Sentido numérico en la resolución de problemas en tres profesores en activo
Barra lateral del artículo
Contenido principal del artículo
Resumen
Está documentado que el sentido numérico es de suma importancia para el desarrollo de habilidades aritméticas tempranas, pero son escasos los estudios que abordan este conocimiento en profesores de matemática en servicio. En este estudio nos hemos propuesto analizar las componentes del sentido numérico que activan profesores en ejercicio, cuando enfrentan problemas matemáticos diversos. Desde un enfoque cualitativo, se realiza un estudio de caso múltiple, que nos permite revelar la predominancia de ciertas componentes del sentido numérico. Destaca en los hallazgos la relación entre los niveles de formación matemática del profesorado y la activación de componentes del sentido numérico.
Descargas
Detalles del artículo
Esta obra está bajo una Licencia Creative Commons Atribución 3.0 España
Bibliografía
Almeida, R., & Bruno, A. (2014). Respuestas de estudiantes de secundaria a tareas de sentido numérico. En M. T. González, M. Codes, D. Arnau y T. Ortega (Eds.), Investigación en Educación Matemática XVIII (pp. 127-136). Salamanca: SEIEM.
Almeida, R., Bruno A., & Perdomo, J. (2014). Estrategias de sentido numérico en estudiantes del Grado en Matemáticas. Enseñanza de las Ciencias, 32(2), 0009-34.
Blum, W., & Niss, M. (1991). Applied Mathematical Problem Solving, Modelling, Applications, and Links to Other Subjects. State, Trends and Issues in Mathematics Instruction. Educational Studies in Mathematics, 22, 37-68. https://doi.org/10.1007/BF00302716
Berch, D. B. (2005). Making Sense of Number Sense: Implications for Children With Mathematical Disabilities. Journal of Learning Disabilities, 38(4), 333-339. https://doi.org/10.1177/00222194050380040901
Cain, C., Faulkner, V., & Fanelli, K. (2020). Developing number sense through an exploration of subtraction. Australian Primary Mathematics Classroom, 25(2), 26-30.
Carlson, M. & Bloom, I. (2005). The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving Framework. Educational Studies in Mathematics. 58. 45-75. 10.1007/s10649-005-0808-x.
Courtney-Clarke, M., & Wessels, H. (2014). Number sense of final year preservice primary school teachers. Pythagoras, 35(1), http://dx.doi.org/10.4102/ pythagoras.v35i1.244
DeBellis, V.A., Goldin, G.A.(2006). Affect and Meta-Affect in Mathematical Problem Solving: a Representational Perspective. Educ Stud Math 63, 131–147 . https://doi.org/10.1007/s10649-006-9026-4
Decreto 352 del 2004. Reglamenta ejercicio de la función docente. 9 de octubre de 2003. Obtenida de https://bcn.cl/2w0z8.
Dehaene, S. (2001). Précis of the number sense. Mind & language, 16(1), 16-36.
Faulkner, V. (2009). The components of number sense: An instructional model for teachers. Teaching Exceptional Children, 41(5), 24-30.
Gaona, J., Soledad, S. & Montoya-Delgadillo, E. (2022) Prospective mathematics teachers learning complex numbers using technology, International Journal of Mathematical Education in Science and Technology. https://doi.org/ 10.1080/0020739X.2022.2133021
Ghazali, M., Othman, A. R., Alias, R., & Saleh, F. (2010). Development of teaching models for effective teaching of number sense in the Malaysian primary schools. Procedia-Social and Behavioral Sciences, 8, 344-350.
Gelman, R., & Meck, B. (1992). Early principles aid initial but not later conceptions of number. In J. Bideaud, C. Meljac, & J.-P. Fischer (Eds.), Pathways to number: Children's developing numerical abilities (pp. 171–189). Lawrence Erlbaum Associates, Inc.
Godino, J. D., Font, V., Konic, P., & Wilhelmi, M. R. (2009). El sentido numérico como articulación flexible de los significados parciales de los números. Investigación en el aula de Matemáticas. Sentido Numérico, 117-184.
Goltz, S. M., Hietapelto, A. B., Reinsch, R. W., & Tyrell, S. K. (2008). Enseñar el trabajo en equipo y la resolución de problemas al mismo tiempo. Revista de Educación Gerencial, 32(5), 541-562. https://doi.org/10.1177/1052562907310739
Goos, M., Galbraith, P. & Renshaw, P. (2002) .Socially mediated metacognition: creating collaborative zones of proximal development in small group problem solving. Educational Studies in Mathematics 49, 193–223. https://doi.org/10.1023/A:1016209010120
Greeno, J. G. (1991). Number Sense as Situated Knowing in a Conceptual Domain. Journal for Research in Mathematics Education, 22(3), 170–218. https://doi.org/10.2307/749074
Griffin, S. (2004). Teaching Number Sense. Educational Leadership, 61(5), 39-42.
Guzmán, B., Rodríguez, C., Sepúlveda, F., & Ferreira, R. A. (2019). Number sense abilities, working memory and RAN: A longitudinal approximation of typical and atypical development in Chilean children. Revista de Psicodidáctica (English ed.), 24(1), 62-70.
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the" Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults. Developmental psychology, 44(5), 1457.
Hollebrands, K. F., Conner, A., & Smith, R. C. (2010). The Nature of Arguments Provided by College Geometry Students With Access to Technology While Solving Problems. Journal for Research in Mathematics Education, 41(4), 324–350. http://www.jstor.org/stable/41103879
Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and individual differences, 20(2), 82-88.
Kaminski, E. (1997). Teacher education students' number sense: Initial explorations. Mathematics Education Research Journal, 9(2), 225-235. doi:10.1007/BF03217312
Lewis, K. E., Sweeney, G., Thompson, G. M., & Adler, R. M. (2020). Integer number sense and notation: A case study of a student with a mathematics learning disability. The Journal of Mathematical Behavior, 59, 100797.
Ley 20.370 del 2005. Fija texto refundido, coordinado y sistematizado de la ley nº20.370 con las normas no derogadas del decreto con fuerza de ley nº 1, de 2005. 16 de diciembre 2009. Obtenida de https://bcn.cl/2me2r
Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education. Springer International Publishing. doi: 10.1007/978-3-319-40730-2
Louange, J.E., & Bana, J. (2010). The Relationship between the Number Sense and Problem Solving Abilities of Year 7 Students. Mathematics Education Research Group of Australasia.
Mason, J., Burton, L., & Stacey, K. (1982). Thinking Mathematically. Londres: Addison Wesley.
Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child development, 82(4), 1224-1237.
Mcintosh, A., Reys, B. & Reys, R. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics. 12. 2-8.
Ministerio de Educación (2015). Bases curriculares 7° Básico a 2° Medio.
Ministerio de Educación (2018). Bases curriculares 1° Básico a 6° Básico.
Ministerio de Educación (2019). Bases curriculares 3° y 4° Medio.
NCTM (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
Noviyanti, M., & Suryadi, D. (2019). Conceptualizing mathematical knowledge for teaching of Indonesian teacher in teaching number sense to early childhood. In Journal of Physics: Conference Series (Vol. 1157, No. 3, p. 032121). IOP Publishing, doi:10.1088/1742-6596/1157/3/032121
OECD (2014), PISA 2012 Results: Creative Problem Solving (Volume V): Students' Skills in Tackling Real-Life Problems, PISA, OECD Publishing, Paris, https://doi.org/10.1787/9789264208070-en.
Orrill, C. H., & Brown, R. E. (2012). Making sense of double number lines in professional development: Exploring teachers’ understandings of proportional relationships. Journal of Mathematics Teacher Education, 15, 381-403.
Pólya, G. (1945). How to solve it. New Jersey: Princeton University.
Praet, M., Titeca, D., Ceulemans, D., & Desoete, A. (2013). Number sense in siblings of children with mathematical learning disabilities: A longitudinal study. Journal of Intellectual Disability–Diagnosis and Treatment, 1, 67-73.
Rodríguez-Jara, Miguel, Vergara-Gómez, Andrea, Mondaca-Saavedra, Alejandra, & Gregori-Huerta, Pablo. (2023). Taller de resolución de problemas no rutinarios para estudiantes de 8 a 9 años: un estudio de caso. Uniciencia, 37(1), 519-541. https://dx.doi.org/10.15359/ru.37-1.28
Rodríguez-Nieto, C. A., Font, V., Rodríguez-Vásquez, F. M., & Pino-Fan, L. R. (2023). Onto-semiotic analysis of one teacher’s and university students’ mathematical connections when problem-solving about launching a projectile. Journal on Mathematics Education, 14(3), 563-584.
Sanfiel, L., Díaz, J. P., & Bruno, A. (2021). Relaciones numéricas establecidas por alumnado de primaria. In Investigación en Educación Matemática XXIV (pp. 563-570). Sociedad Española de Investigación en Educación Matemática, SEIEM.
Sengül, S. (2013). Identification of Number Sense Strategies used by Pre-service Elementary Teachers. Educational Sciences: Theory and Practice, 13(3), 1965-1974.
Sianturi, I., Ismail, Z., & Yang, D. -. (2023). Examining fifth graders’ conceptual understanding of numbers and operations using an online three-tier test. Mathematics Education Research Journal, doi:10.1007/s13394-023-00452-2
Sharma, M. (2016, September 19). Working memory: Role in mathematics learning (Part one). Recuperado de: https://mathlanguage.wordpress.com/2016/09/19/working-memory-role-in-mathematics-learning/
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zdm, 3(29), 75-80.
Sowder, J. T., & Schappelle, B. P. (1989). Establishing Foundations for Research on Number Sense and Related Topics: Report of a Conference (San Diego, California, February 16-17, 1989).
Stake, R. E. (2020). Investigación con estudio de casos. Investigación con estudio de casos, 1-156.
Szabo, A., Tillnert, A.-S., Mattsson, J. (2024). Displaying gifted students’ mathematical reasoning during problem solving: Challenges and possibilities Mathematics Enthusiast, 21 (1-2), pp. 179-202. 1) DOI: 10.54870/1551-3440.1623
Tsao, Y.L. (2004). Effects Of A Problem-Solving-Based Mathematics Course On Number Sense Of Preservice Teachers. Journal of College Teaching & Learning (TLC), 1(2). https://doi.org/10.19030/tlc.v1i2.1913
Whitacre, I., & Nickerson, S. D. (2016). Investigating the improvement of prospective elementary teachers’ number sense in reasoning about fraction magnitude. Journal of Mathematics Teacher Education, 19, 57-77.
Yaman, H. (2015). The Mathematics Education I and II Courses' Effect on Teacher Candidates' Development of Number Sense. Educational Sciences: Theory and Practice, 15(4), 1119-1135.
Yang, DC., Li, Mn. & Lin, CI. A (2008). Study of the Performance of 5th Graders in Number Sense and its Relationship to Achievement in Mathematics. Int J of Sci and Math Educ 6, 789–807, https://doi.org/10.1007/s10763-007-9100-0
Yang, D.C., & Hsu, C. J. (2009). Teaching number sense for 6th graders in Taiwan. International Electronic Journal of Mathematics Education, 4(2), 92-109.
Yang, D.C, Reys, R. & Reys, B. (2009). Number Sense Strategies Used by Pre-Service Teachers in Taiwan. International Journal of Science and Mathematics Education. 7. 383-403. 10.1007/s10763-007-9124-5.
Yin, R. K. (2009). Case study research: Design and methods (Vol. 5). Sage.