Semiotic bundle approach and Onto-Semiotic Approach: a dialogue between two theories on an arithmetic-algebraic problem
DOI:
https://doi.org/10.1590/S1678-4634202349256699engPalabras clave:
Primary School arithmetic-algebraic problem, Networking of theories, Onto-semiotic approach, Semiotic bundle approach, SemiosphereResumen
This research rests on the analysis of a mathematical task, concerning an arithmetic-algebraic problem and its solution, using theoretical tools from two main frames: the Semiotic Bundle Approach (SBA) and the Onto-Semiotic Approach (OSA). The activity has been examined by two original video recordings of the group consisting of five pupils of primary education. By presenting an empirical case of networking of theories, the objective is to begin a dialogue with the two approaches, reading the asymmetries found between their languages, with the aim of getting some new insights into the mathematical problem. Whereas the SBA, in a systematic approach, is particularly apt to focus on the relationships among the different multimodal semiotic resources used by the students in the short timescales of the classroom story (an embodied cognitive focus), the OSA incorporates a set of conceptual tools to address the analysis of the different facets that interact in a mathematical education process. Mainly the SBA describes the importance of the bundle of signs (like gestures, words, written signs) for mathematical thinking and communication and its multimodality, whereas the OSA favours the description of objects and processes that emerge from the mathematical practices. The results from this joint analysis provide a rich insight into the observed phenomenon and help initiate a dialogue between theories in Mathematics Education, within a Semiosphere generated by the networking between SBA and OSA.
Descargas
Referencias
ARTIGUE, Michèle et al. Different theoretical perspectives and approaches in research in mathematics education. In: BOSCH, Marianna (ed.); CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION – CERME, 4., 2006, Sant Feliu de Guíxols, Spain. Proceedings of the […]. Sant Feliu de Guíxols: FUNDEMI IQS – Universitat Ramon Llull and ERME, 2006. p. 1239-1244.
ARTIGUE, Michèle; MARIOTTI, Maria Alessandra. Networking theoretical frames: the ReMath enterprise. Educational Studies in Mathematics, New York, v. 85, n. 3, p. 329-355, 2014. https://doi.org/10.1007/s10649-013-9522-2
» https://doi.org/10.1007/s10649-013-9522-2
ARZARELLO, Ferdinando. Semiosis as a multimodal process. Relime, Ciudad de México, p. 267-299, 2006. Special number.
ARZARELLO, Ferdinando et al. Will Penelope choose another bridegroom? Looking for an answer through signs. In: NOVOTNÁ, Jarmila et al. (ed.); CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION – PME, 30., 2006, Prague. Proceedings of the […]. v. 2. Prague: Charles University, 2006. p. 73-80.
ARZARELLO, Ferdinando et al. Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, New York, v. 70, n. 2, p. 97-109, 2009. https://doi.org/10.1007/s10649-008-9163-z
» https://doi.org/10.1007/s10649-008-9163-z
ARZARELLO, Ferdinando; ROBUTTI, Ornella; SABENA, Cristina. Ostensives through the lenses of two theoretical frameworks. In: PITTA-PANTAZI, Demetra; PHILIPPOU, George N. (ed.); CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION – CERME, 5., 2007, Larnaca, Cyprus. Proceedings of the […]. University of Cyprus and ERME, 2007. p. 1617-1628.
BAZZINI, Luciana; SABENA, Cristina; VILLA, Bruna. Meaningful context in mathematical problem solving: a case study. In: INTERNATIONAL CONFERENCE ON SCIENCE AND MATHEMATICS EDUCATION, 3., 2009, Penang, Malaysia. Proceedings of the […]. Penang: CoSMEd, 2009. p. 343-351.
BORJI, Vahid et al. 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, London, v. 14, n. 6, p. 2301-2315, 2018.
BORJI, Vahid; ERFANI, Hedyeh; FONT, Vicenç. A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates. International Journal of Mathematical Education in Science and Technology, London, v. 51, n. 3, p. 405-423, 2020. https://doi.org/10.1080/0020739X.2019.1578904
» https://doi.org/10.1080/0020739X.2019.1578904
D’AMORE, Bruno; GODINO, Juan. El enfoque ontosemiótico como un desarrollo de la teoría antropológica en didáctica de la matemática. Relime, Mexico, DC, v. 10, n. 2, p. 191-218, 2007.
DREYFUS, Tommy et al. The epistemic role of gestures: a case study on networking of APC and AiC. In: BIKNER-AHSBAHS, Angelika; PREDIGER, Susanne (ed.). Networking of theories as a research practice in mathematics education. Cham: Springer, 2014. p. 127-151.
DRIJVERS, Paul et al. One episode, two lenses: A reflective analysis of student learning with computer algebra from instrumental and onto-semiotic perspectives. Educational Studies in Mathematics, New York, v. 82, n. 1, p. 23-49, 2013. https://doi.org/10.1007/s10649-012-9416-8
» https://doi.org/10.1007/s10649-012-9416-8
ECO, Umberto. A theory of semiotics. Indiana: Indiana University Press, 1976.
ERNEST, Paul. A semiotic perspective of mathematical activity: the case of number. Educational Studies in Mathematics, New York, v. 61, n. 1/2, p. 67-101, 2006. https://doi.org/10.1007/s10649-006-6423-7
» https://doi.org/10.1007/s10649-006-6423-7
FLORES, Jeronimo Becker, LIMA, Valderez Marina Do Rosário;MÜLLER, Thaísa Jacintho. Convergences and complementarities between the theories of the three worlds of mathematics and sociointerativity. Bolema, Rio Claro, v. 34 n. 68, p. 1341-1358, 2020. https://doi.org/10.1590/1980-4415v34n68a24
» https://doi.org/10.1590/1980-4415v34n68a24
FONT, Vicenç et al. Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, New York, v. 91, n. 1, p. 107-122, 2016. https://doi.org/10.1007/s10649-015-9639-6
» https://doi.org/10.1007/s10649-015-9639-6
FONT, Vicenç; GODINO, Juan; GALLARDO, Jesús. The emergence of objects from mathematical practices. Educational Studies in Mathematics, New York, n. 82, p. 97-124, 2013.
FRITZ, Annemarie; HAASE, Vitor Geraldi; RÄSÄNEN, Pekka (ed.). International handbook of mathematical learning difficulties. Cham: Springer, 2019.
GALLESE, Vittorio; LAKOFF, George. The Brain’s concepts: the role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, London, v. 22, n. 3, p. 455-479, 2005.
GIACOMONE, Belén et al. Developing the onto-semiotic analysis competence of prospective mathematics teachers. Revista Complutense de Educación, Madrid, v. 29, n. 4, p. 1109-1131, 2018.
GODINO, Juan et al. Análisis de la actividad matemática mediante dos herramientas teóricas: Registros de representación semiótica y configuración ontosemiótica. Avances de Investigación en Educación Matemática - AIEM, [S. l.], n. 10, p. 91-110, 2016. https://doi.org/10.35763/aiem.v0i10.144
» https://doi.org/10.35763/aiem.v0i10.144
GODINO, Juan. Networking socio-cultural theories in mathematics education from the onto-semiotic approach. In: REUNIÓN LATIONAMERICANA DE MATEMÁTICA EDUCATIVA / Latin American Meeting on Educational Mathematics – RELME-31, 31., 2017, Lima. Plenary Conference of the […]. Lima: Relme, 2017. p. 1-21, 2017 http://enfoqueontosemiotico.ugr.es/pages/articulacion.html Data de acesso: 26.10.2022
» http://enfoqueontosemiotico.ugr.es/pages/articulacion.html
GRUGEON-ALLYS, Brigitte; GODINO, Juan; CASTELA, Corine. Three perspectives on the issue of theoretical diversity. In: HODGSON, Bernard et al. (ed.). The didactics of mathematics: approaches and issues: a homage to Michèle Artigue. New York: Springer, 2016. p. 57-86.
HJEMSLEV, Louis. Prolegomena to a theory of language. Madison: University of Wisconsin Press, 1943.
KIDRON, Ivy. Epistemology and networking theories. Educational Studies in Mathematics, New York, v. 91, n. 2, p. 149-163, 2016.
LOTMAN, Jurij. Universe of the mind: a semiotic theory of culture. London: United Kingdom: IB Taurus, 1990.
MAFFIA, Andrea; SABENA, Cristina. Networking of theories as resource for classroom activities analysis: the emergence of multimodal semiotic chains. Quaderni di Ricerca Didattica, Palermo, v. 25, n. 2, p. 405-417, 2015.
MANOLINO, Carola. The semiosphere lens to look at lesson study practices in their cultural context: a case study. In: INPRASITHA, Maitree; CHANGSRI, Narumon; BOONSENA, Nisakorn (ed.); CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION – PME, 44., 2021, Khon Kaen, Thailand. Proceedings of the […]. v. 3. Khon Kaen: PME, 2021. p. 263-272.
PINO-FAN, Luis R. et al. The theory of registers of semiotic representation and the onto-semiotic approach to mathematical cognition and instruction: linking looks for the study of mathematical understanding. In: BESWICK, Kim; MUIR, Tracey; WELL, Jill (ed.); CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION – PME, 39., 2015, Hobart, Australia. Proceedings of the […]. v. 4. Hobart: PME, 2015. p. 33-40.
PREDIGER, Susanne; BIKNER-AHSBAHS, Angelika; ARZARELLO, Ferdinando. Networking strategies and methods for connecting theoretical approaches: first steps towards a conceptual framework. International Journal on Mathematics Education, [S. l.], v. 40, n. 2, p. 165-178, 2008.
RADFORD, Luis. Gestures, speech, and the sprouting of signs: a semiotic-cultural approach to students’ types of generalization. Mathematical Thinking and Learning, [S. l.], v. 51, n. 1, p. 37-70, 2003.
RADFORD, Luis. Connecting theories in mathematics education: challenges and possibilities. ZDM – Mathematics Education, Berlin, v. 40, n. 2, p. 317-327, 2008. https://doi.org/10.1007/s11858-008-0090-3
» https://doi.org/10.1007/s11858-008-0090-3
RADFORD, Luis; SCHUBRING, Gert; SEEGER, Falk (ed.). Semiotics in mathematics education: epistemology, history, classroom, and culture. Rotterdam: Sense, 2008.
RODRÍGUEZ-MUÑIZ, Luis J. et al. (ed.). Investigación en educación matemática XXII. Gijón: Seiem, 2018.
WITTGENSTEIN, Ludwig. Philosophical investigations. New York: MacMillan, 1953.
Descargas
Publicado
Número
Sección
Licencia
Derechos de autor 2023 Educação e Pesquisa
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.
Los conceptos emitidos en los artículos son de exclusiva responsabilidad de sus autores y no reflejan necesariamente la opinión de la redacción.
Está permitida la reproducción total o parcial de los trabajos, siempre y cuando se indique explícitamente la fuente.
