Desafíos experimentados al detallar el análisis de las conexiones matemáticas y etnomatemáticas desde una visión ontosemiótica

• Camilo Andrés Rodríguez Nieto ^[1] ; Vicenç Font Moll ^[2] ; Flor Monserrat Rodríguez Vásquez ^[3]
  1. [1] Universidad de la Costa

     Universidad de la Costa

     Colombia

     
  2. [2] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  3. [3] Universidad Autónoma de Guerrero

     Universidad Autónoma de Guerrero

     México

     

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• Localización: Paradigma, ISSN 1011-2251, Nº. Extra 2, 2023 (Ejemplar dedicado a: Enfoque ontosemiótico de la congnición e instrucción matemáticos (EOS)), págs. 509-538
• Idioma: español
• Títulos paralelos:
  • Challenges experienced when detailing the analysis of mathematical and ethnomathematical connections from an onto-semiotic perspective
  • Desafios vivenciados ao detalhar a análise das conexões matemáticas e etnomatemáticas a partir de uma perspectiva ontossemiótica
• Enlaces
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• Resumen
  • español

    Desde una visión ontosemiótica se analizaron las conexiones matemáticas y etnomatemáticasa partir de tres desafíos. Teóricamente se usó la articulación entre la Teoría Ampliada de las Conexiones (TAC) y el Enfoque Ontosemiótico (EOS). La metodología fue cualitativa donde participaron estudiantes universitarios de licenciatura en matemáticas, un artesano de cometas y un profesor de matemáticas en servicio. Los datos se recolectaron a través de cuestionarios, producciones escritas, entrevistas semiestructuradas y la observación participante. El análisis de datos se entiende a manera de tres desafíos: en el primero se analizaron las conexiones matemáticas de los estudiantes cuando resuelven problemas sobre la recta tangentey derivada; en el segundo desafío se analizaron las conexiones etnomatemáticas evidenciadas en la elaboración de cometas por un artesano que usa unidades de medidas convencionales y no convencionales y nociones geométricas; en el tercer desafío se analizaron las conexiones etnomatemáticas y matemáticas activadas por el profesor en servicio cuando construye la cometa y la usa para explicar la existencia de triángulos isósceles y ángulos opuestos por el vértice. Cabe destacar que las conexiones se detallaron en términos de prácticas, procesos, objetos y funciones semióticas.

  • English

    From an onto-semiotic perspective, mathematical and ethnomathematical connections were analyzed based on three challenges. Theoretically, the articulation between the Extended Theory of Connections (ETC) and the Onto-semiotic Approach (OSA) was used. The methodology was qualitative with the participation of university students with a degree in mathematics, a kite craftsman and an in-service mathematics teacher. Data was collected through questionnaires, written productions, semi-structured interviews, and participant observation. Data analysis is understood in the form of three challenges: in the first, the students' mathematical connections were analyzed when they solve problems on the tangent and derivative lines; In the second challenge, the ethnomathematical connections evidenced in the elaboration of kites by an artisan who uses conventional and non-conventional units of measurement and geometric notions were analyzed; In the third challenge, the ethnomathematical and mathematical connections activated by the teacher in service when he builds the kite and uses it to explain the existence of isosceles triangles and angles opposite by the vertex were analyzed. It should be noted that the connections were detailed in terms of practices, processes, objects, and semiotic functions.

  • português

    A partir de uma perspectiva ontossemiótica, as conexões matemáticas e etnomatemáticas foram analisadas a partir de três desafios. Teoricamente, foi utilizada a articulação entre a Teoria Expandida das Conexões (TAC) e a Abordagem Ontossemiótica (OSA). A metodologia foi qualitativa com a participação de universitários formados em matemática, artesão de pipas e um professor de matemática em serviço. Os dados foram coletados por meio de questionários, produções escritas, entrevistas semiestruturadas e observação participante. A análise dos dados é compreendida na forma de três desafios: no primeiro, foram analisadas as conexões matemáticas dos alunos ao resolverem problemas de retas tangentes e derivadas; No segundo desafio, foram analisadas as conexões etnomatemáticas evidenciadas na elaboração de pipas por uma artesã que utiliza unidades de medida convencionais e não convencionais e noções geométricas; no terceiro desafio, foram analisadas as conexões etnomatemáticas e matemáticas ativadas pelo professor em serviço quando constrói a pipa e a utiliza para explicar a existência de triângulos isósceles e ângulos opostos ao vértice. Deve-se notar que as conexões foram detalhadas em termos de práticas, processos, objetos e funções semióticas.

• Referencias bibliográficas
  • Citas ARZARELLO, F.; OLIVERO, F. Theories and empirical researches: towards a common framework. Proceedings of the 4th Conference of the...
  • BIKNER-AHSBAHS, A.; PREDIGER, S. Networking theories—an approach for exploiting the diversity of theoretical approaches. In B. Sriraman &...
  • BIKNER-AHSBAHS, A.; PREDIGER, S. (Eds). Networking of theories as a research practice in mathematics education. Dordrecht: Springer, 2014.
  • BIKNER-AHSBAHS, A.; VOHNS, A. Theories of and in Mathematics Education. In Traditions in German-Speaking Mathematics Education Research, pp....
  • BIKNER-AHSBAHS, A. Adaptive teaching of covariational reasoning: Networking “the way of being” on two layers. The Journal of Mathematical...
  • BOERO, P.; DREYFUS, T.; GRAVEMEIJER, K.; GRAY, E.; HERSHKOWITZ, R.; SCHWARZ, B.; SIERPINSKA, A.; TALL, D. Abstraction: Theories about the...
  • BORJI, V.; FONT, V.; ALAMOLHODAEI, H.; SÁNCHEZ, A. Application of the Complementarities of Two Theories, APOS and OSA, for the Analysis of...
  • BORJI, V.; ERFANI, H.; FONT, V. A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates....
  • BOSCH, M.; GASCÓN, J.; TRIGUEROS, M. Dialogue between theories interpreted as research praxeologies: The case of APOS and the ATD. Educational...
  • BUSINSKAS, A. M. Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections....
  • CAMPO-MENESES, K.; GARCÍA-GARCÍA, J. Explorando las conexiones matemáticas asociadas a la función exponencial y logarítmica en estudiantes...
  • COHEN, L.; MANION, L.; MORRISON, K. Research methods in education. London and New York: Routledge, 2018.
  • D’AMBROSIO, U. Etnomatemática: Elo entre las tradições e a modernidad. Colección: Tendencias en educación matemática. Belo Horizonte: Autêtica,...
  • DOLORES-FLORES, C.; GARCÍA-GARCÍA, J. Conexiones intramatemáticas y extramatemáticas que se producen al resolver problemas de Cálculo en contexto:...
  • DRIJVERS, P.; GODINO, J. D.; FONT, V.; TROUCHE, L. One episode, two lenses. Educational Studies in Mathematics, Dordrecht, v. 82, n. 1, p....
  • EVITTS, T. Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula....
  • FONT, V. Una perspectiva ontosemiótica sobre cuatro instrumentos de conocimiento que comparten un aire de familia: Particular/general, representación,...
  • FONT, V.; TRIGUEROS, M.; BADILLO, E.; RUBIO, N. Mathematical objects through the lens of two different theoretical perspectives: APOS and...
  • FONT, V.; GODINO, J.; GALLARDO, J. The emergence of objects from mathematical practices. Educational Studies in Mathematics, Dordrecht, 2013,...
  • FONT, V. Coordinación de Teorías en Educación Matemática: el caso del enfoque ontosemiótico. Perspectivas da Educação Matemática, Campo Grande,...
  • GARCÍA-GARCÍA, J.; DOLORES-FLORES, C. Intra-mathematical connections made by high school students in performing Calculus tasks, International...
  • GARCÍA-GARCÍA, J.; DOLORES-FLORES, C. Pre-university students' mathematical connections when sketching the graph of derivative and antiderivative...
  • GODINO, J. D.; BATANERO, C.; FONT, V. The onto-semiotic approach to research in mathematics education. ZDM–The International Journal on Mathematics...
  • GODINO, J.; D., BATANERO, C.; FONT, V. The onto-semiotic approach: implications for the prescriptive character of didactics. For the Learning...
  • GODINO, J. D.; BELTRÁN-PELLICER, P.; BURGOS, M. Concordancias y complementariedades entre la Teoría de la Objetivación y el Enfoque Ontosemiótico....
  • GODINO, J. D.; BATANERO, C. Significado institucional y personal de los objetos matemáticos. Recherches en didactique des Mathématiques, Grenoble,...
  • HIEBERT, J.; CARPENTER, T. Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research of mathematics teaching and...
  • KIDRON, I.; BIKNER-AHSBAHS, A. Advancing research by means of the networking of theories. In A. Bikner-Ahsbahs, Ch., Knipping, & N. Presmeg...
  • LEDEZMA, C.; FONT, V.; SALA, G. Analysing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives....
  • MHLOLO, M. K. Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice. African Journal of Research...
  • NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS [NCTM]. Principles and standards for school mathematics. Reston: National Council of Teachers...
  • PINO-FAN, L.; GUZMÁN, I.; FONT, V.; DUVAL, R. Analysis of the underlying cognitive activity in the resolution of a task on derivability of...
  • PREDIGER, S.; BIKNER-AHSBAHS, A.; ARZARELLO, F. Networking strategies and methods for connection theoretical approaches: First steps towards...
  • RADFORD, L. Connecting theories in mathematics education: challenges and possibilities. ZDM-The International Journal on Mathematics Education,...
  • RODRÍGUEZ-NIETO, C. A. Explorando las conexiones entre sistemas de medidas usados en prácticas cotidianas en el municipio de Baranoa. IE Revista...
  • RODRÍGUEZ-NIETO, C. A. Conexiones etnomatemáticas entre conceptos geométricos en la elaboración de las tortillas de Chilpancingo, México....
  • RODRÍGUEZ-NIETO, C. A.; ALSINA, Á. Networking Between Ethnomathematics, STEAM Education, and the Globalized Approach to Analyze Mathematical...
  • RODRÍGUEZ-NIETO, C. A.; CERVANTES-BARRAZA, J. A.; FONT, V. Exploring mathematical connections in the context of proof and mathematical argumentation:...
  • RODRÍGUEZ-NIETO, C. A.; ESCOBAR-RAMÍREZ, Y. Conexiones Etnomatemáticas en la Elaboración del Sancocho de Guandú y su Comercialización en Sibarco,...
  • RODRÍGUEZ-NIETO, C. A.; FONT, V.; BORJI, V.; RODRÍGUEZ-VÁSQUEZ, F. M. Mathematical connections from a networking of theories between extended...
  • RODRÍGUEZ-NIETO, C. A.; FONT, V.; RODRÍGUEZ-VÁSQUEZ, F. M. Literature review on networking of theories developed in mathematics education...
  • RODRÍGUEZ-NIETO, C.; RODRÍGUEZ-VÁSQUEZ, F.; FONT, V. A new view about connections: the mathematical connections established by a teacher when...