Conocimiento interpretativo de futuros profesores de educación infantil e años iniciales: potencialidades para la mejora de la formación
DOI:
https://doi.org/10.18593/r.v46i.23792Palabras clave:
Conocimiento Interpretativo, Conocimiento especializado del profesor, RestaResumen
El conocimiento del profesor de matemáticas es especializado, y tal especialización no se refiere sólo al dominio pedagógico del contenido, sino incluye, obviamente, el dominio del contenido matemático. Esa especialización del conocimiento del profesor es considerada en la perspectiva del denominado Conocimiento Interpretativo, y ese conocimiento se basa en la atribución de significado que se da a los comentarios y producciones de los alumnos, aun cuando éstos contengan errores (o inadecuaciones matemáticas) o sean basados en razonamientos no convencionales. En este artículo, discutimos el Conocimiento Interpretativo revelado por un grupo de futuros profesores de Educación Infantil y Primaria, en el contexto de una tarea para la formación de profesores (tarea interpretativa) en el ámbito de la resta. Los resultados muestran un conocimiento que limita las interpretaciones y atribución de significado a los razonamientos matemáticos en que los alumnos establecen sus producciones, cuando éstas son distintas del abordaje “tradicional”. También, la interpretación dada se encuentra en un nivel de descripción y limita la calidad del feedback entregado, el que se muestra de una naturaleza esencialmente evaluativa y que no contribuye al aprendizaje comprensivo de los alumnos. La discusión apunta a algunos elementos matemáticamente críticos que deben ser considerados centrales en la formación de profesores, en particular en lo que se refiere al desarrollo de su Conocimiento Interpretativo.
Descargas
Citas
AGUILAR, Á. et al. Un marco teórico para el conocimiento especializado del profesor de matemáticas. Huelva, Espanha: Universidad de Huelva Publicaciones, 2014.
BALL, D. L.; HILL, H. C.; BASS, H. Knowing mathematics for teaching: who knows mathematics well enough to teach third grade, and how can we decide? American Educator, p. 14-46, Fall 2005.
BALL, D. L.; THAMES, M. H.; PHELPS, G. Content knowledge for teaching: what makes it special? Journal of Teacher Education, v. 59, n. 5, p. 389-407, 2008. DOI: https://doi.org/10.1177/0022487108324554
BAROODY, A. J.; TORBEYNS, J.; VERSCHAFFEL, L. Young children’s understanding and application of subtraction-related principles. Mathematical Thinking and Learning, v. 11, p. 2-9, 2009. DOI: https://doi.org/10.1080/10986060802583873
BAUMERT, J. et al. Teachers’ mathematical knowledge, cognitive activation in the classroom and student progress. American Educational Research Journal, v. 47, n. 1, p. 133-180, 2010. DOI: https://doi.org/10.3102/0002831209345157
BOYD, D. J. et al. Teacher preparation and student achievement. Educational Evaluation and Policy Analysis, v. 31, n. 4, p. 416-440, 2009. DOI: https://doi.org/10.3102/0162373709353129
BRASIL. Base Nacional Comum Curricular. Brasília, DF: Ministério da Educação, 2018.
BRASIL, S. de E. F. Parâmetros curriculares nacionais: matemática. Brasília, DF: MEC/SEF, 1997.
CARRILLO, J. et al. The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, p. 236-256, 2018. DOI: https://doi.org/10.1080/14794802.2018.1479981
CHARALAMBOUS, C. Y. Mathematical knowledge for teaching and tasks. Journal of Teacher Education, v. 60, n. 1-2, p. 21-34, 2010.
CLARKE, B.; CLARKE, D. M.; HORNE, M. A longitudinal study of children´s mental computation strategies. Proceedings of PME, v. 2, n. 30, p. 329-336, 2006.
DAVIS, B. Listening for differences: an evolving conception of mathematics teaching. Journal for Research in Mathematics Education, v. 28, n. 3, p. 355-376, 1997. DOI: https://doi.org/10.5951/jresematheduc.28.3.0355
DI MARTINO, P. et al. Prospective teachers’ interpretative knowledge: giving sense to subtraction algorithms. In: ERME TOPIC CONFERENCE MATHEMATICS TEACHING, RESOURCES AND TEACHER PROFESSIONAL DEVELOPMENT, 2016. Proceedings [...] Hall: ERME, 2016. DOI: https://doi.org/10.4171/NEWS/102/12
DI MARTINO, P.; MELLONE, M.; RIBEIRO, M. Interpretative Knowledge. In: LERMAN, S. (ed.). Encyclopedia of Mathematics Education. Cham: Springer International Publishing, 2019. p. 1-5. DOI: https://doi.org/10.1007/978-3-319-77487-9_100019-1
ELLEMOR-COLLINS, D.; WRIGHT, R. J. From counting by ones to facile higher decade edition: the case of Robyn. Proceedings of PME, v. 2, n. 32, p. 439-446, 2008.
FUSON, K. C. et al. Children’s conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, v. 28, p. 130-162, 1997. DOI: https://doi.org/10.5951/jresematheduc.28.2.0130
GALLEGUILLOS, J.; RIBEIRO, M. Prospective mathematics teachers’ interpretative knowledge: focus on the provided feedback. In: CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION, 11., 2019, Utrecht. Proceedings […] Utrecht: Utrecht University, 2019. p. 1-8.
GERVASONI, A. Insights about the addition strategies used by grade 1 and grade 2 children who are vulnerable in number learning. Proceedings of PME, v. 3, n. 30, p. 177-184, 2006.
JAKOBSEN, A.; RIBEIRO, M.; MELLONE, M. Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, v. 19, n. 3-4, p. 135-150, 2014.
KAMII, C.; LEWIS, B.; KIRKLAND, L. Fluency in subtraction compared with addition. Journal of Mathematical Behaviour, v. 20, p. 33-42, 2001. DOI: https://doi.org/10.1016/S0732-3123(01)00060-8
KLEIN, F. Elementary mathematics from an advanced standpoint: arithmetic, algebra, analysis. 3. ed. New York: Macmillan, 1932. v. 1.
LORTIE, D. Schoolteacher: a sociological study. 2. ed. Chicago: The University of Chicago Press, 1975.
MANDARINO, M. C. F. Que conteúdos da Matemática escolar professores dos anos iniciais do Ensino Fundamental priorizam. In: GUIMARÃES, G.; BORBA, R. (ed.). Reflexões sobre o ensino de matemática nos anos iniciais de escolarização. Recife: SBEM, 2009.
MCCLAIN, K.; COBB, P. M.; BOWERS, J. A contextual investigation of three-digit addition and subtraction. In: MORROW, L. J.; KENNEY, M. J. (ed.). The teaching and learning of algorithms in school mathematics. Reston, VA: National Council of Teachers of Mathematics, 1998. p. 141-150.
MELLONE, M. et al. Prospective teachers interpret student responses: Between assessment, educational design and research. In: CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION, 10., 2017, Dublin. Proceedings [...] Dublin: Institute of Education, Dublin City University and ERME, 2017.
MENDONÇA, T. M. et al. As estruturas aditivas nas séries iníciais do ensino fundamental: um estudo diagnóstico em contextos diferentes. Revista latinoamericana de investigación en matemática educativa, v. 10, n. 2, p. 219-239, jul. 2007.
NYE, B.; KONSTANTOPOULOS, S.; HEDGES, L. How large are teacher effects?. Educational evaluation and policy analysis. Educational Evaluation and Policy Analysis, v. 26, n. 3, p. 237-257, 2004. DOI: https://doi.org/10.3102/01623737026003237
RIBEIRO, M. Tareas para alumnos y tareas para la formación: discutiendo el conocimiento especializado del profesor y del formador de profesores de matemáticas. In: JORNADAS NACIONALES DE EDUCACIÓN MATEMÁTICA – SOCHIEM, 20., 2016, Valparaíso. Anais [...] Valparaíso, Chile, 2016.
RIBEIRO, M.; ALMEIDA, A. R.; MELLONE, M. Desenvolvendo as especificidades do conhecimento interpretativo do professor e tarefas para a formação. In: GIRALDO, V.; VIOLA, J.; ELIAS, H. R. (ed.). Problematizações sobre a Formação Matemática na Licenciatura em Matemática. [S. l.] SBEM, 2019.
RIBEIRO, M.; CARRILLO, J.; MONTEIRO, R. We teach what we know, but do we know what we teach? The pratical “distinction” between squares and rectangles in a primary shcool class. In: INTERNATIONAL SYMPOSIUM ELEMENTARY MMATHS TEACHING, 9., 2009, Prague. Anais [...] Prague, Czech Republic: Charles University, Faculty of Education, 2009.
RIBEIRO, M.; MELLONE, M.; JAKOBSEN, A. Give sense to students’ productions: a particular task in teacher education. In: INTERNATIONAL SYMPOSIUM ELEMENTARY MATHS TEACHING, 12., 2013, Prague. Proceedings […] Prague, Czech Republic: Charles University, Faculty of Education, 2013.
ROWLAND, T.; HUCKSTEP, P.; THWAITES, A. Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, v. 8, n. 3, p. 255-281, 2005. DOI: https://doi.org/10.1007/s10857-005-0853-5
SHULMAN, L. Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, v. 57, n. 1, p. 1-22, 1987. DOI: https://doi.org/10.17763/haer.57.1.j463w79r56455411
SHULMAN, L. Those who understand: knowledge growth in teaching. Educational Researcher, v. 15, n. 2, p. 4-14, 1986. DOI: https://doi.org/10.3102/0013189X015002004
SMITH, M. S. Practice-based professional development for teachers of mathematics. Reston VA: The National Council of Teachers of Mathematics, 2001
STEIN, M. K. et al. Implementing standards-based mathematics instruction: a casebook for professional development. New York: Teachers College Press, 2000.
SWAN, M. The impact of task-based professional development on teachers’ practices and beliefs: a design research study. Journal of Mathematics Teacher Education, v. 10, p. 217-237, 2007. DOI: https://doi.org/10.1007/s10857-007-9038-8
![](https://periodicos.unoesc.edu.br/public/journals/14/submission_23792_19320_coverImage_pt_BR.jpg)
Publicado
Cómo citar
Número
Sección
Licencia
Derechos de autor 2020 Miguel Ribeiro, Milena Soldá Policastro
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
Declaración de Derechos de Autor
Los autores conservan los derechos de autor y otorgan a la Revista el derecho de primera publicación, con el trabajo licenciado simultáneamente bajo una Licencia Creative Commons – Atribución – 4.0 Internacional.