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Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 25 No. 1 (2022): March

DIFFERENT PROFILE OF COGNITIVE FLEXIBILITY IN BRAZILIAN STUDENTS OF 2ND AND 4TH YEARS OF ENSINO FUNDAMENTAL

DOI
https://doi.org/10.12802/relime.2022.76
Submitted
November 8, 2022
Published
2022-03-31

Abstract

This article aims to identify, characterize and compare the cognitive flexibility profile of the mental calculations of Brazilian students, based on the analysis of cognitive elements, namely the characteristics of the problems and the solution procedures, used during the resolution of problems. arithmetic calculations. The sample for this study included 42 second-year students (7 to 8 years old) and 42 fourth-year students (9 to 11 years old), from four public schools in Porto Alegre. Each child was encouraged to classify 12 arithmetic calculations, demonstrating their numerical knowledge by explaining the reasoning involved in solving, through a specific assessment instrument on cognitive flexibility. The results revealed that the differences in the proportions of use of numerical knowledge differentiated the profiles of cognitive flexibility: flexible, mixed or rigid.

References

  1. Andrews, P., Sunde, P. B., Nosrati, M., Petersson, J., Rosenqvist, E., Sayers, J. e Xenofontos, C. (2021). Computational Estimation and Mathematics Education: A Narrative Literature Review. Journal of Mathematics Education, 14(1), 6-27. https://doi.org/10.26711/007577152790061
  2. Aunio, P. (2019). Early Numeracy Skills Learning and Learning Difficulties - Evidence-based Assessment and Interventions. Em Geary, D. C., Berch, D. B. e Koepke, K. M. (Eds.). Cognitive Foundations for Improving Mathematical Learning (pp. 195-214). Academic Press. https://doi.org/10.1016/B978-0-12-815952-1.00008-6
  3. Aunio, P. e Räsänen, P. (2015). Core numerical skills for learning mathematics in children aged five to eight years–a working model for educators. European Early Childhood Education Research Journal, 24(5), 684-704. https://doi.org/10.1080/1350293X.2014.996424
  4. Brasil. (2021a). Resultados do Índice de Desenvolvimento da Educação Básica: resumo técnico. Brasília, Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira.
  5. Brasil. (2021b). Relatório de resultados do Saeb 2019: volume 1: 5o e 9o anos do Ensino Fundamental e séries finais do Ensino Médio. Brasília, Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira.
  6. Buys, K. (2001). Mental arithmetic. In van den Heuvel-Panhuizen, M. (Ed.), Children learn mathematics (pp. 121-146). Rotterdam, The Netherlands: Sense Publishers.
  7. Carvalho, R., e Rodrigues, M. (2021). Day number routine: An opportunity to understand students’ uses of numbers and operations. Journal of Mathematics Education, 14(1), 28-46. https://doi.org/10.26711/007577152790062.
  8. Caviola, S., Mammarella, I. C., Pastore, M. e Lefevre, J. A. (2018). Children’s strategy choices on complex subtraction problems: Individual differences and developmental changes. Frontiers in psychology, 9, Article 1209. https://doi.org/10.3389/fpsyg.2018.01209.
  9. Ching, B. H.-H. e Nunes, T. (2017). The Importance of Additive Reasoning in Children’s Mathematical Achievement: A Longitudinal Study. Journal of Educational Psychology, 109(4), 477-508. https://doi.org/10.1037/edu0000154.
  10. Heirdsfield, A. M. e Cooper, T. J. (2004). Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers. The Journal of Mathematical Behavior, 23(4), 443-463. https://doi.org/10.1016/j.jmathb.2004.09.005.
  11. Heinze, A., Grüßing, M., Arend, J. e Lipowsky, F. (2020). Fostering Children’s Adaptive Use of Mental Arithmetic Strategies: A Comparison of Two Instructional Approaches. Journal of Mathematics Education, 13(1), 18-34. https://doi.org/10.26711/007577152790052.
  12. Korten, L. (2020). Developing Flexibility in Mental Arithmetic in Interactive-Cooperative Learning Situations: Interaction as an Occasion for Productive Learning Processes. Journal of Mathematics Education, 13(1), 73-94. https://doi.org/10.26711/007577152790055.
  13. McMullen, J., Brezovszky, B., Hannula-Sormunen, M. M., Veermans, K., Rodríguez-Aflecht, G., Pongsakdi, N. e Lehtinen, E. (2017). Adaptive number knowledge and its relation to arithmetic and pre-algebra knowledge. Learning and Instruction, 49, 178-187. http://dx.doi.org/10.1016/j.learninstruc.2017.02.001.
  14. McMullen, J., Brezovszky, B., Rodríguez-Aflecht, G., Pongsakdi, N., Hannula-Sormunen, M. M. e Lehtinen, E. (2016). Adaptive number knowledge: Exploring the foundations of adaptivity with whole-number arithmetic. Learning and Individual Differences, 47, 172-181. https://doi.org/10.1016/j.lindif.2016.02.007.
  15. Mendes, M. F. P. C. (2012). A aprendizagem da multiplicação numa perspectiva de desenvolvimento do sentido de número: um estudo com alunos do 1. º ciclo [Tese de Doutorado, Instituto de Educação da Universidade de Lisboa]. Repositório da Universidade de Lisboa. http://hdl.handle.net/10451/5893.
  16. Rechtsteiner-Merz, C. e Rathgeb-Schnierer, E. (2015). Flexible mental calculation and "Zahlenblickschulung". Em K. Krainer e N. Vondrová (Eds.), Proceedings of the Ninth Conference of the European Society for Research in Mathematics Education (pp. 354-360). Charles University in Prague, Faculty of Education and ERME. https://hal.inria.fr/CERME9-TWG02/hal-01281864v1.
  17. Rathgeb-Schnierer, E. e Green, M. (2013). Flexibility in mental calculation in elementary students from different math classes. Em Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (pp. 353-362). Middle East Technical University and ERME. http://cerme8.metu.edu.tr/wgpapers/WG2/WG2_Rathgeb_Schnierer.pdf.
  18. Rathgeb-Schnierer, E. e Green, M. (2015). Cognitive flexibility and reasoning patterns in American and German elementary students when sorting addition and subtraction problems [Conference presentation]. CERME 9-Ninth Congress of the European Society for Research in Mathematics Education, Prague, Czech Republic.
  19. Rathgeb-Schnierer, E. e Green, M. (2017). Profiles of cognitive flexibility in arithmetic reasoning: A cross-country comparison of German and American elementary students. Journal of Mathematics Education, 10(1), 1-16. https://doi.org/10.26711/007577152790009.
  20. Rathgeb-Schnierer, E. e Green, M. (2019). Desenvolvendo Flexibilidade no Cálculo Mental. Educação e Realidade, 44(2), Article e87078. http://dx.doi.org/10.1590/2175-623687078.
  21. Serrazina, M. D. L. e Rodrigues, M. (2017). 'Day number': A promoter routine of flexibility and conceptual understanding. Journal of Mathematics Education, 10, 67-82. https://doi.org/10.26711/007577152790013.
  22. Serrazina, L. e Rodrigues, M. (2021). Number sense and flexibility of calculation: A common focus on number relations. Em Spinillo, A.G., Lautert, S.L. e Borba, R.E.d.S.R. (eds). Mathematical Reasoning of Children and Adults (pp. 19-40). Springer, Cham. https://doi.org/10.1007/978-3-030-69657-3_2.
  23. Spinillo, A. G. (2014). Usos e funções do número em situações do cotidiano. Em Brasil. Pacto Nacional pela Alfabetização na Idade Certa: Quantificações, registros e agrupamentos (pp. 20-29). Ministério da Educação, Secretaria da Educação Básica.
  24. Star, J. R., Newton, K., Pollack, C., Kokka, K., Rittle-Johnson, B. e Durkin, K. (2015). Student, teacher, and instructional characteristics related to students' gains in flexibility. Contemporary Educational Psychology, 41, 198-208. https://doi.org/10.1016/j.cedpsych.2015.03.001.
  25. Stein, L. M. (1994). TDE: teste de desempenho escolar: manual para aplicação e interpretação. São Paulo: Casa do Psicólogo.
  26. Thompson, I. (1999). Mental calculation strategies for addition and subtraction. Part 1. Mathematics in school, 28(5), 2-4. http://www.jstor.org/stable/30215422.
  27. Threlfall, J. (2002). Flexible mental calculation. Educational studies in Mathematics, 50(1), 29-47. https://link.springer.com/article/10.1023/A:1020572803437.
  28. Threlfall, J. (2009). Strategies and flexibility in mental calculation. ZDM, 41(5), 541-555. https://link.springer.com/article/10.1007/s11858-009-0195-3.
  29. Verschaffel, L., Greer, B. e de Corte, E. (2007). Whole number concepts and operations. Em F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). Reston, VA: NCTM.

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