Ir al menú de navegación principal Ir al contenido principal Ir al pie de página del sitio

Artículos

Vol. 26 Núm. 1 (2023): Marzo

UMA CARACTERIZAÇÃO DO CONHECIMENTO ESPECIALIZADO DO PROFESSOR DE MATEMÁTICA DA EDUCAÇÃO INFANTIL E ANOS INICIAIS EM TÓPICOS DE MEDIDA

  • Milena Policastro
  • Miguel Ribeiro
DOI
https://doi.org/10.12802/relime.23.2614
Enviado
octubre 5, 2023
Publicado
2023-10-04

Resumen

En este estudio consideramos las dimensiones matemáticas y pedagógicas del conocimiento del profesor como especializadas, con el objetivo de caracterizar el contenido de este conocimiento, específicamente asociado a los temas de Medidas. Empleando el marco del Mathematics Teacher’s Specialised Knowledge (MTSK), exploramos y describimos el contenido del conocimiento  especializado revelado por un grupo de profesores de Educación Primaria en el Brasil mientras abordan una tarea para la formación,  en un curso de desarrollo profesional. Los resultados aportan un refinamiento de la categorización del conocimiento  docente asociado a los temas (KoT), considerando por separado el detalle del contenido de este conocimento relativo a definiciones,  propiedades y fundamentos. Además, el estudio presenta un conjunto de descriptores de conocimiento que resaltan las particularidades y especificidades de este componente del conocimiento docente relacionado con los temas de Medida,  permitiendo una especie de mapeo de los elementos estructurales y estructurantes de este conocimiento.

Citas

  1. Ainsworth, S. (2006). A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183–198. https://doi.org/10.1016/j.learninstruc.2006.03.001
  2. Barrett, J. E., Cullen, C., Sarama, J., Clements, D. H., Klanderman, D., Miller, A. L., & Rumsey, C. (2011). Children’s unit concepts in measurement: A teaching experiment spanning grades 2 through 5. ZDM, 43(5), 637-650. https://doi.org/10.1007/s11858-011-0368-8
  3. Barrett, J. E., Sarama, J., Clements, D. H., Cullen, C., McCool, J., Witkowski-Rumsey, C., & Klanderman, D. (2012). Evaluating and improving a learning trajectory for linear measurement in elementary grades 2 and 3: A longitudinal study. Mathematical Thinking and Learning, 14, 28–54. https://doi.org/10.1080/10986065.2012.625075
  4. Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235–268. https://doi.org/10.1007/BF00376322
  5. Berka, K. (1983). Measurement: its concepts, theories and problems (Vol. 72). Springer Netherlands. https://doi.org/10.1007/978-94-009-7828-7
  6. Boyd, D. J., Grossman, P. L., Lankford, H., Loeb, S., & Wyckoff, J. (2009). Teacher preparation and student achievement. Educational Evaluation and Policy Analysis, 31(4), 416–440. https://doi.org/10.3102/0162373709353129
  7. Bragg, P., & Outhred, L. (2004). A measure of rulers—The importance of units in a measure. International Group for the Psycholog y of Mathematics Education, 2, 159–166. https://files.eric.ed.gov/fulltext/ED489702.pdf
  8. Caldatto, M. E., Fiorentini, D. & Pavanello, R. M. (2018). Uma análise do Projeto de formação profissional de professores privilegiada pelo PROFMAT. Zetetiké, 26, 260–281. https://doi.org/10.20396/zet.v26i2.8651034
  9. Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, Á., Ribeiro, M., & Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236–256. https://doi.org/10.1080/14794802.2018.1479981
  10. Charalambous, C. Y. (2015). Working at the intersection of teacher knowledge, teacher beliefs, and teaching practice: A multiple-case study. Journal of Mathematics Teacher Education, 18, 427–445. https://doi.org/10.1007/s10857-015-9318-7
  11. Charles, R. I. (2005). Big ideas and understandings as the foundation for elementary and middle school Mathematics. Journal of Mathematics Education Leadership, 7(3), 9–24. https://jaymctighe.com/wp-content/uploads/2011/04/MATH-Big-Ideas_NCSM_Spr05v73p9-24.pdf
  12. Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. Em F. K. Lester (Org.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp.461–555). Information Age Publishing.
  13. Clements, D. H., & Sarama, J. (2009). Learning and teaching early Math: The learning trajectory approach. Routledge.
  14. Clements, D., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. Em D. Clements, J. Sarama & A.-M. DiBiase (Orgs.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 299–317).
  15. Di Bernardo, R., Policastro, M., Almeida, A. R. de, Ribeiro, M., Melo, J. M. de, & Aiub, M. (2018). Conhecimento matemático especializado de professores da educação infantil e anos iniciais: Conexões em medidas. Cadernos Cenpec, 8(1), 98–124. http://dx.doi.org/10.18676/
  16. cadernoscenpec.v8i1.391
  17. Gamboa, G., Badillo, E., Ribeiro, M., Montes, M., & Sanchéz-Matamoros, G. (2020). The role of teachers’ knowledge in the use of learning opportunities triggered by mathematical connections. In S. Zehetmeier, D. Potari, & M. Ribeiro, Professional development and knowledge of Mathematics teachers (1ª ed., pp. 24–43). Routledge.
  18. Godino, J. D., Batanero, C., & Roa, R. (2002). Magnitudes y medida. Em Medida de magnitudes y su didáctica para maestros. (p. 611–654). Universidad de Granada, Proyecto de Investigación y Desarrollo del Ministerio de Ciencia y Tecnología.
  19. Gómez, P., & Cañadas, M. C. (2016). Dificultades de los profesores de matemáticas en formación en el aprendizaje del análisis fenomenológico. Revista Latinoamericana de Investigación en Matemática Educativa, 19(3), 311–334. https://doi.org/10.12802/relime.13.1933
  20. Hiebert, J. (1984). Why do some children have trouble learning measurement concepts? The Arithmetic Teacher, 31(7), 19–24. http://www.jstor.org/stable/41192320
  21. Hill, H. C., & Chin, M. (2018). Connections between teachers’ knowledge of students, instruction, and achievement outcomes. American Educational Research Journal, 55(5), 1076–1112. https://doi.org/10.3102/000283121876961
  22. Ho, A., & McMaster, H. (2019). Is’ capacity’volume? Understandings of 11 to 12-year-old children. Em G. Hine, S. Blackley & A. Cooke (eds.), Mathematics Education research: Impacting practice (Proceedings of the 42nd annual conference of the Mathematics Education Research
  23. Group of Australasia) (pp. 356–363). MERGA. https://files.eric.ed.gov/fulltext/ED604312.pdf
  24. Irwin, K. C., Ell, F. R., & Vistro-Yu, C. P. (2004). Understanding linear measurement: A comparison of Filipino and New Zealand children. Mathematics Education Research Journal, 16(2), 3–24. https://doi.org/10.1007/BF03217393
  25. Klein, F. (1932). Elementary mathematics from an andvanced standpoint: Arithmetic, algebra, analysis (3a ed., Vol. 1). Macmillan.
  26. Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of measurement in the elementary grades. Learning and Teaching Measurement, 1, 100–121.
  27. Ma, L. (1999). Knowing and teaching elementary Mathematics: Teacher’s understanding of fundamental Mathematics in China and the United States. Lawrence Erlbaum Associates.
  28. Mariotti, M. A., & Fischbein, E. (1997). Defining in classroom activities. Educational Studies in Mathematics, 34(3), 219–248. http://www.jstor.org/stable/3482837
  29. Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2), 10–32. https://doi.org/10.1007/BF03217543
  30. Ministério da Educação (2018). Base Nacional Comum Curricular. http://basenacionalcomum.mec.gov.br/
  31. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics—National Council of Teacher of Mathematics. Reston, VA.
  32. Norton, A., & Boyce, S. (2015). Provoking the construction of a structure for coordinating n+1 levels of units. The Journal of Mathematical Behavior, 40, 211–232. https://doi.org/10.1016/j.jmathb.2015.10.006
  33. Organisation for Economic Co-operation and Development (2010). PISA 2009 results: What students know and can do. Student performance in reading, mathematics, and science (Vol. 1). OECD.
  34. Pape, S., & Tchoshanov, M. A. (2001). The role of representation(s) in developing mathematical understanding. Theory into Practice, 40(2), 118–127. https://doi.org/10.1207/s15430421tip4002_6
  35. Panorkou, N. (2020). Dynamic measurement reasoning for area and volume. For the Learning of Mathematics, 40(3), 9–13. https://www.jstor.org/stable/27091164
  36. Panorkou, N. (2021). Exploring students’ dynamic measurement reasoning about right prisms and cylinders. Cognition and Instruction, 1–35. https://doi.org/10.1080/07370008.2021.1958218
  37. Passalaigue, D., & Munier, V. (2015). Schoolteacher trainees’ difficulties about the concepts of attribute and mesaurement. Educational Studies in Mathematics, 89, 307–336. https://doi.org/10.1007/s10649-015-9610-6
  38. Policastro, M. S., Almeida, A. R., & Ribeiro, M. (2017). Conhecimento especializado revelado por professores da educação infantil e dos anos iniciais no tema de medida de comprimento e sua estimativa. Revista Espaço Plural, 36(1), 123–154. https://e-revista.unioeste.br/index.php/
  39. espacoplural/article/view/19714
  40. Policastro, M. S., Almeida, A. R., Ribeiro, M., & Jakobsen, A. (2020). Kindergarten teacher’s knowledge to support a mathematical discussion with pupils on measurement strategies and procedures. In M. Carlsen, I. Erfjord, & P. S. Hundeland. Mathematics education in early
  41. years (pp. 263–279). Springer.
  42. Policastro, M. S., & Ribeiro, M. (2021). Conhecimento especializado do professor que ensina matemática relativo ao tópico de divisão. Zetetiké, 29, 1–24. https://doi.org/10.20396/zet.v29i00.8661906
  43. Ribeiro, M., Almeida, A. R. de, & Mellone, M. (2021). Conceitualizando tarefas formativas para desenvolver as especificidades do conhecimento interpretativo e especializado do professor. Perspectivas da Educação Matemática, 14(35), 1–32. https://doi.org/1046312/pem.v14i35.13263
  44. uma caracterização do conhecimento especializado do professor 135
  45. Ribeiro, M., Carrillo, J., & Monteiro, R. (2012). Cognições e tipo de comunicação do professor de matemática. Exemplificação de um modelo de análise num episódio dividido. Revista latinoamericana de investigación en matemática educativa, 15(1), 93–121. https://www.redalyc.org/journal/335/33523151005/html/
  46. Ribeiro, M., Gibim, G., & Alves, C. (2021). A necessária mudança de foco na formação de professores de e que ensinam matemática: Discussão de tarefas para a formação e o desenvolvimento do conhecimento interpretativo. Perspectivas da Educação Matemática, 14(34), 1–24. https://doi.org/10.46312/pem.v14i34.12686
  47. Ribeiro, M., Jakobsen, A., & Mellone, M. (2018). Secondary prospective teachers’ interpretative knowledge in a measurement situation. In E. Bergqvist, M. Österholm, C. Granberg, & L.Sumpter, Proceedings of the 42nd Conference of the International Group for the Psychology
  48. of Mathematics Education (Vol. 4, p. 35–42). PME.
  49. Ribeiro, M., & Policastro, M. (2021). As medidas e as especificidades do conhecimento do professor para que os alunos aprendam Matemática com significado (1.ª ed., vol. 2). CRV.
  50. Sarama, J., Clements, D. H., Barret, J., Van Dine, D. W., & MacDonel, J. S. (2011). Evaluation of a learning trajectory for length in the early years. ZDM Mathematics Education, 43, 667–680. https://doi.org/10.1007/s11858-011-0326-5
  51. Scheiner, T., Montes, M. A., Godino, J. D., Carrillo, J., & Pino-Fan, L. R. (2017). What makes Mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education, 1–20. https://doi.org/10.1007/s10763-017-9859-6
  52. Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum. American Educator, Summer, 1–18. https://www.math.mun.ca/~hsgaskill/refs/curriculum.pdf
  53. Smith, J. P., Van den Heuvel-Panhuizen, M., & Teppo, A. R. (2011). Learning, teaching, and using measurement: Introduction to the issue. ZDM Mathematics Education, 43(5), 617–620. https://doi.org/10.1007/s11858-011-0369-7
  54. Stake, R. E. (1995). The art of case study research. (1.ª ed.). Sage Publications.
  55. Steffe, L. P. (2003). Fractional commensurate, composition, and adding schemes: Learning trajectories of Jason and Laura: Grade 5. The Journal of Mathematical Behavior, 22(3), 237–295. https://doi.org/10.1016/S0732-3123(03)00022-1
  56. Stephan, M., & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. Em D. H. Clements & G. Bright (eds.), Learning and teaching measurement: 2003 yearbook (pp. 3–16). National Council of Teachers of Mathematics.
  57. Strauss, A., & Corbin, J. (1994). Grounded theory methodology: An overview. Sage Publications.
  58. Subramaniam, K. (2014). Prospective secondary mathematics teachers’ pedagogical knowledge for teaching the estimation of length measurements. Journal of Mathematics Teacher Education, 17, 177–198. https://doi.org/10.1007/s10857-013-9255-2
  59. Szilagyi, J., Clements, D. H., & Sarama, J. (2013). young children’s understandings of length measurement: Evaluating a learning trajectory. Journal for Research in Mathematics Education., 44(3), 581–620. https://doi.org/10.5951/jresematheduc.44.3.0581
  60. Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics wiht particular reference to limits and continuity. Educational Studes in Mathematics, 12, 151–169. https://doi.org/10.1007/BF00305619
  61. Vale, C., McAndrew, A., & Krishnan, S. (2010). Connecting with the horizon: Developing teachers’ appreciation of mathematical structure. Journal of Mathematics Teacher Education, 14,193–212. https://doi.org/10.1007/s10857-010-9162-8
  62. Van den Heuvel-Panhuizen, M., & Elia, I. (2011). Kindergartners’ performance in length measurement and the effect of picture book reading. ZDM Mathematics Education, 43(5), 621–635. https://doi.org/10.1007/s11858-011-0331-8
  63. Venturi, G. (2014). Foundation of Mathematics between theory and practice. Philosophia Scientiæ, 18(1), 45–80. https://doi.org/10.4000/philosophiascientiae.912
  64. Vinner, S. (2002). The role of definitions in the teaching and learning of mathematics. Em D. Tall (ed.), Advanced mathematical thinking (pp. 65–81). Springer.
  65. Vysotskaya, E., Lobanova, A., Rekhtman, I., & Yanishevskaya, M. (2020). The challenge of proportion: Does it require rethinking of the measurement paradigm? Educational Studies in Mathematics, 106, 429-446. https://doi.org/10.1007/s10649-020-09987-8
  66. Weber, K. (2002). Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique. For the Learning of Mathematics, 22(3), 14–17. https://www.jstor.org/stable/40248396
  67. Zakaryan, D., & Ribeiro, M. (2018). Mathematics teachers’ specialized knowledge: A secondary teacher’s knowledge of rational numbers. Research in Mathematics Education, 21(3), 1–19. https://doi.org/10.1080/14794802.2018.1525422
  68. Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education, 36(4), 317–346. https://www.jstor.org/stable/30035043
  69. Zazkis, R., & Leikin, R. (2008). Exemplifying definitions: A case of a square. Educational Studies in Mathematics, 69(2), 131–148. https://doi.org/10.1007/s10649-008-9131-7

Descargas

Los datos de descargas todavía no están disponibles.

Artículos similares

1 2 3 4 5 6 7 8 9 10 > >> 

También puede {advancedSearchLink} para este artículo.