-vending-machine-applet/
  • McCulloch, A.W., Lovett, J.N., Sherman, M., & Meagher, M. (2020). Challenging preservice secondary mathematics teachers' conceptions of function. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-020-00347-6
  • McGowen, M., DeMarois, P., & Tall, D. (2000). Using the function machine as a cognitive root. In M. L. Fernandez (Ed.), Proceedings of the 22nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 247–254).
  • Merriam, S. B. (1998). Qualitative research and case study applications in education. Jossey-Bass Publishers.
  • Mezirow, J. (2009). Transformative learning theory. In J. Merizow & E. W. Taylor (Eds.), Transformative learning in practice: Insights from community, workplace, and higher education (pp. 18–31). Jossey-Bass.
  • Ministry of Education. (2007). The New Zealand curriculum. Learning Media.
  • National Governors Association Center for Best Practice & Council of Chief State School Officers. (2010). Common core state standards for mathematics.
  • Pehkonen, E., & Pietilä, A. (2003, February 28–March 3). On relationships between beliefs and knowledge in mathematics education. In M. Mariotti (Ed.), Proceedings of the third congress of European Society for Research in Mathematics Education (CD/ROM). University of Pisa. http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG2/TG2_pehkonen_cerme3.pdf
  • Rasmussen, C. L. (2000). New directions in differential equations: A framework for interpreting students’ understandings and difficulties. Journal of Mathematical Behavior, 20(1), 55–87. https://doi.org/10.1016/S0732-3123(01)00062-1
  • Rasslan, S., & Vinner, S. (1998). Images and definitions for the concept of increasing/decreasing function. In A. Oliver, & K. Newstead (Eds.), Proceedings of the 22nd conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 33–40). University of Stellenbosch.
  • 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.
  • Tabach, M., & Nachlieli, T. (2015). Classroom engagement towards using definitions for developing mathematical objects: The case of function. Educational Studies in Mathematics, 90(2), 163–187. https://doi.org/10.1007/s10649-015-9624-0
  • Tall, D., McGowen, M., & DeMarois, P. (2000). The function machine as a cognitive root for the function concept. In M. L. Fernandez (Ed.), Proceedings of the 22nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 255–261).
  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/BF00305619
  • Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421–456). Tucson, AZ: National Council of Teachers of Mathematics.
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Taback, M. (2015). Early-years teachers’ concept images and concept definitions: Triangles, circles, and cylinders. ZDM Mathematics Education, 47(3), 497–509. https://doi.org/10.1007/s11858-014-0641-8
  • Vinner, S. (1983). Concept definition, concept image, and the notion of function. International Journal of Mathematics Education in Science and Technology, 14(3), 293–305. https://doi.org/10.1080/0020739830140305
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356–366. https://doi.org/10.5951/jresematheduc.20.4.0356
  • Wilson, M. R. (1994). One preservice secondary teachers’ understanding of function: The impact of course integrating mathematical content and pedagogy. Journal for Research in Mathematics Education, 25(4), 346–370. https://doi.org/10.5951/jresematheduc.25.4.0346
  • Yin, R. K. (2009). Case study research: Design and methods (4th ed.). SAGE Publications.

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