1,008
Views
28
CrossRef citations to date
0
Altmetric
Original Articles

Constructing the integral concept on the basis of the idea of accumulation: suggestion for a high school curriculum

&
Pages 641-651 | Received 19 Sep 2012, Accepted 21 Apr 2013, Published online: 08 Jun 2013

References

  • Orton A. Students’ understanding of integration. Educ Stud Math. 1983;14:1–18.
  • Sealey V. Student understanding of definite integrals, Riemann sums and area under a curve: What is necessary and sufficient? In: Alvatore S, Luis Cortina JSM, Mendez A, editors. Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Vol. 2; Merida, Yucatan (Mexico): PME-NA; 2006. p. 46–53.
  • Thomas MO, Hong YY. The Riemann integral in calculus: students’ processes and concepts. In: Clarkson PC, editor. Proceedings of the 19th Mathematics Education Research Group of Australasia Conference; Melbourne; 1996. p. 572–579.
  • Mundy J. Analysis of errors of first year calculus students. In: Bell A, Love B, Kilpatrick J, editors. Theory, research and practice in mathematics education.Proceedings of ICME 5; Nottingham (UK): Shell Centre; 1984. p. 170–172.
  • Bagni GT. A multidimensional approach to learning in mathematics and sciences, In: Gagatsis A, editor. Integral and continuity in high school students’ conceptions; Nicosia: Intercollege Press; 1999. p. 171–182.
  • Thompson PW. Images of rate and operational understanding of the Fundamental Theorem of Calculus. Educ Stud Math. 1994;26:229–274.
  • Belova O. Computer based approach to integral calculus for prospective teachers [Ph.D. dissertation]. Krasnoyarsk State Pedagogical University; 2006. (In Russian)
  • Rösken B, Rolka K. Integrating intuition: the role of concept image and concept definition for students’ learning of integral calculus. The Montana Mathematics Enthusiast, Monograph 2007;3:181–204.
  • Apostol TM. Calculus. Waltham, MA: Wiley; 1967.
  • Courant R. Differential and integral calculus. Glasgow: Blackie & Son; 1934.
  • Taylor PD. Calculus: the analysis of functions. Toronto: Wall & Emerson; 1992.
  • Turegano P. Del area a la integral. Un estudio en el contexto educativo. Ensenanza de las Ciencias 1998;26:233–249.
  • Shtein I. The introduction of the integral and the connections between the integral and the derivative, by means of problems and models from the real life in the framework of the teaching of the calculus to the students for the economy and management [Ph.D. dissertation]. Tel-Aviv University; 1995. (In Hebrew)
  • Kouropatov A, Dreyfus T. Integral as accumulation: a didactical perspective for school mathematics. In: Tzekaki M, Kaldrimidou M, Sakonidis H, editors. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education Vol. 3; Thessaloniki: PME; 2009. p. 417–424.
  • Thompson PW, Silverman J. The concept of accumulation in calculus, In: Carlson M, Rasmussen C, editors. Making the connection: research and teaching in undergraduate mathematics. Washington, DC: MAA; 2008. p. 117–131.
  • Carlson MP, Persson J, Smith N. Developing and connecting calculus students’ notions of rate-of-change and accumulation: The FTC. In: Pateman NA, Dougherty BJ, Zilliox JT, editors. Proceedings of the 27th Meeting of the International Group for the Psychology of Mathematics Education Vol. 2; Honolulu, HI: University of Hawaii; 2003. p. 153–166.
  • Oehrtman M. Approximation as a foundation for understanding limit concepts. In: McDougall DE, Ros JA, editors. Proceedings of the 26th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Vol. 1; Toronto: PME-NA; 2004. p. 95–102.
  • Sealey V, Oehrtman M. Student understanding of accumulation and Riemann sums. In: Lloyd GM, Lloyd M, Wilkins JLM, Behm SL, editors. Proceedings of the 27th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Vol. 2; Roanoke, VA: PME-NA; 2005. p. 84–91.
  • Newton I. Philosophiae naturalis principia mathematica. Berkeley, CA: University of California Press; 1686/1999.
  • Kouropatov A, Dreyfus T. Constructing the concept of approximation. In: Ubuz B, editor. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education Vol. 3; Ankara: PME; 2011. p. 97–105.
  • Kouropatov A, Dreyfus T. Constructing the accumulation function concept. In: Tso TY, editor. Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education Vol. 3; Taipei: PME; 2012. p. 11–19.
  • Hershkowitz R, Schwarz B, Dreyfus T. Abstraction in context: epistemic actions. J Res Math Educ. 2001;32:195–222.
  • Schwarz B, Dreyfus T, Hershkowitz R. In: Schwarz B, Dreyfus T, Hershkowitz R, editors. The nested epistemic actions model for abstraction in context, in Transformation of knowledge through classroom interaction. London (UK): Routledge; 2009. p. 11–41.
  • Tabach M, Hershkowitz R. Construction of knowledge and its consolidation. In: Cockburn AD, Nardi E, editors. Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4; Norwich (UK): PME; 2002. p. 256–272.
  • Williams G. Abstracting in the context of spontaneous learning. Math Educ Res J. 2007;19:69–88.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.