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Articles

A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates

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Pages 405-423 | Received 15 Nov 2018, Published online: 26 Feb 2019

References

  • Moore KC, Paoletti J, Musgrave S. Complexities in students’ construction of the polar coordinate system. J Math Behav. 2014;36:135–149.
  • Haber, S. Students’challenges with polar functions: covariational reasoning and plotting in the polar coordinate system. Int J Math Educ Sci Technol 2017;48(1), 48–66.
  • Borji V, Voskoglou MG. Designing an ACE approach for teaching the polar coordinates. Am J Educ Res. 2017;5(3):303–309.
  • Montiel M, Vidakovic D, Kabael T. Relationship between students’ understanding of functions in Cartesian and polar coordinate systems. Investig Math Learn. 2008;1(2):52–70.
  • Montiel M, Wilhelmi M, Vidakovic D, et al. Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context. Educ Stud Math. 2009;72(2):139–160.
  • Moore KC, Paoletti T, Musgrave S. Covariational reasoning and invariance among coordinate systems. J Math Behav. 2013;32(3):461–473.
  • Sayre E, Wittman M. Intermediate mechanics students’ coordinate system choice. In Electronic proceedings for the tenth special interest group of the mathematical association of America on research in undergraduate mathematics education conference on research in undergraduate mathematics education San Diego; 2007.
  • Badillo E, Azcárate C, Font V. Analysis of mathematics teachers’ level of understanding of the objects f' (a) and f' (x). Enseñanza de las ciencias. 2011;29(2):191–206.
  • Haspekian M, Bikner-Ahsbahs A, Artigue M. When the fiction of learning is kept: a case of networking two theoretical views. In: A Lindmeier, A Heinze, editors. Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, vol. 3. Kiel: PME; 2013. pp. 9–16.
  • Pino-Fan L, Guzmán I, Duval R, et al. The theory of registers of semiotic representation and the onto-semiotic approach to mathematical cognition and instruction: linking looks for the study of mathematical understanding. In: Beswick K, Muir T, Wells J, editors. Proceedings of the 39th Conference of the International Group for the Psychology of mathematics education, Vol. 4. Hobart: PME; 2015. p. 33–40.
  • Stewart S, Thomas MOJ. A framework for mathematical thinking: the case of linear algebra. Int J Math Educ Sci Technol 2009;40(7):951–961.
  • Arnon I, Cottrill J, Dubinsky E, et al. APOS theory: a framework for research and curriculum development in mathematics education. New York: Springer; 2014.
  • Font V, Godino JD, Gallardo J. The emergence of objects from mathematical practices. Educ Stud Math 2013;82(1):97–124.
  • Godino J, Batanero C, Font V. The onto-semiotic approach to research in mathematics education. ZDM. Zentralblatt für Didaktik der Mathematik 2007;39(1–2):127–135.
  • Borji V, Font V, Alamolhodaei H, Sánchez A. Application of the complementarities of two theories, APOS and OSA, for the analysis of the university students’ understanding on the graph of the function and its derivative. EURASIA J Math Sci Technol Educ 2018;14(6):2301–2315.
  • Borji V, Font V, Alamolhodaei H, et al. On students’ understanding of implicit differentiation, based on two lenses: APOS and OSA. In: Bergqvist E, Österholm M, Granberg C, Sumpter L, editors. Proceedings of the 42nd Conference of the International Group for the Psychology of mathematics education, Vol. 5. Umeå: PME; 2018. p. 25.
  • Font V, Trigueros M, Badillo E, et al. Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educ Stud Math 2016;91(1):107–122.
  • Font V, Contreras A. The problem of the particular and its relation to the general in mathematics education. Educ Stud Math. 2008;69(1):33–52.
  • Pino-Fan L, Font V, Gordillo W, et al. Analysis of the meanings of the antiderivative used by students of the first engineering courses. Int J Sci Math Educ 2018;16(6):1091–1113.
  • Asiala M, Brown A, Dubinsky E, et al. A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education;1996.
  • Piaget J, García R. Psychogenesis and the history of science. New York: Columbia University Press; 1983.
  • Zengin Y, Tatar E. The teaching of polar coordinates with dynamic mathematics software. Int J Math Educ Sci Technol 2015;46(1):127–139.
  • Stewart J. Calculus, 7th Edition. Brooks/Cole Cengage Learning, Mason; 2010.
  • Pino-Fan L, Godino JD, Font V. Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: the case of the derivative. J Math Teach Educ 2018;21(1):63–94.
  • Borji V, Voskoglou MG. Applying the APOS theory to study the student understanding of the polar coordinates. Am J Educ Res 2016;4(16):1149–1156.
  • Akkoc H. Pre-service mathematics teachers’ concept image of radian. Int J Math Educ Sci Technol. 2008;39(7):857–878.
  • Moore KC. Making sense by measuring arcs: a teaching experiment in angle measure. Educ Stud Math. 2013;83(2):225–245.
  • Topcu T, Kertil M, Akkoc H, et al. Pre-service and in-service mathematics teachers’ concept images of radian. In: J Novotná, H Moraová, M Krátká, N Stehlíková, editor. Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol.5). Prague: PME; 2006. p. 281–288.

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