Volume 16 · Number 3 · Pages 289–294
Authors’ Response: Fathoming the Enactive Metaphorizing Elephant in the Dark…

Daniela Díaz-Rojas, Jorge Soto-Andrade & Ronnie Videla-Reyes

Log in download the full text in PDF

> Citation > Similar > References > Add Comment


Abstract: We offer a response to three themes arising from the commentators’ inquiries and critiques: (a) The epistemological compatibility of enactivism and conceptual metaphor theory; (b) the way enactive metaphorization works in the teaching and learning of mathematics, particularly in problem-posing and problem-solving activities; and (c) the nature of mathematical abstraction and its relation with enactive metaphorizing.


Díaz-Rojas D., Soto-Andrade J. & Videla-Reyes R. (2021) Authors’ response: Fathoming the enactive metaphorizing elephant in the dark…. Constructivist Foundations 16(3): 289–294. https://constructivist.info/16/3/289

Export article citation data: Plain Text · BibTex · EndNote · Reference Manager (RIS)


Abrahamson D. & Sánchez-García R. (2016) Learning is moving in new ways: The ecological dynamics of mathematics education. Journal of the Learning Sciences 25(2): 203–239. ▸︎ Google︎ Scholar
Brousseau G. & Warfield V. (2014) Didactic situations in mathematics education. In: Lerman S. (ed.) Encyclopedia of mathematics education. Springer, Berlin: 163–170. ▸︎ Google︎ Scholar
Díaz-Rojas D. & Soto-Andrade J. (2017) Enactive metaphors in mathematical problem solving. In: Doole T. & Gueudet G. (eds.) Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10), 1–5 February 2017. DCU Institute of Education and ERME, Dublin, Ireland: 3904–3911. https://cepa.info/6173
Dickson L. (1910) Hensel’s theory of algebraic numbers. Bulletin of the American Mathematical Society 17(1): 23–36. ▸︎ Google︎ Scholar
Gibbs R. W. (2011) Evaluating conceptual metaphor theory. Discourse Processes 48(8): 529–562. ▸︎ Google︎ Scholar
Knops A., Thirion B., Hubbard E., Michel V. & Dehaene S. (2009) Recruitment of an area involved in eye movements during mental arithmetic. Science 324(5934): 1583–1585. ▸︎ Google︎ Scholar
Maturana H. R. & Varela F. J. (1980) Autopoiesis and cognition: The realization of the living. Reidel, Dordrecht. ▸︎ Google︎ Scholar
Petitmengin C. (2006) Describing one’s subjective experience in the second person: An interview method for the science of consciousness. Phenomenology and the Cognitive Sciences 5: 229–269. https://cepa.info/2376
Ricoeur P. (1975) La métaphore vive. Éditions du Seuil, Paris. English translation: Ricoeur P. (1977) The rule of metaphor: Multi-disciplinary studies of the creation of meaning in language. Translated by Robert Czerny, Kathleen McLaughlin and John Costello. University of Toronto Press, Toronto. ▸︎ Google︎ Scholar
Ryan J. A. (1996) Leibniz’ Binary System and Shao Yong’s “Yijing”. Philosophy East and West 46(1): 59–90. ▸︎ Google︎ Scholar
Sáenz-Ludlow A. (2004) Metaphors and numerical diagrams in the arithmetical activity of a fourth-grade class. Journal for Research in Mathematics Education 1(35): 34–56. ▸︎ Google︎ Scholar
Sfard A. (1997) Commentary: On metaphorical roots of conceptual growth. In: English L. D. (ed.) Mathematical reasoning: Analogies, metaphors, and images. Lawrence Erlbaum Associates, Mahwah NJ: 339–371. ▸︎ Google︎ Scholar
Soto-Andrade J. & Varela F. J. (1984) Self-reference and fixed points. Acta Applicandae Mathematicae 2(1): 1–19. ▸︎ Google︎ Scholar
Soto-Andrade J. (2018) Enactive metaphorising in the learning of mathematics. In: Kaiser G., Forgasz H., Graven M., Kuzniak A., Simm E. & Xu B. (eds.) Invited lectures from the 13th International Congress on Mathematical Education. Springer, Cham: 619–638. https://cepa.info/6219
Soto-Andrade J., Jaramillo S., Gutiérrez C. & Letelier J. C. (2011) Ouroboros avatars: A mathematical exploration of self-reference and metabolic closure. In: Lenaerts T., Giacobini M., Bersini H., Bourgine P., Dorigo M. & Doursat R. (eds.) Advances in artificial life: Proceedings of the Eleventh European Conference on the Synthesis and Simulation of Living Systems (ECAL 2011) MIT Press, Cambridge MA: 763–770. ▸︎ Google︎ Scholar
Varela F. J. (1996) Neurophenomenology: A methodological remedy to the hard problem. Journal of Consciousness Studies 3(4): 330–349. https://cepa.info/1893

Comments: 0

To stay informed about comments to this publication and post comments yourself, please log in first.