Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories

Extended theory of mathematical connections (ETC) and theory of mathematical argumentation (TMA) based on Toulmin’s (1984) model were articulated for the study of mathematical connections activated in the argumentation process. For this purpose, a “networking of theories” was made to obtain the comp...

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Autores:
Rodríguez-Nieto, Camilo Andrés
Cervantes-Barraza, JONATHAN
Font, Vicenç
Tipo de recurso:
Article of investigation
Fecha de publicación:
2023
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/10514
Acceso en línea:
https://hdl.handle.net/11323/10514
https://repositorio.cuc.edu.co/
Palabra clave:
Networking of theories
Extended theory of connections
Theory of mathematical argumentation
Proof
Derivative
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openAccess
License
Atribución 4.0 Internacional (CC BY 4.0)
id RCUC2_a381f3d2c5e6d982802292b76af433a1
oai_identifier_str oai:repositorio.cuc.edu.co:11323/10514
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.eng.fl_str_mv Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories
title Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories
spellingShingle Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories
Networking of theories
Extended theory of connections
Theory of mathematical argumentation
Proof
Derivative
title_short Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories
title_full Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories
title_fullStr Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories
title_full_unstemmed Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories
title_sort Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theories
dc.creator.fl_str_mv Rodríguez-Nieto, Camilo Andrés
Cervantes-Barraza, JONATHAN
Font, Vicenç
dc.contributor.author.none.fl_str_mv Rodríguez-Nieto, Camilo Andrés
Cervantes-Barraza, JONATHAN
Font, Vicenç
dc.subject.proposal.eng.fl_str_mv Networking of theories
Extended theory of connections
Theory of mathematical argumentation
Proof
Derivative
topic Networking of theories
Extended theory of connections
Theory of mathematical argumentation
Proof
Derivative
description Extended theory of mathematical connections (ETC) and theory of mathematical argumentation (TMA) based on Toulmin’s (1984) model were articulated for the study of mathematical connections activated in the argumentation process. For this purpose, a “networking of theories” was made to obtain the complementarities between both theories. Then, a class episode was selected that dealt with the demonstration of the continuity theorem of functions of real variable “if a function is derivable at a point then it is continuous at that point”, made by an in-service mathematics teacher of differential calculus, who participated in a non-participant observation, where his classes were videotaped. The arguments of this episode were analyzed through with Toulmin’s (1984) model, after with thematic analysis method to identify mathematical connections, and, finally, the connections in the proof and mathematical argumentation were analyzed. The main result of the research reveals that the mathematical connections play a fundamental role in the argumentation process of the episode, given that, connection is important for the establishment and identification the argument and the warrant that supports it. In addition, complementarities were found between both theories, which makes this networking a useful tool for a better analysis of mathematical argumentation processes.
publishDate 2023
dc.date.accessioned.none.fl_str_mv 2023-09-26T20:24:12Z
dc.date.available.none.fl_str_mv 2023-09-26T20:24:12Z
dc.date.issued.none.fl_str_mv 2023-04-03
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/ART
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.citation.spa.fl_str_mv Rodríguez-Nieto, C. A., Cervantes-Barraza, J. A., & Font Moll, V. (2023). Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2264. https://doi.org/10.29333/ejmste/13157
dc.identifier.issn.spa.fl_str_mv 1305-8223
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/11323/10514
dc.identifier.doi.none.fl_str_mv 10.29333/ejmste/13157
dc.identifier.eissn.spa.fl_str_mv 1305-8215
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
identifier_str_mv Rodríguez-Nieto, C. A., Cervantes-Barraza, J. A., & Font Moll, V. (2023). Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2264. https://doi.org/10.29333/ejmste/13157
1305-8223
10.29333/ejmste/13157
1305-8215
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/10514
https://repositorio.cuc.edu.co/
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.ispartofjournal.spa.fl_str_mv Eurasia Journal of Mathematics, Science and Technology Education
dc.relation.references.spa.fl_str_mv 1. AMTE. (2017). Standards for preparing teachers of mathematics. Association of Mathematics Teacher Educators. https://amte.net/standards
2. Artigue, M., & Mariotti, M. A. (2014). Networking theoretical frames: The ReMath enterprise. Educational Studies in Mathematics, 85, 329-355. https://doi.org/10.1007/s10649-013-9522-2
3. Arzarello, F., & Olivero, F. (2006). Theories and empirical research: Towards a common framework. In Proceedings of the 4th Conference of the European Society for Research in Mathematics Education (pp. 1305-1315).
4. Bikner-Ahsbahs, A. (2016). Networking of theories in the tradition of TME. In Theories in and of mathematics education. ICME-13 topical surveys (pp. 33-42). https://doi.org/10.1007/978-3-319-42589-4_5
5. Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking theories–an approach for exploiting the diversity of theoretical approaches. In B. Sriraman, & L. English (Eds.), Theories of mathematics education (pp. 589-592). Springer. https://doi.org/10.1007/978-3-642-00742-2_46
6. Bikner-Ahsbahs, A., & Prediger, S. (Eds.). (2014). Networking of theories as a research practice in mathematics education. Springer. https://doi.org/10.1007/978-3-319-05389-9
7. Boero, P., N., Douek, F., Morselli, F., & Pedemonte, B. (2010). Argumentation and proof: a contribution to theoretical perspectives and their classroom implementation. In M. F. F. Pinto, & T. F. Kawasaki (Eds.), Proceedings of the 34th Conference of the International Group for the Psychology.
8. Borji, V., Font, V., Alamolhodaei, H., & Sánchez, A. (2018). Application of the complementarities of two theories, APOS and OSA, for the analysis of the university students’ understanding on the graph of the function and its derivative. EURASIA Journal of Mathematics, Science and Technology Education, 14(6), 2301-2315.https://doi.org/10.29333/ejmste/89514
9. Borromeo, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer. https://doi.org/10.1007/978-3- 319-68072-9
10. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/1478088706qp063oa
11. Brousseau, G. (2002). Theory of didactical situations in mathematics: Didactique des mathématiques [Mathematics didactics], 1970-1990 (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Trans.). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2
12. Brown, L. (Ed.). (1993). The new shorter Oxford English dictionary on historical principles. Clarendon Press.
13. Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections [Unpublished PhD thesis]. Simon Fraser University.
14. CCSSI. (2018). Common core state standards for mathe¬matics. National Governors Association Center for Best Practices and the Council of Chief State School Officers.
15. Cervantes-Barraza, J. A. & Cabañas-Sánchez, G. (2020). Teacher promoting student mathematical arguments through questions. In M. Inprasitha, N. Changsri, & N. Boonsena (Eds), Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education, Interim Vol, (pp. 81-89). PME.
16. Cervantes-Barraza, J. A. (2020). Argumentos que construyen estudiantes de quinto grado de primaria [Arguments constructed by fifth grade students] [Unpublished doctoral dissertation] Universidad Autónoma de Guerrero.
17. Cervantes-Barraza, J. A., & Cabañas-Sánchez, M. G. (2022). Argumentación matemática basada en refutaciones [Mathematical argumentation based on refutations]. REDIMAT –Journal of Research in Mathematics Education, 11(2), 159-179. https://doi.org/10.17583/redimat.4015
18. Cervantes-Barraza, J. A., Cabañas-Sánchez, G. & Mercado-Porras, K. (2020). El rol del profesor en la construcción de conocimiento matemático a través de la argumentación colectiva [The role of the teacher in the construction of mathematical knowledge through collective argumentation]. En H. Hernández, J. Juárez, & J. Slisko (Eds.), Tendencias en la educación matemática basada en la investigación (vol. 4). El errante Editor.
19. Cervantes-Barraza, J. A., Cabañas-Sánchez, G. & Reid, D. (2019). Complex argumentation in elementary school. PNA, 13(4), 221-246. https://doi.org/10.30827/pna.v13i4.8279
20. Chevallard, Y. (1992). Concepts fondamentaux de la didactique: Perspectives apportées par une aproche anthropologique [Fundamental concepts of didactics: perspectives brought by an anthropological approach]. Recherches en Didactique des Mathématiques [Research in Didactics of Mathematics], 12(1), 73-112.
21. Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education. Routledge. https://doi.org/10.4324/9781315456539
22. Conner, A., Singletary. L., Smith. R., Wagner. P., & Francisco, R. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies Mathematics, 86(2), 401-429. https://doi.org/10.1007/s10649-014-9532-8
23. De la Fuente, A., & Deulofeu, J. D. (2022). Uso de las conexiones entre representaciones por parte del profesor en la construcción del lenguaje algebraico [Use of connections between representations by the teacher in the construction of algebraic language]. Bolema: Mathematics Education Bulletin, 36, 389-410. https://doi.org/10.1590/1980-4415v36n72a17
24. DE. (2017). Competències bàsiques de l’àmbit matemàtic [Basic skills in the mathematical field]. Departament d’Ensenyament [Education Department]. http://ensenyament.gencat.cat/web/.content/home/departament/publicacions/colleccions/competenc ies-basiques/eso/eso-matematic.pdf
25. Dolores-Flores, C., & García-García, J. (2017). Conexiones intramatemáticas y extramatemáticas que se producen al resolver problemas de cálculo en contexto: Un estudio de casos en el nivel superior [Intra-mathematical and extra-mathematical connections that occur when solving calculus problems in context: A case study at the higher level]. Bolema: Mathematics Education Bulletin, 31(57), 158-180. https://doi.org/10.1590/1980-4415v31n57a08
26. Dolores-Flores, C., Rivera-López, M. I., & García-García, J. (2019). Exploring mathematical connections of pre-university students through tasks involving rates of change. International Journal of Mathematics Education in Science and Technology, 50(3), 369-389. https://doi.org/10.1080/0020739X.2018.1507050
27. Duval, R. (2000). Ecriture, raisonnement et découverte de la démonstration en mathématiques [Writing, reasoning and discovering the proof in mathematics]. Recherche en Didactique des Mathématiques [Research in Didactics of Mathematics], 20(2), 135-170.
28. Duval, R. (2017). Understanding the mathematical way of thinking–The registers of semiotic representations. Springer. https://doi.org/10.1007/978-3-319-56910-9
29. Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-0
30. Erkek, O., & Isiksal-Bostan, M. I. (2019). Prospective middle school mathematics teachers’ global argumentation structures. International Journal of Science and Mathematics Education, 17(3), 613-633. https://doi.org/10.1007/s10763-018-9884-0
31. Font, V., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, 91(1), 107-122. https://doi.org/10.1007/s10649-015-9639-6
32. Galindo-Illanes, M. K., Breda, A., Chamorro-Manríquez, D. D., & Alvarado-Martínez, H. A. (2022). Analysis of a teaching learning process of the derivative with the use of ICT oriented to engineering students in Chile. EURASIA Journal of Mathematics, Science and Technology Education, 18(7), em2130. https://doi.org/10.29333/ejmste/12162
33. García-García, J. G. (2019). Escenarios de exploración de conexiones matemáticas [Math connections exploration scenarios]. Números: Revista de Didáctica de las Matemáticas [Numbers: Mathematics Didactics Magazine], 100, 129-133. https://hdl.handle.net/11162/224840
34. García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994
35. García-García, J., & Dolores-Flores, C. (2019). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33, 1-22. https://doi.org/10.1007/s13394-019-00286-x
36. García-García, J., & Dolores-Flores, C. (2020). Exploring pre-university students’ mathematical connections when solving calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936. https://doi.org/10.1080/0020739X.2020.1729429
37. Giannakoulias, E., Mastorides, E., Potari, D., & Zachariades, T. (2010). Studying teachers’ mathematical argumentation in the context of refuting students’ invalid claims. The Journal of Mathematical Behavior, 29(3), 160-168. https://doi.org/10.1016/j.jmathb.2010.07.001
38. Godden, D., & Walton, G. (2007). A Theory of presumption for everyday argumentation. Pragmatics & Cognition, 15(2), 313-346. https://doi.org/10.1075/pc.15.2.06god
39. Godino, J., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM – Mathematics Education, 39(1), 127–135. https://doi.org/10.1007/s11858-006- 0004-1
40. Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517-545). Lawrence Erlbaum Associates.
41. Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research of mathematics teaching and learning (pp. 65-79). Macmillan.
42. Kidron, I., & Bikner-Ahsbahs, A. (2015). Advancing research by means of the networking of theories. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative methods in mathematics education–Examples of methodology and methods (pp. 221-232). Springer. https://doi.org/10.1007/978-94-017-9181-6_9
43. Knipping, C., & Reid, D. (2015). Reconstructing argumentation structures: A Perspective on proving processes in secondary mathematics classroom interactions. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 75-101). Springer. https://doi.org/10. 1007/978-94-017-9181-6_4
44. Knipping, C., & Reid, D. A. (2019). Argumentation analysis for early career researchers. In G. Kaiser, & N. Presmeg (Eds.) Compendium for early career researchers in mathematics education. (pp. 3-31). Springer. https://doi.org/10.1007/978-3-030-15636-7_1
45. Krummheuer, G. (1995). The ethnology of argumentation. In P. Cobb, & H. Bauersfeld (Eds.). The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229-269). Erlbaum.
46. Krummheuer, G. (2015). Methods for reconstructing processes of argumentation and participation in primary mathematics classroom interaction. In A. Bikner-Ahsbahs, C. Knipping., & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 75-101). Springer. https://doi.org/10.1007/978-94-017-9181-6_4
47. Kuzniak, A. (2011). L’Espace de travail mathématique et ses génèses [The mathematical working spaces and its geneses]. Annales de Didactique et de Sciences Cognitives [Annals of Didactics and Cognitive Sciences], 16, 9–24.
48. Ledezma, C., Font, V., & Sala, G. (2022). Analyzing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-022-00411-3
49. Liljedahl, P., & Santos-Trigo, M. (Eds.). (2019). Mathematical problem solving: Current themes, trends, and research. Springer. https://doi.org/10.1007/978-3-030-10472-6
50. Lin, P. J. (2018). The development of students mathematical argumentation in a primary classroom. Educação y Realidade, Porto Alegre [Education and Reality, Porto Alegre], 43(3), 1171-1192. https://doi.org/10.1590/2175-623676887
51. MEN. (2006). Estándares básicos de competencias en lenguaje, matemáticas, ciencia y ciudadanas [Basic standards of competences in language, mathematics, science and citizenship]. Ministerio de Educación Nacional [Ministry of National Education].
52. Metaxas, N. (2015). Mathematical argumentation of students participating in a mathematics–information technology project. International Research in Education, 3(1), 82-92. https://doi.org/10.5296/ire.v3i1.6767
53. Mhlolo, M. K. (2012). Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice. African Journal of Research in Mathematics, Science and Technology Education, 16(2), 176-191. https://doi.org/10.1080/10288457.2012.10740738
54. Mhlolo, M. K., Venkat, H., & Schäfer, M. (2012). The nature and quality of the mathematical connections teachers make. Pythagoras, 33(1), 1-9. https://doi.org/10.4102/pythagoras.v33i1.22
55. Molina, O., Font, V., & Pino-Fan, L. (2019). Estructura y dinámica de argumentos analógicos, abductivos y deductivos: Un curso de geometría del espacio como contexto de reflexión [Structure and dynamics of analogical, abductive and deductive arguments: A course on the geometry of space as a context for reflection]. Enseñanza de las Ciencias [Science Education], 37(1), 93-116. https://doi.org/10.5565/rev/ensciencias.2484
56. Moon, K., Brenner, M., Jacob, B., & Okamoto, Y. (2013). Prospective secondary mathematics teachers’ understanding and cognitive difficulties in making connections among representations. Mathematical Thinking and Learning, 15(3), 201-227. https://doi.org/10.1080/10986065.2013.794322
57. Mumcu, H. Y. (2018). Matematiksel ilişkilendirme becerisinin kuramsal boyutta incelenmesi: Türev kavramı örneği [Examining the mathematical association skill in the theoretical dimension: An example of the concept of derivative]. Turkish Journal of Computer and Mathematics Education, 9(2), 211-248. https://doi.org/10.16949/turkbilmat.379891
58. Mwakapenda, W. (2008). Understanding connections in the school mathematics curriculum. South African Journal of Education, 28(2), 189-202. ttps://doi.org/10.15700/saje.v28n2a170
59. Nardi, E., Biza, I., & Zachariades, T. (2012). ‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79, 157-173. https://doi.org/10.1007/s10649-011-9345-y
60. NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
61. Pedemonte, B. & Balacheff, N. (2016). Establishing links between conceptions, argumentation and proof through the ck¢-enriched Toulmin model. Journal of Mathematical Behavior, 41, 104-122. https://doi.org/10.1016/j.jmathb.2015.10.008
62. Pino-Fan, L., Godino, J, D., & Font, V. (2018). Assessing key epistemic features of didactic mathematical knowledge of prospective teachers: The case of the derivative. Journal of Mathematics Teacher Education, 21, 63-94. https://doi.org/10.1007/s10857-016-9349-8
63. Pino-Fan, L., Guzmán, I., Font, V., & Duval, R. (2017). Analysis of the underlying cognitive activity in the resolution of a task on derivability of the absolute-value functions: Two theoretical perspectives. PNA: Revista de Investigación en Didáctica de la Matemática [PNA: Research Journal on Mathematics Didactics], 11(2), 97-124. https://doi.org/10.30827/pna.v11i2.6076
64. Pólya, G. (1989). Cómo plantear y resolver problemas [How to suggest and solve problems]. Editorial Trillas.
65. Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connection theoretical approaches: First steps towards a conceptual framework. ZDM-The International Journal on Mathematics Education, 40(2), 165-178. https://doi.org/10.1007/s11858-008-0086-z
66. Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In Á. Gutiérrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205-235). Sense Publishers. https://doi.org/10.1163/9789087901127_009
67. Radford, L. (2008). Connecting theories in mathematics education: challenges and possibilities. ZDM –Mathematics Education, 40(2), 317-327. https://doi.org/10.1007/s11858-008-0090-3
68. Radford, L. (2013). Three key concepts of the theory of objectification: Knowledge, knowing, and learning. Journal of Research in Mathematics Education, 2(1), 7-44. https://doi.org/10.4471/redimat.2013.19
69. Rigotti, E. & Greco, S. (2009). Argumentation as an object of interest and as a social and cultural resource. In N. Muller, & A. Perret-Clermont (Eds.), Argumentation and education. Springer. https://doi.org/10.1007/978-0-387-98125-3_2
70. Rodríguez-Nieto, C. A. (2021). Conexiones etnomatemáticas entre conceptos geométricos en la elaboración de las tortillas de Chilpancingo, México [Ethnomatematical connections between geometric concepts in the making of tortillas from Chilpancingo, Mexico]. Revista de Investigación Desarrollo e Innovación [Journal of Research, Development and Innovation], 11(2), 273-296. https://doi.org/10.19053/20278306.v11.n2.2021.12756
71. Rodríguez-Nieto, C. A., & Escobar-Ramírez, Y. C. (2022). Conexiones etnomatemáticas en la elaboración del Sancocho de Guandú y su comercialización en Sibarco, Colombia [Ethnomathematical connections in the elaboration of Sancocho de Guandú and its commercialization in Sibarco, Colombia]. Bolema: Boletim de Educação Matemática [Bulletin: Mathematics Education Bulletin], 36, 971-1002. https://doi.org/10.1590/1980-4415v36n74a02
72. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & García-García, J. (2021a). Pre-service mathematics teachers’ mathematical connections in the context of problem-solving about the derivative. Turkish Journal of Computer and Mathematics Education, 12(1), 202-220. https://doi.org/10.16949/turkbilmat.797182
73. Rodríguez-Nieto, C. A., Font, V., Borji, V., & Rodríguez-Vásquez, F. M. (2021b). Mathematical connections from a networking theory between extended theory of mathematical connections and onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 53(9), 2364-2390. https://doi.org/10.1080/0020739X.2021.1875071
74. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & García-García, J. (2021c). Exploring university Mexican students’ quality of intra-mathematical connections when solving tasks about derivative concept. EURASIA Journal of Mathematics, Science and Technology Education, 17(9), em2006. https://doi.org/10.29333/ejmste/11160
75. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., Font, V. & Morales-Carballo, A. (2021d). Una visión desde el networking TAC-EOS sobre el papel de las conexiones matemáticas en la comprensión de la derivada [A view from the TAC-EOS network on the role of mathematical connections in understanding the derivative]. Revemop, 3, e202115, 1-32. https://doi.org/10.33532/revemop. e202115
76. Rodríguez-Nieto, C. A., & Alsina, Á. (2022). Networking between ethnomathematics, STEAM education, and the globalized approach to analyze mathematical connections in daily practices. EURASIA Journal of Mathematics Science and Technology Education, 18(3), 2-22. https://doi.org/10.29333/ejmste/11710
77. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & Font, V. (2022a). A new view about connections: the mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology, 53(6), 1231-1256. https://doi.org/10.1080/0020739 X.2020.1799254
78. Rodríguez-Nieto, C. A., Font, V., & Rodríguez-Vásquez, F. M. (2022b). Literature review on networking of theories developed in mathematics education context. EURASIA Journal of Mathematics, Science and Technology Education, 18(11), em2179. https://doi.org/10.29333/ejmste/12513
79. Rumsey, C., Guarino, J., Gildea, R., Cho, C. Y., & Lockhart, B. (2019). Tools to support K–2 students in mathematical argumentation. Teaching Children Mathematics, 25(4), 208-217. https://doi.org/10.5951/teacchilmath.25.4.0208
80. Solar, H. (2018). Implicaciones de la argumentación en el aula de matemáticas [Implications of argumentation in the mathematics classroom]. Revista Colombiana de Educación [Colombian Magazine of Education], 1(74), 155-176. https://doi.org/10.17227/rce.num74-6902
81. SPE. (2011). Plan de estudios 2011. Educación básica [2011 study plan. Basic education]. Secretaría de Educación Pública [Secretary of Public Education]. http://issuu.com/dgeb/docs/planedu2011?e=3503076/2622744
82. Stewart, J. (1999). Cálculo. Conceptos y contextos [Calculation. Concepts and contexts]. International Thomson Editores.
83. Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289-321. https://doi.org/10.2307/30034869
84. Tabach, M., Rasmussen, C., Dreyfus, T., & Apkarian, N. (2020). Towards an argumentative grammar for networking: A case of coordinating two approaches. Educational Studies in Mathematics, 103, 139-155. https://doi.org/10.1007/s10649-020-09934-7
85. Toulmin, S. (1984). An introduction to reasoning. Macmillan.
86. Toulmin, S. (2003). The uses of argument. Cambridge University Press. https://doi.org/10.1017/CBO9780511840005
87. Van Eemeren, F. H., & Grootendorst, R. (2015). From analysis to presentation: A pragma-dialectical approach to writing argumentative texts. In Reasonableness and effectiveness in argumentative discourse. Argumentation Library (vol. 27). Springer, Cham. https://doi.org/10.1007/978-3-319-20955-5_38
88. Walton, D., Reed, C., & Macagno, F. (2008). Argumentation schemes. Cambridge University Press. https://doi.org/10.1017/CBO9780511802034
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spelling Atribución 4.0 Internacional (CC BY 4.0)© 2023 by the authors; licensee Modestum.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Rodríguez-Nieto, Camilo AndrésCervantes-Barraza, JONATHANFont, Vicenç2023-09-26T20:24:12Z2023-09-26T20:24:12Z2023-04-03Rodríguez-Nieto, C. A., Cervantes-Barraza, J. A., & Font Moll, V. (2023). Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2264. https://doi.org/10.29333/ejmste/131571305-8223https://hdl.handle.net/11323/1051410.29333/ejmste/131571305-8215Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Extended theory of mathematical connections (ETC) and theory of mathematical argumentation (TMA) based on Toulmin’s (1984) model were articulated for the study of mathematical connections activated in the argumentation process. For this purpose, a “networking of theories” was made to obtain the complementarities between both theories. Then, a class episode was selected that dealt with the demonstration of the continuity theorem of functions of real variable “if a function is derivable at a point then it is continuous at that point”, made by an in-service mathematics teacher of differential calculus, who participated in a non-participant observation, where his classes were videotaped. The arguments of this episode were analyzed through with Toulmin’s (1984) model, after with thematic analysis method to identify mathematical connections, and, finally, the connections in the proof and mathematical argumentation were analyzed. The main result of the research reveals that the mathematical connections play a fundamental role in the argumentation process of the episode, given that, connection is important for the establishment and identification the argument and the warrant that supports it. In addition, complementarities were found between both theories, which makes this networking a useful tool for a better analysis of mathematical argumentation processes.20 páginasapplication/pdfengModestum Ltd.Turkeyhttps://www.ejmste.com/article/exploring-mathematical-connections-in-the-context-of-proof-and-mathematical-argumentation-a-new-13157Exploring mathematical connections in the context of proof and mathematical argumentation: a new proposal of networking of theoriesArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Eurasia Journal of Mathematics, Science and Technology Education1. AMTE. (2017). Standards for preparing teachers of mathematics. Association of Mathematics Teacher Educators. https://amte.net/standards2. Artigue, M., & Mariotti, M. A. (2014). Networking theoretical frames: The ReMath enterprise. Educational Studies in Mathematics, 85, 329-355. https://doi.org/10.1007/s10649-013-9522-23. Arzarello, F., & Olivero, F. (2006). Theories and empirical research: Towards a common framework. In Proceedings of the 4th Conference of the European Society for Research in Mathematics Education (pp. 1305-1315).4. Bikner-Ahsbahs, A. (2016). Networking of theories in the tradition of TME. In Theories in and of mathematics education. ICME-13 topical surveys (pp. 33-42). https://doi.org/10.1007/978-3-319-42589-4_55. Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking theories–an approach for exploiting the diversity of theoretical approaches. In B. Sriraman, & L. English (Eds.), Theories of mathematics education (pp. 589-592). Springer. https://doi.org/10.1007/978-3-642-00742-2_466. Bikner-Ahsbahs, A., & Prediger, S. (Eds.). (2014). Networking of theories as a research practice in mathematics education. Springer. https://doi.org/10.1007/978-3-319-05389-97. Boero, P., N., Douek, F., Morselli, F., & Pedemonte, B. (2010). Argumentation and proof: a contribution to theoretical perspectives and their classroom implementation. In M. F. F. Pinto, & T. F. Kawasaki (Eds.), Proceedings of the 34th Conference of the International Group for the Psychology.8. Borji, V., Font, V., Alamolhodaei, H., & Sánchez, A. (2018). Application of the complementarities of two theories, APOS and OSA, for the analysis of the university students’ understanding on the graph of the function and its derivative. EURASIA Journal of Mathematics, Science and Technology Education, 14(6), 2301-2315.https://doi.org/10.29333/ejmste/895149. Borromeo, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer. https://doi.org/10.1007/978-3- 319-68072-910. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/1478088706qp063oa11. Brousseau, G. (2002). Theory of didactical situations in mathematics: Didactique des mathématiques [Mathematics didactics], 1970-1990 (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Trans.). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-212. Brown, L. (Ed.). (1993). The new shorter Oxford English dictionary on historical principles. Clarendon Press.13. Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections [Unpublished PhD thesis]. Simon Fraser University.14. CCSSI. (2018). Common core state standards for mathe¬matics. National Governors Association Center for Best Practices and the Council of Chief State School Officers.15. Cervantes-Barraza, J. A. & Cabañas-Sánchez, G. (2020). Teacher promoting student mathematical arguments through questions. In M. Inprasitha, N. Changsri, & N. Boonsena (Eds), Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education, Interim Vol, (pp. 81-89). PME.16. Cervantes-Barraza, J. A. (2020). Argumentos que construyen estudiantes de quinto grado de primaria [Arguments constructed by fifth grade students] [Unpublished doctoral dissertation] Universidad Autónoma de Guerrero.17. Cervantes-Barraza, J. A., & Cabañas-Sánchez, M. G. (2022). Argumentación matemática basada en refutaciones [Mathematical argumentation based on refutations]. REDIMAT –Journal of Research in Mathematics Education, 11(2), 159-179. https://doi.org/10.17583/redimat.401518. Cervantes-Barraza, J. A., Cabañas-Sánchez, G. & Mercado-Porras, K. (2020). El rol del profesor en la construcción de conocimiento matemático a través de la argumentación colectiva [The role of the teacher in the construction of mathematical knowledge through collective argumentation]. En H. Hernández, J. Juárez, & J. Slisko (Eds.), Tendencias en la educación matemática basada en la investigación (vol. 4). El errante Editor.19. Cervantes-Barraza, J. A., Cabañas-Sánchez, G. & Reid, D. (2019). Complex argumentation in elementary school. PNA, 13(4), 221-246. https://doi.org/10.30827/pna.v13i4.827920. Chevallard, Y. (1992). Concepts fondamentaux de la didactique: Perspectives apportées par une aproche anthropologique [Fundamental concepts of didactics: perspectives brought by an anthropological approach]. Recherches en Didactique des Mathématiques [Research in Didactics of Mathematics], 12(1), 73-112.21. Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education. Routledge. https://doi.org/10.4324/978131545653922. Conner, A., Singletary. L., Smith. R., Wagner. P., & Francisco, R. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies Mathematics, 86(2), 401-429. https://doi.org/10.1007/s10649-014-9532-823. De la Fuente, A., & Deulofeu, J. D. (2022). Uso de las conexiones entre representaciones por parte del profesor en la construcción del lenguaje algebraico [Use of connections between representations by the teacher in the construction of algebraic language]. Bolema: Mathematics Education Bulletin, 36, 389-410. https://doi.org/10.1590/1980-4415v36n72a1724. DE. (2017). Competències bàsiques de l’àmbit matemàtic [Basic skills in the mathematical field]. Departament d’Ensenyament [Education Department]. http://ensenyament.gencat.cat/web/.content/home/departament/publicacions/colleccions/competenc ies-basiques/eso/eso-matematic.pdf25. Dolores-Flores, C., & García-García, J. (2017). Conexiones intramatemáticas y extramatemáticas que se producen al resolver problemas de cálculo en contexto: Un estudio de casos en el nivel superior [Intra-mathematical and extra-mathematical connections that occur when solving calculus problems in context: A case study at the higher level]. Bolema: Mathematics Education Bulletin, 31(57), 158-180. https://doi.org/10.1590/1980-4415v31n57a0826. Dolores-Flores, C., Rivera-López, M. I., & García-García, J. (2019). Exploring mathematical connections of pre-university students through tasks involving rates of change. International Journal of Mathematics Education in Science and Technology, 50(3), 369-389. https://doi.org/10.1080/0020739X.2018.150705027. Duval, R. (2000). Ecriture, raisonnement et découverte de la démonstration en mathématiques [Writing, reasoning and discovering the proof in mathematics]. Recherche en Didactique des Mathématiques [Research in Didactics of Mathematics], 20(2), 135-170.28. Duval, R. (2017). Understanding the mathematical way of thinking–The registers of semiotic representations. Springer. https://doi.org/10.1007/978-3-319-56910-929. Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-030. Erkek, O., & Isiksal-Bostan, M. I. (2019). Prospective middle school mathematics teachers’ global argumentation structures. International Journal of Science and Mathematics Education, 17(3), 613-633. https://doi.org/10.1007/s10763-018-9884-031. Font, V., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, 91(1), 107-122. https://doi.org/10.1007/s10649-015-9639-632. Galindo-Illanes, M. K., Breda, A., Chamorro-Manríquez, D. D., & Alvarado-Martínez, H. A. (2022). Analysis of a teaching learning process of the derivative with the use of ICT oriented to engineering students in Chile. EURASIA Journal of Mathematics, Science and Technology Education, 18(7), em2130. https://doi.org/10.29333/ejmste/1216233. García-García, J. G. (2019). Escenarios de exploración de conexiones matemáticas [Math connections exploration scenarios]. Números: Revista de Didáctica de las Matemáticas [Numbers: Mathematics Didactics Magazine], 100, 129-133. https://hdl.handle.net/11162/22484034. García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.135599435. García-García, J., & Dolores-Flores, C. (2019). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33, 1-22. https://doi.org/10.1007/s13394-019-00286-x36. García-García, J., & Dolores-Flores, C. (2020). Exploring pre-university students’ mathematical connections when solving calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936. https://doi.org/10.1080/0020739X.2020.172942937. Giannakoulias, E., Mastorides, E., Potari, D., & Zachariades, T. (2010). Studying teachers’ mathematical argumentation in the context of refuting students’ invalid claims. The Journal of Mathematical Behavior, 29(3), 160-168. https://doi.org/10.1016/j.jmathb.2010.07.00138. Godden, D., & Walton, G. (2007). A Theory of presumption for everyday argumentation. Pragmatics & Cognition, 15(2), 313-346. https://doi.org/10.1075/pc.15.2.06god39. Godino, J., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM – Mathematics Education, 39(1), 127–135. https://doi.org/10.1007/s11858-006- 0004-140. Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517-545). Lawrence Erlbaum Associates.41. Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research of mathematics teaching and learning (pp. 65-79). Macmillan.42. Kidron, I., & Bikner-Ahsbahs, A. (2015). Advancing research by means of the networking of theories. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative methods in mathematics education–Examples of methodology and methods (pp. 221-232). Springer. https://doi.org/10.1007/978-94-017-9181-6_943. Knipping, C., & Reid, D. (2015). Reconstructing argumentation structures: A Perspective on proving processes in secondary mathematics classroom interactions. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 75-101). Springer. https://doi.org/10. 1007/978-94-017-9181-6_444. Knipping, C., & Reid, D. A. (2019). Argumentation analysis for early career researchers. In G. Kaiser, & N. Presmeg (Eds.) Compendium for early career researchers in mathematics education. (pp. 3-31). Springer. https://doi.org/10.1007/978-3-030-15636-7_145. Krummheuer, G. (1995). The ethnology of argumentation. In P. Cobb, & H. Bauersfeld (Eds.). The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229-269). Erlbaum.46. Krummheuer, G. (2015). Methods for reconstructing processes of argumentation and participation in primary mathematics classroom interaction. In A. Bikner-Ahsbahs, C. Knipping., & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 75-101). Springer. https://doi.org/10.1007/978-94-017-9181-6_447. Kuzniak, A. (2011). L’Espace de travail mathématique et ses génèses [The mathematical working spaces and its geneses]. Annales de Didactique et de Sciences Cognitives [Annals of Didactics and Cognitive Sciences], 16, 9–24.48. Ledezma, C., Font, V., & Sala, G. (2022). Analyzing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-022-00411-349. Liljedahl, P., & Santos-Trigo, M. (Eds.). (2019). Mathematical problem solving: Current themes, trends, and research. Springer. https://doi.org/10.1007/978-3-030-10472-650. Lin, P. J. (2018). The development of students mathematical argumentation in a primary classroom. Educação y Realidade, Porto Alegre [Education and Reality, Porto Alegre], 43(3), 1171-1192. https://doi.org/10.1590/2175-62367688751. MEN. (2006). Estándares básicos de competencias en lenguaje, matemáticas, ciencia y ciudadanas [Basic standards of competences in language, mathematics, science and citizenship]. Ministerio de Educación Nacional [Ministry of National Education].52. Metaxas, N. (2015). Mathematical argumentation of students participating in a mathematics–information technology project. International Research in Education, 3(1), 82-92. https://doi.org/10.5296/ire.v3i1.676753. Mhlolo, M. K. (2012). Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice. African Journal of Research in Mathematics, Science and Technology Education, 16(2), 176-191. https://doi.org/10.1080/10288457.2012.1074073854. Mhlolo, M. K., Venkat, H., & Schäfer, M. (2012). The nature and quality of the mathematical connections teachers make. Pythagoras, 33(1), 1-9. https://doi.org/10.4102/pythagoras.v33i1.2255. Molina, O., Font, V., & Pino-Fan, L. (2019). Estructura y dinámica de argumentos analógicos, abductivos y deductivos: Un curso de geometría del espacio como contexto de reflexión [Structure and dynamics of analogical, abductive and deductive arguments: A course on the geometry of space as a context for reflection]. Enseñanza de las Ciencias [Science Education], 37(1), 93-116. https://doi.org/10.5565/rev/ensciencias.248456. Moon, K., Brenner, M., Jacob, B., & Okamoto, Y. (2013). Prospective secondary mathematics teachers’ understanding and cognitive difficulties in making connections among representations. Mathematical Thinking and Learning, 15(3), 201-227. https://doi.org/10.1080/10986065.2013.79432257. Mumcu, H. Y. (2018). Matematiksel ilişkilendirme becerisinin kuramsal boyutta incelenmesi: Türev kavramı örneği [Examining the mathematical association skill in the theoretical dimension: An example of the concept of derivative]. Turkish Journal of Computer and Mathematics Education, 9(2), 211-248. https://doi.org/10.16949/turkbilmat.37989158. Mwakapenda, W. (2008). Understanding connections in the school mathematics curriculum. South African Journal of Education, 28(2), 189-202. ttps://doi.org/10.15700/saje.v28n2a17059. Nardi, E., Biza, I., & Zachariades, T. (2012). ‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79, 157-173. https://doi.org/10.1007/s10649-011-9345-y60. NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.61. Pedemonte, B. & Balacheff, N. (2016). Establishing links between conceptions, argumentation and proof through the ck¢-enriched Toulmin model. Journal of Mathematical Behavior, 41, 104-122. https://doi.org/10.1016/j.jmathb.2015.10.00862. Pino-Fan, L., Godino, J, D., & Font, V. (2018). Assessing key epistemic features of didactic mathematical knowledge of prospective teachers: The case of the derivative. Journal of Mathematics Teacher Education, 21, 63-94. https://doi.org/10.1007/s10857-016-9349-863. Pino-Fan, L., Guzmán, I., Font, V., & Duval, R. (2017). Analysis of the underlying cognitive activity in the resolution of a task on derivability of the absolute-value functions: Two theoretical perspectives. PNA: Revista de Investigación en Didáctica de la Matemática [PNA: Research Journal on Mathematics Didactics], 11(2), 97-124. https://doi.org/10.30827/pna.v11i2.607664. Pólya, G. (1989). Cómo plantear y resolver problemas [How to suggest and solve problems]. Editorial Trillas.65. Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connection theoretical approaches: First steps towards a conceptual framework. ZDM-The International Journal on Mathematics Education, 40(2), 165-178. https://doi.org/10.1007/s11858-008-0086-z66. Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In Á. Gutiérrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 205-235). Sense Publishers. https://doi.org/10.1163/9789087901127_00967. Radford, L. (2008). Connecting theories in mathematics education: challenges and possibilities. ZDM –Mathematics Education, 40(2), 317-327. https://doi.org/10.1007/s11858-008-0090-368. Radford, L. (2013). Three key concepts of the theory of objectification: Knowledge, knowing, and learning. Journal of Research in Mathematics Education, 2(1), 7-44. https://doi.org/10.4471/redimat.2013.1969. Rigotti, E. & Greco, S. (2009). Argumentation as an object of interest and as a social and cultural resource. In N. Muller, & A. Perret-Clermont (Eds.), Argumentation and education. Springer. https://doi.org/10.1007/978-0-387-98125-3_270. Rodríguez-Nieto, C. A. (2021). Conexiones etnomatemáticas entre conceptos geométricos en la elaboración de las tortillas de Chilpancingo, México [Ethnomatematical connections between geometric concepts in the making of tortillas from Chilpancingo, Mexico]. Revista de Investigación Desarrollo e Innovación [Journal of Research, Development and Innovation], 11(2), 273-296. https://doi.org/10.19053/20278306.v11.n2.2021.1275671. Rodríguez-Nieto, C. A., & Escobar-Ramírez, Y. C. (2022). Conexiones etnomatemáticas en la elaboración del Sancocho de Guandú y su comercialización en Sibarco, Colombia [Ethnomathematical connections in the elaboration of Sancocho de Guandú and its commercialization in Sibarco, Colombia]. Bolema: Boletim de Educação Matemática [Bulletin: Mathematics Education Bulletin], 36, 971-1002. https://doi.org/10.1590/1980-4415v36n74a0272. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & García-García, J. (2021a). Pre-service mathematics teachers’ mathematical connections in the context of problem-solving about the derivative. Turkish Journal of Computer and Mathematics Education, 12(1), 202-220. https://doi.org/10.16949/turkbilmat.79718273. Rodríguez-Nieto, C. A., Font, V., Borji, V., & Rodríguez-Vásquez, F. M. (2021b). Mathematical connections from a networking theory between extended theory of mathematical connections and onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 53(9), 2364-2390. https://doi.org/10.1080/0020739X.2021.187507174. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & García-García, J. (2021c). Exploring university Mexican students’ quality of intra-mathematical connections when solving tasks about derivative concept. EURASIA Journal of Mathematics, Science and Technology Education, 17(9), em2006. https://doi.org/10.29333/ejmste/1116075. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., Font, V. & Morales-Carballo, A. (2021d). Una visión desde el networking TAC-EOS sobre el papel de las conexiones matemáticas en la comprensión de la derivada [A view from the TAC-EOS network on the role of mathematical connections in understanding the derivative]. Revemop, 3, e202115, 1-32. https://doi.org/10.33532/revemop. e20211576. Rodríguez-Nieto, C. A., & Alsina, Á. (2022). Networking between ethnomathematics, STEAM education, and the globalized approach to analyze mathematical connections in daily practices. EURASIA Journal of Mathematics Science and Technology Education, 18(3), 2-22. https://doi.org/10.29333/ejmste/1171077. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & Font, V. (2022a). A new view about connections: the mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology, 53(6), 1231-1256. https://doi.org/10.1080/0020739 X.2020.179925478. Rodríguez-Nieto, C. A., Font, V., & Rodríguez-Vásquez, F. M. (2022b). Literature review on networking of theories developed in mathematics education context. EURASIA Journal of Mathematics, Science and Technology Education, 18(11), em2179. https://doi.org/10.29333/ejmste/1251379. Rumsey, C., Guarino, J., Gildea, R., Cho, C. Y., & Lockhart, B. (2019). Tools to support K–2 students in mathematical argumentation. Teaching Children Mathematics, 25(4), 208-217. https://doi.org/10.5951/teacchilmath.25.4.020880. Solar, H. (2018). Implicaciones de la argumentación en el aula de matemáticas [Implications of argumentation in the mathematics classroom]. Revista Colombiana de Educación [Colombian Magazine of Education], 1(74), 155-176. https://doi.org/10.17227/rce.num74-690281. SPE. (2011). Plan de estudios 2011. Educación básica [2011 study plan. Basic education]. Secretaría de Educación Pública [Secretary of Public Education]. http://issuu.com/dgeb/docs/planedu2011?e=3503076/262274482. Stewart, J. (1999). Cálculo. Conceptos y contextos [Calculation. Concepts and contexts]. International Thomson Editores.83. Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289-321. https://doi.org/10.2307/3003486984. Tabach, M., Rasmussen, C., Dreyfus, T., & Apkarian, N. (2020). Towards an argumentative grammar for networking: A case of coordinating two approaches. Educational Studies in Mathematics, 103, 139-155. https://doi.org/10.1007/s10649-020-09934-785. Toulmin, S. (1984). An introduction to reasoning. Macmillan.86. Toulmin, S. (2003). The uses of argument. Cambridge University Press. https://doi.org/10.1017/CBO978051184000587. Van Eemeren, F. H., & Grootendorst, R. (2015). From analysis to presentation: A pragma-dialectical approach to writing argumentative texts. In Reasonableness and effectiveness in argumentative discourse. Argumentation Library (vol. 27). Springer, Cham. https://doi.org/10.1007/978-3-319-20955-5_3888. Walton, D., Reed, C., & Macagno, F. (2008). Argumentation schemes. 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texttext/plain93870https://repositorio.cuc.edu.co/bitstreams/95db19ed-f6c8-4d85-b60c-3221e12b4c7c/download1c27897989a697ce9bb39deef8c41a04MD53THUMBNAILExploring mathematical connections in the context of proof and mathematical argumentation.pdf.jpgExploring mathematical connections in the context of proof and mathematical argumentation.pdf.jpgGenerated Thumbnailimage/jpeg16606https://repositorio.cuc.edu.co/bitstreams/b78966f1-1d49-4815-b48c-b6e52d935b79/downloadc6eda32be929cc9f46b785cab06fa4ddMD5411323/10514oai:repositorio.cuc.edu.co:11323/105142024-09-17 14:23:34.476https://creativecommons.org/licenses/by/4.0/© 2023 by the authors; licensee Modestum.open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa 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ada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.


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