Análisis cognitivo de tareas de comparación de probabilidades por futuro profesorado de Educación Primaria

  1. Burgos, María 1
  2. López-Martín, María del Mar 2
  3. Aguayo-Arriagada, Carmen Gloria 2
  4. Albanese, Verónica 1
  1. 1 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

  2. 2 Universidad de Almería
    info

    Universidad de Almería

    Almería, España

    ROR https://ror.org/003d3xx08

Revue:
Uniciencia

ISSN: 2215-3470

Année de publication: 2022

Titre de la publication: Uniciencia. January-December, 2022

Volumen: 36

Número: 1

Type: Article

DOI: 10.15359/RU.36-1.38 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

D'autres publications dans: Uniciencia

Résumé

Para aperfeiçoar o aprendizado matemático, os professores devem ser capazes de analisar, interpretar e avaliar a atividade matemática de seus estudantes, tomando decisões sobre sua compreensão e dificuldades em resolver tarefas matemáticas. Esta competência de análise cognitiva permite ao professor compreender os processos de aprendizagem matemática e estabelecer diferentes possibilidades de institucionalização dos conhecimentos matemáticos envolvidos. [Objetivo] O objetivo deste trabalho é descrever os resultados da avaliação dos conhecimentos e habilidades dos futuros professores da escola primária na interpretação das respostas dos estudantes às tarefas de comparação de probabilidades, identificando estratégias incorretas e reconhecendo o raciocínio proporcional na atividade matemática. Ela também analisa as diferentes formas de ação propostas pelos futuros professores com o objetivo de levar os estudantes a superar as dificuldades que os guiaram a dar uma solução inadequada. [Metodologia] Para este fim, foi realizada uma pesquisa descritiva e qualitativa com a colaboração de 116 futuros professores de Educação Primária da Universidade de Almeria (Espanha). A intervenção foi realizada uma vez concluído o processo de formação sobre o conteúdo matemático do bloco de Estatística e Probabilidade. [Resultados] Entre os resultados obtidos, destacamos um conhecimento didático-matemático de raciocínio proporcional e probabilístico que impede que futuros professores interpretem e tomem decisões em relação às respostas dos estudantes. [Conclusões] Estes resultados destacam a necessidade de implementar intervenções de treinamento que nos permitam resolver adequadamente estas situações comuns nas escolas.

Références bibliographiques

  • References Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/ 10.1177/0022487108324554
  • Bartell, T. G., Webel, C., Bowen, B., & Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education, 16(1), 57-79. https://doi.org/10.1007/s10857-012-9205-4
  • Batanero, C., Godino, J. D., & Roa, R. (2004). Training teachers to teach probability. Journal of statistics Education, 12(1). https://doi.org/10.1080/10691898.2004.11910715
  • Batanero, C., Gómez, E., Contreras, J. M., & Díaz, C. (2015). Conocimiento matemático de profesores de primaria en formación para la enseñanza de la probabilidad: Un estudio exploratorio. Práxis Educativa, 10(1), 11-34. https://doi.org/10.5212/PraxEduc.v.10i1.0001
  • Batanero, C., Gómez, E., Serrano, L., & Contreras, J. M. (2012). Comprensión de la aleatoriedad por futuros profesores de educación primaria. Redimat, 1(3), 222-245. https://dx.doi.org/10.4471/redimat.2012.13
  • Begolli, K. N., Dai, T., McGinn, K. M., & Booth, J. L. (2021). Could probability be out of proportion? Self-explanation and example-based practice help students with lower proportional reasoning skills learn probability. Instructional Science 49, 441–473. https://doi.org/10.1007/s11251-021-09550-9
  • Ben-Chaim, D., Keret, Y., & Ilany, B. (2012). Ratio and proportion: Research and teaching in mathematics teachers’ education. Sense Publisher.
  • Berk, D., Taber, S. B., Gorowara, C. C., & Petzl, C. (2009). Developing prospective elementary teachers’ flexibility in the domain of proportional reasoning. Mathematical Thinking and Learning, 11(3), 113-135. https://doi.org/ 0.1080/10986060903022714
  • Bisquerra, R., & Alzina, R. B. (2004). Metodología de la investigación educativa. Editorial La Muralla.
  • Biza, I., Nardi, E., & Zhachariades, T. (2007). Using tasks to explore teacher knowledge in situation-specific contexts. Journal of Mathematics Teacher Education, 10, 301–309. https://doi.org/10.1007/s10857-007-9043-y
  • Boyer, T. W., & Levine, S. C. (2015). Prompting Children to Reason Proportionally: Processing Discrete Units as Continuous Amounts. Developmental Psychology, 51(5), 615–620. https://dx.doi.org/10.1037/a0039010
  • Bryant, P., & Nunes, T. (2012). Children’s understanding of probability: A literature review (full report). The Nuffield Foundation.
  • Buforn, A., Llinares, S., & Fernández, C. (2018). Características del conocimiento de los estudiantes para maestros españoles en relación con la fracción, razón y proporción. Revista Mexicana de Investigación Educativa, 23, 229-251. https://doi.org/10.1007/s10857-005-0853-5
  • Burgos, M., & Godino, J. D. (2020). Modelo ontosemiótico de referencia de la proporcionalidad: Implicaciones para la planificación curricular en primaria y secundaria. AIEM Avances de Investigación en Educación Matemática, 18, 1–20. https://doi.org/10.35763/aiem.v0i18.255
  • Chapman, O. (2014). Overall commentary: understanding and changing mathematics teachers. In: J. J. Lo; K. R. Leatham; L. R. Van Zoest (Eds.) Research Trends in Mathematics Teacher Education (pp. 295-309). Springer International Publishing. https://doi.org/10.1007/978-3-319-02562-9_16
  • Choy, B. H. (2016). Snapshots of mathematics teacher noticing during task design. Mathematics Education Research Journal, 28(3), 421-440. https://doi.org/10.1007/s13394-016-0173-3
  • English, L. D. (2008). Setting an agenda for international research in mathematics education. In Handbook of international research in mathematics education, 2nd Edition, p 3-19. New York y London: Taylor and Francis (Routledge). https://doi.org/10.4324/9780203930236
  • Fernández, C., Llinares, S., & Valls, J. (2011). Características del desarrollo de una mirada profesional en estudiantes para profesor de matemáticas en un contexto b-learning. Acta Scientiae, 13(1), 10-28.
  • Fernández, C., Llinares, C., & Valls, J. (2012). Learning to notice students' mathematical thinking through online discussions. ZDM. Mathematics Education. https://doi.org/ 10.1007/s11858-012-0425-y
  • Gea, M.M., Parraguez, R., & Batanero, C. (2017). Comprensión de la probabilidad clásica y frecuencial por futuros profesores. En J. M. Muñoz-Escolano; A. Arnal-Bailera; P. Beltrán-Pellicer; M. L. Callejo; J. Carrillo (Eds.), Investigación en educación matemática XXI (pp. 267-276). SEIEM. https://cutt.ly/eRfVp0C
  • Godino, J. D. (2009). Categorías de análisis de los conocimientos del profesor de matemáticas. Unión, Revista Iberoamericana de Educación Matemática, 20, 13-31. https://cutt.ly/lRfVk8e
  • Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
  • Godino, J. D., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas. Bolema, 31(57), 90-113. https://doi.org/10.1590/1980-4415v31n57a05
  • Gómez, E., Batanero, C., & Contreras, C. (2013). Conocimiento matemático de futuros profesores para la enseñanza de la probabilidad desde el enfoque frecuencial. Bolema, 28(48), 209-229. https://doi.org/10.1590/1980-4415v28n48a11
  • Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400. https://doi.org/10.5951/jresematheduc.39.4.0372
  • Jacobs, V. R., Lamb, L. C. & Philipp, R. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
  • Jakobsen, A., Ribeiro, C. M., & Mellone, M. (2014). Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, 19(3-4), 135-150. https://cutt.ly/URfVnFm
  • Lamon, S. (2007). Rational number and proportional reasoning: toward a theoretical framework for research. In: F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). NCTM.
  • Langrall, C. W., & Mooney, E. S. (2005). Characteristics of elementary school students’ probabilistic reasoning. In G. Jones (Ed.), Exploring probability in school (pp. 95–119). Springer. https://doi.org/10.1007/0-387-24530-8_5
  • Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In: J. Hiebert; M. Behr (Eds.), Number concepts and operations for the middle grades (pp. 93-118). Reston, VA: NCTM.
  • Llinares, S. (2013). Professional Noticing: A component of the mathematics teacher’s professional practice. Sisyphus, Journal of Education, 1(3), 76-93. https://doi.org/10.25749/sis.3707
  • Mason, J. (2016). Perception, interpretation and decision making: understanding gaps between competence and performance-a commentary. ZDM, 48(1-2), 219-226. https://doi.org/10.1007/s11858-016-0764-1
  • Mohamed, N. (2012). Evaluación del conocimiento de los futuros profesores de educación primaria sobre probabilidad (Doctoral dissertation). Universidad de Granada. https://cutt.ly/BRfVYdY
  • Pereira-Mendoza, L. (2002). Would you allow your accountant to perform surgery? Implications for the education of primary teachers. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on the Teaching of Statistics. Hawthorn, VIC: International Statistical Institute. https://cutt.ly/fRfVSaO
  • Pino-Fan, L., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers' didactic-mathematical knowledge. EURASIA Journal of Mathematics, Science and Technology Education, 11(6), 1429-1456. https://doi.org/10.12973/eurasia.2015.1403a
  • Pino-Fan, L., & Godino, A. (2015). Perspectiva ampliada del conocimiento didáctico-matemático del profesor. PARADIGMA, 36(1), 87-109. https://cutt.ly/dRfVXUo
  • Simpson, A., & Haltiwanger, L. (2017). This is the first time I’ve done this: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. Journal of Mathematics Teacher Education, 20(4), 335-355. https://doi.org/10.1007/s10857-016-9352-0
  • Son, J. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84, 49–70. https://doi.org/10.1007/s10649-013-9475-5
  • Stahnke, R., Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision making: a systematic review of empirical mathematics education research. ZDM. Mathematics Education, 48(1-2), 1-27. https://doi.org/10.1007/s11858-016-0775-y
  • Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16, 181-204. https://doi.org/10.1007/PL00020739
  • Van Dooren, W. (2014). Probabilistic thinking: analyses from a psychological perspective. In Chernoff E., Sriraman B. (Eds.), Probabilistic Thinking. Advances in Mathematics Education (pp. 123-126). Springer. https://doi.org/10.1007/978-94-007-7155-0_7
  • Vásquez, C., & Alsina, Á. (2015a). Conocimiento didáctico-matemático del profesorado de educación primaria sobre probabilidad: Diseño, construcción y validación de un instrumento de evaluación. BOLEMA, 29 (52), 681-703. https://doi.org/10.1590/1980-4415v29n52a13
  • Vásquez, C., & Alsina, A. (2015b). El conocimiento del profesorado para enseñar probabilidad: Un análisis global desde el modelo del conocimiento didáctico-matemático. Avances de Investigación en Educación Matemática,7, 27-48. https://doi.org/10.35763/aiem.v1i7.104
  • Watson, J. (2005). The probabilistic reasoning of middle school students. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 145-169). Springer. https://doi.org/10.1007/0-387-24530-8_7
  • Watson, J. M., Collis, K. F., & Moritz, J. B. (2007). The development of chance measurement. In: Stepping Stones for the 21st Century (pp. 113-138). Brill Sense. https://doi.org/10.1163/9789087901509_008