APOS Theory pp 175-187 | Cite as

Frequently Asked Questions

  • Ilana Arnon
  • Jim Cottrill
  • Ed Dubinsky
  • Asuman Oktaç
  • Solange Roa Fuentes
  • María Trigueros
  • Kirk Weller


This chapter consists of answers to questions about APOS Theory that either have appeared in print or have arisen in personal communications with the authors. The format for this chapter is similar to that of an interview: there is a question or statement followed by a response from the authors. Where appropriate, the response will include a reference to one or more of the chapters in this book.


Mental Object Binary Operation Mathematical Concept Cooperative Learning Student Thinking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Beth, E. W., & Piaget, J. (1974). Mathematical epistemology and psychology (W. Mays, Trans.). Dordrecht, The Netherlands: D. Reidel. (Original work published 1966).Google Scholar
  2. Brown, A., McDonald, M., & Weller, K. (2010). Step by step: Infinite iterative processes and actual infinity. In Research in Collegiate Mathematics Education VII. CBMS Issues in Mathematics Education (Vol. 16, pp. 115–141). Providence, RI: American Mathematical Society.Google Scholar
  3. Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95–123). Dordrecht, The Netherlands: Kluwer.Google Scholar
  4. Dubinsky, E., Weller, K., McDonald, M. A., & Brown, A. (2005b). Some historical issues and paradoxes regarding the concept of infinity: An APOS analysis: Part 2. Educational Studies in Mathematics, 60, 253–266.CrossRefGoogle Scholar
  5. Dubinsky, E., & Wilson, R. (2013). High school students’ understanding of the function concept. The Journal of Mathematical Behavior, 32, 83–101.CrossRefGoogle Scholar
  6. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, The Netherlands: D. Reidel.Google Scholar
  7. Herman, J., Ilucova, L., Kremsova, V., Pribyl, J., Ruppeldtova, J., Simpson, A., et al. (2004). Images of fractions as processes and images of fractions in processes. In M. Hoines & A. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 249–256). Bergen, Norway.Google Scholar
  8. Radu, I., & Weber, K. (2011). Refinements in mathematics undergraduate students’ reasoning on completed infinite iterative processes. Education Studies in Mathematics, 78, 165–180.CrossRefGoogle Scholar
  9. Tirosh, D., & Tsamir, P. (1996). The role of representations in students’ intuitive thinking about infinity. Educational Studies in Mathematics, 27, 33–40.Google Scholar
  10. Weller, K., Clark, J. M., Dubinsky, E., Loch, S., McDonald, M. A., & Merkovsky, R. (2003). Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle. In Research in Collegiate Mathematics Education V. CBMS Issues in Mathematics Education (Vol. 12, pp. 97–131). Providence, RI: American Mathematical Society.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Ilana Arnon
    • 1
  • Jim Cottrill
    • 2
  • Ed Dubinsky
    • 3
  • Asuman Oktaç
    • 4
  • Solange Roa Fuentes
    • 5
  • María Trigueros
    • 6
  • Kirk Weller
    • 7
  1. 1.College of EducationGivat Washington AcademicTel AvivIsrael
  2. 2.Department of MathematicsOhio Dominican UniversityColumbusUSA
  3. 3.School of EducationUniversity of MiamiMiamiUSA
  4. 4.Departamento de Matemática EducativaCinvestav-IPNMexico CityMexico
  5. 5.Escuela de MatemáticasUniversidad Industrial de SantanderBucaramangaColombia
  6. 6.Departamento de MatemáticasInstituto Tecnológico Autónomo de MéxicoSan AngelMexico
  7. 7.Department of MathematicsFerris State UniversityBig RapidsUSA

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