Abstract
Chapter 12 contains an extensive annotated bibliography of publications related to APOS Theory. The list of all the references cited in the text has been placed in “References.”
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Notes
- 1.
For BMI, see: Lakoff, G., & Nunez, R. (2000). Where mathematics comes from. New York: Basic Books.
References
Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. In Research in Collegiate Mathematics Education II. CBMS Issues in Mathematics Education (Vol. 6, pp. 1–32). Providence, RI: American Mathematical Society.
Baker, B., Cooley, L., & Trigueros, M. (2000). A calculus graphing schema. Journal for Research in Mathematics Education, 31, 557–578.
Beth, E. W., & Piaget, J. (1974). Mathematical epistemology and psychology (W. Mays, Trans.). Dordrecht, The Netherlands: D. Reidel. (Original work published 1966).
Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of functions. Educational Studies in Mathematics, 23, 247–285.
Clark, J. M., Cordero, F., Cottrill, J., Czarnocha, B., DeVries, D. J., St. John, D., et al. (1997). Constructing a schema: The case of the chain rule. The Journal of Mathematical Behavior, 16, 345–364.
Cooley, L., Trigueros, M., & Baker, B. (2007). Schema thematization: A theoretical framework and an example. Journal for Research in Mathematics Education, 38, 370–392.
Dubinsky, E. (1986a). On teaching mathematical induction, I. The Journal of Mathematical Behavior, 5, 305–317.
Dubinsky, E. (1986b). Reflective abstraction and computer experiences: A new approach to teaching theoretical mathematics. In G. Lappan & R. Even (Eds.), Proceedings of the 8th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. East Lansing, MI.
Dubinsky, E., Dautermann, J., Leron, U., & Zazkis, R. (1994). On learning fundamental concepts of group theory. Educational Studies in Mathematics, 27, 267–305.
Dubinsky, E., Elterman, F., & Gong, C. (1988). The student’s construction of quantification. For the Learning of Mathematics—An International Journal of Mathematics Education, 8, 44–51.
Dubinsky, E., & Leron, U. (1994). Learning abstract algebra with ISETL. New York: Springer.
Dubinsky, E., & Lewin, P. (1986). Reflective abstraction and mathematics education: The genetic decomposition of induction and compactness. The Journal of Mathematical Behavior, 5, 55–92.
Dubinsky, E., & McDonald, M. (2001). APOS: A constructivist theory of learning in undergrad mathematics education. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 273–280). Dordrecht, The Netherlands: Kluwer.
Hazzan, O. (1999). Reducing abstraction level when learning abstract algebra concepts. Educational Studies in Mathematics, 40, 71–90.
Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
Piaget, J. (1976). The grasp of consciousness (S. Wedgwood, Trans.). Cambridge, MA: Harvard University Press. (Original work published 1974).
Piaget, J., & García, R. (1989). Psychogenesis and the history of science (H. Feider, Trans.). New York: Columbia University Press. (Original work published 1983).
Roa-Fuentes, S., & Oktaç, A. (2010). Construcción de una descomposición genética: Análisis teórico del concepto transformación lineal. Revista Latinoamericana de Investigación en Matemática Educativa, 13(1), 89–112.
Trigueros, M., & Martínez-Planell, R. (2010). Geometrical representations in the learning of two-variable functions. Educational Studies in Mathematics, 73, 3–19.
Weller, K., Arnon, I., & Dubinsky, E. (2009). Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion. Canadian Journal of Science, Mathematics, and Technology Education, 9, 5–28.
Weller, K., Arnon, I., & Dubinsky, E. (2011). Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion: Strength and stability of belief. Canadian Journal of Science, Mathematics, and Technology Education, 11, 129–159.
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Arnon, I. et al. (2014). Annotated Bibliography. In: APOS Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7966-6_12
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