DOI：http://dx.doi.org/10.26855/er.2023.02.002

Date: February 22,2023 Hits: 366

In the present work, it is argued how the transition from the procedural activity to the formation of the concept is developed, it is explained how students should work with pre-concepts of limit so that they can arrive at the mathematical definition of functional limit and appropriate the concept and its essential characteristics, which is analyzed from the results that arise in the specialized literature on the transition from the process to the object; also taking into account the function as a fundamental element of mathematical language and the need to use different semiotic representations of the object being studied. It arrives at a didactic proposal for the aforementioned transition from the process to the concept, with the objective of sensitizing teachers to the need for students to appropriate the concept. Several examples are included to guide teachers in the application of the proposal.

Amaya, T., Pino-Fan, L., and Medina, A. (2016). Evaluation of the knowledge of future mathematics teachers about the transformations of the representations of a function. Mathematics Education, vol. 28, no. 3, pp. 111-144.

Baez, N. & Blanco, R. (2020). The epistemology of mathematics in its didactics. Mikarimin. Multidisciplinary Scientific Journal ISSN 2528-7842. pg. 105-115.

Baez, N. (2018). Didactic strategy for the formation of concepts in the teaching-learning process of the Differential Calculus of a real variable in engineering careers. Doctoral Thesis. Center for the Study of Educational Sciences. University of Camaguey, Cuba.

Baker, W., Dias, O. & Czarnocha, B. (2016). Creating action schema based on conceptual knowledge. DIDACTICA MATHEMATICAE, Vol. 38, pp. 5-31.

De Olivera, L. & Cheng, D. (2011). Language and the Multisemiotic Nature of Mathematics. The Reading Matrix, Vol. 11, No. 3. pp. 255-268.

Domingos, A. (2010). Learning advanced mathematical concepts: the concept of limit. Proceedings of CERME 6, Lyon France. <www.inrp.fr/editions/cerme6>.

Dubinsky, E. & M. McDonald. (2001). “APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research”, en D. Holton (ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study, Kluwer Academic Publishers, pp. 273-280.

Duval, R. (1999). Representation, vision and visualization: cognitive function in mathematical thinking. In proceedings of the annual meeting of North American chapter of the International Group for the Psychology of Mathematics Education. ED 466 379 SE. 066 315 pp. 3-25.

Hernández, C., Prada, R., & Ramírez, P. (2017). Epistemological obstacles on the concepts of limit and continuity. Perspectives, Volume 2 (2), pp. 73-83. dx.doi.org/10.22463/25909215.1316.

Hughes, E. & Fries, K. (2015). The languages of Mathematics: The importance of teaching and learning Mathematical vocabulary. Research Gate, pp. 231-252. Doi: 10.1080/1053569.2015.1030995.

Kidron, I. (2015). The epistemological dimension revisited. CERME 9 -Ninth Congress of the European Society for Research in Mathematics Education, Prague, Czech Republic. Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. pp. 2662-2667, <hal-01289449>.

Sjögren, J. (2011). Concept Formation in Mathematics. Acta universitatis gothoburgensis. ISBN 978-91-7346-705-6.

Tall, D. & Vinner, S. (1981). Concept image and concept definition in mathematics with special reference to limits and continuity. Educational Studies in Mathematics, 12, 151-69.

Tall, D. (1988). Concept Image and Concept Definition Rev: Senior Secondary Mathematics Education, (ed. Jan de Lange, Michiel Doorman), OW&OC Utrecht, 37-41.

**From Process to Concept, Exemplified in the Functional Limit**

**How to cite this paper:** Báez Ureña Neel, Lalondriz Rincón Michelle Elizabeth, Blanco Sánchez Ramón. (2023). From Process to Concept, Exemplified in the Functional Limit. *The Educational Review, USA*, **7**(**2**), 121-130.

**DOI: http://dx.doi.org/10.26855/er.2023.02.002**

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