Uma perspectiva ontosemiótica dos problemas e métodos de pesquisa em educação matemática
Resumo
Uma crítica tradicional à pesquisa científica no campo educacional tem sido a desconexão com a prática docente, motivada pela divisão dos problemas de pesquisa. Para resolver essa dissociação, as investigações de design instrucional apresentam problemas preditivos mais próximos a essa prática, mas devem ser complementados com uma interface que forneça os componentes avaliativos e normativos que são deduzidos da aplicação eficiente dos resultados da literatura anterior. Neste trabalho utilizaremos algumas ferramentas da Abordagem Ontosemiótica (OS) para traçar uma agenda de pesquisa que leve em consideração os componentes científicos (descritivos, explicativos e preditivos) e tecnológicos (avaliativos e normativos) da pesquisa didática. Do mesmo modo, descrevemos as ferramentas metodológicas disponibilizadas pela EOS para abordar os problemas referidos, em particular a noção de adequação didática que serve de elo entre a componente científico-tecnológica e a prática docente.
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ARTEAGA, Pedro; BATANERO, Carmen; GEA, María Magdalena. La componente mediacional del conocimiento didáctico matemático de futuros profesores sobre Estadística: un estudio de evaluación exploratorio. Educação Matemática Debate, v.1, n. 1, p. 54-75, 2017.
ARTIGUE, Michèle. Perspectives on Design Research: The Case of Didactical Engineering. In A. BIKNER-AHSBAHS; C. KNIPPING; N. PRESMEG (Eds), Approaches to Qualitative Research in Mathematics Education. Examples of Methodology and Methods. (pp. 467-496). Springer, 2015.
BAKKER, Arthur; VAN EERDE, Dolly. An introduction to design-based research with an example from statistics education. In Angelika BIKNER-AHSBAHS; Christine KNIPPING; Norma PRESMEG (Eds.), Approaches to qualitative research in mathematics education. Examples of methodology and methods. (pp. 429-466). Springer, 2015.
BATANERO, Carmen; DÍAZ, Carmen. The meaning and understanding of mathematics. The case of probability, In Philosophical dimensions in mathematics education (pp. 107-127). Springer, Boston, M.A., 2007.
BIKNER-AHSBAHS, Angelica; KNIPPING, Christine; PRESMEG, Norma. Approaches to qualitative research in mathematics education. Examples of methodology and methods. Springer, 2015.
RUGINA, Anghel N. The problem of values and value‐judgments in science and a positive solution: Max Weber and Ludwig Wittgenstein revisited. International Journal of Social Economics, v. 25, n. 5, p. 805-854, 1998. https://doi.org/10.1108/EUM0000000004522
BREDA, Adriana; FONT, Vicenç; LIMA, Valderez Marina do Rosário. A noção de idoneidade didática e seu uso na formação de professores de matemática. Jornal Internacional de Estudos em Educação Matemática, v. 8, n. 2, p. 1-41, 2015.
BREDA, Adriana; FONT, Vicenç; y PINO-FAN, Luis. Criterios valorativos y normativos en la Didáctica de las Matemáticas: el caso del constructo idoneidad didáctica. Bolema, v. 32, n. 60, p. 255 – 278, 2018.
BROWN, Ann L. Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, v. 2, n. 2, p. 141-178, 1992.
BUNGE, Mario. Las ciencias sociales en discusión: una perspectiva filosófica. Buenos Aires, Editorial Sudamericana, 1999.
BURGOS, María; BELTRÁN-PELLICER, Pablo; GODINO, Juan D. La cuestión de la idoneidad de los vídeos educativos de matemáticas: una experiencia de análisis con futuros maestros de educación primaria. Revista Española de Pedagogía, v. 78, n. 275, p. 27-49, 2020.
BURGOS, María et al. Onto-semiotic complexity of the Definite Integral. Implications for teaching and learning Calculus. REDIMAT – Journal of Research in Mathematics Education, v. 10, n. 1, p. 4-40, 2021.
BURGOS, María y GODINO, Juan D. Modelo ontosemiótico de referencia de la proporcionalidad. Implicaciones para la planificación curricular en primaria y secundaria. AIEM, v. 18, p.1-20, 2020.
CLEMENTS, Ken. Past, present and future dimensions of mathematics education: introduction to the third international handbook of mathematics education. In Ken CLEMENTS; Alan J. BISHOP: Christine KEITEL; Jeremy KILPATRICK; Frederic K. S. LEUNG (Eds.) Third International Handbook of Mathematics Education (pp. v-ix). Springer, 2013.
COBB, Paul; GRAVEMEIJER, Koeno. Experimenting to support and understand learning processes. In Anthony E. KELLY; Richard A. LESH; John Y. BAEK (Eds.), Handbook of design research methods in education. Innovations in Science, Technology,Engineering and Mathematics Learning and Teaching (pp. 68-95). Mahwah, NJ: Lawrence Erlbaum, 2008.
COHEN, Louis; MANION, Lawrence; MORRISON, Keith. Research methods in education. Routledge, 2007.
D'AMORE, Bruno; FONT, Vicenç; GODINO, Juan D. La dimensión metadidáctica en los procesos de enseñanza y aprendizaje de las matemáticas. Paradigma, v. XXVIII, n. 2, p. 49-77, 2007.
ENGLISH, Lyn D.; KIRSHNER, David. Handbook of International Research in Mathematics Education (3rd edition). Taylor & Francis, 2016.
FELDT, Leonard S.; BRENNAN, Robert L. Reliability. In R. L. LINN (Ed.), Educational measurement (Third ed.), (pp. 263-331). New York, American Council on Education and Macmillan Publ., 1991.
FONT, Vicenç; CONTRERAS, Ángel. The problem of the particular and its relation to the general in mathematics education. Educational Studies in Mathematics, v. 69, p. 33-52, 2008.
GASCÓN, Josep; NICOLÁS, Pedro. Incidencia de los paradigmas didácticos sobre la investigación didáctica y la práctica docente. Educación Matemática, v. 33, n. 1, p.7-40, 2021.
GEA, María Magdalena; BATANERO, Carmen; ARTEAGA, Pedro; ESTEPA, Antonio. Conocimiento especializado de correlación y regresión en futuros profesores de educación secundaria. Profesorado, Revista de Currículum y Formación del Profesorado, v. 23, p. 397-416, 2019.
GIACOMONE, Belén; GODINO, Juan D.; BELTRÁN-PELLICER, Pablo. Desarrollo de la competencia de análisis de la idoneidad didáctica en futuros profesores de matemáticas. Educação e Pesquisa, v. 44, e172011, 2018.
GODINO, Juan D. Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques, v. 22, n. (2/3), p. 237-284, 2002.
GODINO, Juan D. Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas. Cuadernos de Investigación y Formación en Educación Matemática, v. 11, p. 111-132, 2013.
GODINO, Juan D. et al. Didactic engineering as design-based research in mathematics education. In Ubuz, B., Haser, C., & Mariotti, M. A. (Eds.). Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (p. 2810-2819) (CERME 8, February 6 - 10, 2013). Ankara, Turkey: Middle East Technical University and ERME, 2013. Disponible en, http://cerme8.metu.edu.tr/wgpapers/WG16/WG16_Godino.pdf
GODINO, Juan D.; BATANERO, Carmen; FONT, Vicenç. The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, v. 39, n. 1-2, p. 127-135, 2007.
GODINO, Juan D.; BATANERO, Carmen; FONT, Vicenç. The onto-semiotic approach: implications for the prescriptive character of didactics. For the Learning of Mathematics, v. 39, n. 1, p. 37- 42, 2019.
GODINO, Juan D.; BURGOS, María. ¿Cómo enseñar las matemáticas y las ciencias experimentales? Resolviendo el dilema de la indagación y transmisión. Paradigma, v. XLI, p. 80–106, 2020.
GODINO, Juan D.; BURGOS, María; GEA, Maria Magdalena. Analysing theories of meaning in mathematics education from the onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 2021. DOI: 10.1080/0020739X.2021.1896042
GODINO, Juan D.; CONTRERAS, Ángel; FONT, Vicenç. Análisis de procesos de instrucción basado en el enfoque ontológico-semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques, v. 26, n. 1, p. 39-88, 2006.
GODINO, Juan D. et al. Aproximación a la dimensión normativa en Didáctica de la Matemática desde un enfoque ontosemiótico. Enseñanza de las Ciencias, v. 27, n. 1, p. 59–76, 2009.
GODINO, Juan D. et al. Orlando. Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects. Educational Studies in Mathematics, v. 77, n. 2, p. 247-265, 2011.
GODINO, Juan D. et al. Ingeniería didáctica basada en el enfoque ontológico - semiótico del conocimiento y la instrucción matemáticos, Recherches en Didactique des Mathématiques, v. 34, n. 2/3, p. 167-200, 2014.
HART, Lynn C. et al. An examination of research methods in mathematics education. Journal of Mixed Methods Research, v. 3, n. 1, p. 26-41, 2009.
HENRICK, Erin; COBB, Paul; JACKSON, Kara. Educational design research to support system-wide instructional improvement. In Angelica BIKNER-AHSBAHS; Christine KNIPPING; Norma PRESMEG (Eds), Approaches to Qualitative Research in Mathematics Education. Examples of Methodology and Methods. (pp. 497-530). Springer, 2015.
HUMMES, Viviane Beatriz; FONT, Vicenç; BREDA, Adriana. Uso combinado del estudio de clases y la idoneidad didáctica para el desarrollo de la reflexión sobre la propia práctica en la formación de profesores de matemáticas. Acta Scientiae, v. 21, n. 1, p. 64-82, 2019.
INGLIS, Matthew; FOSTER, Colin. Five decades of mathematics education research. Journal for Research in Mathematics Education, v. 49, n. 4, p. 462-500, 2018.
JOHNSON, Burke; ONWUEGBUZIE, Anthony J. Mixed methods research: A research paradigm whose time has come. Educational Researcher, v. 33, n. 7, p. 14-26, 2004.
KELLY, Anthony E.; LESH, Richard A.; BAEK, John Y. (Eds.). Handbook of design research in methods in education. Innovations in science, technology, engineering, and mathematics learning and teaching. New York, NY: Routledge, 2008.
KILPATRICK, Jeremy; SWAFFORD, Jane; FINDELL, Bradford. (Eds.). Adding it up: Helping children learn mathematics. National Academy Press, 2001.
KORTHAGEN, Fred A. J. The gap between research and practice revisited. Educational Research and Evaluation, v. 13, n. 3, p. 303 – 310, 2007.
LAMPERT, Magdalene et al. Using Designed Instructional Activities to Enable Novices to Manage Ambitious Mathematics Teaching. In M. K. STEIN; L. KUCAN, (Eds), Instructional Explanations in the Disciplines (pp. 129-141). Springer, 2010.
LERMAN, Stephen. The social turn in mathematics education research. In Joan BOALER (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport, CT: Ablex, 2000.
MCINTYRE, Donald. Bridging the gap between research and practice. Cambridge Journal of Education, v. 35, n. 3, p. 357–382, 2005.
MESSICK, Samuel Validity. In R. L. LINN (Ed.), Educational measurement (Third ed.), pp. 13-104). New York, American Council on Education and Macmillan Publ., 1991.
RAND MATHEMATICS STUDY PANEL. Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education. Santa Monica, CA: Rand, 2003.
SCHOENFELD, Alan H. Methods. In Frank K. Lester (Ed.). Second Handbook of Research on Mathematics Teaching and Learning (pp. 66-110). NCTM & IAP (Information Age Publishing Inc.), 2007.
SNOW, Richard E.; LOHMAN, David R. Implication of cognitive psychology for educational measurement. In R. L. LINN (Ed.), Educational measurement (Third ed.), pp. 263-331, New York. American Council on Education and Macmillan Publ., 1991.
WEBB, Norman L. Assessment of student’s knowledge of mathematics: step toward a theory. In Douglas A. Grouws, (Ed.), Handbook of research on mathematics teaching and learning. New York, Macmillan, 1992.
WEBER, Max. Por qué no se deben hacer juicios de valor en la sociología y en la economía. (Trad. Abellán, J.). Madrid, Alianza Editorial, 1917/2010.
WHEELER, David. Epistemological issues and challenges to assessment: What is mathematical knowledge? In: M. NISS (Ed.), Investigations into assessment in mathematics education. An ICMI Study. Dordrecht, Kluwer A.P., 1993.
WILHELMI, Miguel R.; GODINO, Juan D.; LACASTA, Eduardo. Configuraciones epistémicas asociadas a la noción de igualdad de números reales. Recherches en Didactique des Mathematiques, v. 27, n. 1, p. 77 – 120, 2007.
VYGOTSKY, Lev S. El desarrollo de los procesos psicológicos superiores. Barcelona: Crítica-Grijalbo, 1934.