La notación musical: herramienta para el aprendizaje de las fracciones

  1. Guillermo Luengo 1
  2. Maria T. Sanz 1
  3. Carlos Valenzuela 2
  4. Emilia López-Iñesta 1
  1. 1 Departamento Didáctica de la Matemática, Universidad de Valencia
  2. 2 Departamento de Matemáticas, Universidad de Guadalajara
Revista:
Educación matemática

ISSN: 1665-5826,  0187-8298

Año de publicación: 2024

Volumen: 36

Número: 1

Páginas: 187-221

Tipo: Artículo

DOI: 10.24844/EM3601.07 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Educación matemática

Resumen

En este estudio se examinó el efecto de una intervención académica, asociada a la música, sobre la comprensión conceptual de la notación musical y la representación, orden, equivalencia y adición de fracciones de estudiantes de primero de Educación Secundaria Obligatoria (ESO) de un centro escolar público multicultural y socioeconómico mixto español. Los estudiantes (N= 12) tenían conceptos previos acerca de instrucción musical, así como de los con ceptos a evaluar sobre fracciones. Se trata de un estudio observacional en el que se les administró una batería de cuatro tareas antes y después de una instrucción basada en un entorno musical, siendo la notación musical función semiótica. La instrucción contó con 9 sesiones de 50 minutos cada una. Los resultados previos a la intervención evidencian carencias en un concepto que no era nuevo para el alumnado, sin embargo, tras la intervención, el alumnado se vio competente en todos los conceptos. En particular, la notación musical fue un instrumento utilizado de forma potencial como soporte para la representación, ordenación y equivalencia de las fracciones.

Referencias bibliográficas

  • Adiel, M. (2021). Agrega Suma y resta de fracciones no homogéneas [[Web; accedido el 10-06-2021]]. http://agrega.educacion.es/visualizar/es/es_2013120913_9122920/false
  • An, S., Capraro, M. M., & Tillman, D. A. (2013). Elementary Teachers Integrate Music Activities into Regular Mathematics Lessons: Effects on Students’ Mathematical Abilities. Journal for Learning through the Arts, 9(1), n1. https://doi.org/10.21977/D99112867
  • An, S. A., & Tillman, D. A. (2015). Music activities as a meaningful context for teaching elementary students mathematics: A quasi-experiment time series design with random assigned control group. European Journal of Science and Mathematics Education, 3(1), 45–60.
  • Arzarello, F., (2006). Semiosis as a Multimodal Process. Revista Latinoamericana de Investigación en Matemática Educativa, RELIME, (Esp), 267-299. https://www.redalyc. org/comocitar.oa?id=33509913
  • Arzarello, F. (2015). Semiosis as a multimodal process. Revista Latinamericana de Investigación en Matemática Educativa (RELIME), 9(1), 267–300, http://math.unipa.it/~grim/YESS-5/arzarello%20relime.pdf
  • Azaryahu, L., Courey, S.J., Elkoshi, R., & Adi-Japha, E. (2020). ‘MusiMath’ and ‘Academic Music’ – Two music-based intervention programs for fractions learning in fourth grade students. Development Science , 23(4), e12882. https://doi.org/10.1111/ desc.12882
  • Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–333). Macmillan.
  • Behr, M., Lesh, R., Post, T., & Silver E. (1983). Rational Number Concepts. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91-125). Academic Press.
  • Braithwaite, D. W., Tian, J., & Siegler, R. S. (2017) Do children understand fraction addition? Developmental Science, 21(4), 1-9. https://doi.org/10.1111/desc.12601
  • Brown, G. & Quinn, R. J. (2006). Algebra students’ difficulty with fractions: An error analysis. The Australian Mathematics Teacher, 62(4), 28-40. https://files.eric.ed.gov/fulltext/ EJ765838.pdf
  • Carpenter, T. P., Coburn, T. G., Reys, R. E., & Wilson, J. W. (1976). Using research in teaching: Notes from National Assessment: addition and multiplication with fractions, The Arithmetic Teacher, 23(2), 137-142. https://pubs.nctm.org/view/journals/at/23/2/article-p137.xml
  • Castrillón, M., Gil, O., & Vázquez, M.J. (2019). Engineering and Mathematics: harmonies. Mathematical Thought, 9(2), 37–48. https://dialnet.unirioja.es/descarga/articulo/7552162.pdf
  • Ciscar, S. L., & Garcia, M. V. S. (1997). Fractions: The part-whole relationship. Synthesis. Clarke, D. M. & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127-138. https://doi.org/10.1007/s10649-009-9198-9
  • Cramer, K., & Henry, A. (2002). Using Manipulative Models to Build Number Sense for Addition of Fractions. In B. Litwiller & G. Bright (Eds.), Making Sense of Fractions, Ratios, and Proportions: 2002 Yearbook (pp. 41-48). National Council of Teachers of Mathematics.
  • Cramer, K., Post, T. & delMas, R. (2002). Initial Fraction Learning by Fourthand Fif th-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum. Journal for Research in Mathematics Education, 33(2),111-144. https://doi.org/10.2307/749646
  • Colera, J., & Gaztelu, I. (2020). Mathematics 1. Anaya. Courey, S. J., Balogh, E., Siker, J. R., & Paik, J. (2012). Academic music: music instruction to engage third-grade students in learning basic fraction concepts. Educational Studies in Mathematics, 81, 251–278. https://doi.org/10.1007/s10649-012-9395-9
  • Cuchillo, E. (2020). Matemáticas 1º E.S.O. Marea Verde. Edelson, R. J., & Johnson, G. (2003). Music makes math meaningful. Childhood Education, 80(2), 65–70. https://doi.org/10.1080/00094056.2004.10521259
  • Godino, J. D. (2004). Didáctica de las Matemáticas para Maestros. Proyecto Edumat-Maestros.
  • Hart, K. (1981). Fractions. Mathematics in School, 10(2), 13-15.
  • Hamilton, T. J., Doai, J., Milne, A., Saisanas, V., Calilhanna, A., Hilton, C., Goldwater, M, & Cohn, R. (2018). Teaching mathematics with music: A pilot study. Proceedings of 2018 -EEE International Conference on Teaching, Assessment, and Learning for Engineering (TALE) (pp. 927-931). Wollongong, NSW, Autralia. https://doi.org/10.1109/ TALE.2018.8615262
  • Harkleroad, L. (2006). The math behind the music . Cambridge University Press
  • Howard, A. C. (1991). Addition of Fractions—the Unrecognized Problem, The Mathematics Teacher, 84(9), 710–713. https://pubs.nctm.org/view/journals/mt/84/9/article-p710.xml
  • Kamii, C., & Vlark, F. B. (1995). Equivalent fractions: Their difficulty and educational implications. The Journal of Mathematical Behaviour, 14(4). 365-378. https://doi. org/10.1016/0732-3123(95)90035-7
  • Keller, M. W., Shreve, D. R. & Remmers, H. H. (1940). Diagnostic Testing Program in Purdue University. The American Mathematical Monthly, 47(8), 544-548.
  • Kennedy, L. M., & Steve, T. (1997). Guiding children’s learning of mathematics (8th ed.). Wadsworth/Thomson.
  • Kerslake, D. (1986). Fractions: Children’s Strategies and Errors. A Report of the Strategies and Errors in Secondary Mathematics Project. NFER-NELSON Publishing Company.
  • Kieren, T. (1980). The rational number constructs. Its elements and mechanisms. In T. Kieren (Ed.) Recent Research on Number Learning (pp. 125–149). Eric/smeac.
  • Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 49–84). Lawrence Erlbaum Associates, Inc.
  • Johnson, G. L., & Edelson, R. J. (2003). Integrating music and mathematics in the elementary classroom. Teaching Children Mathematics, 9(8), 474-479. https://link.gale.com/ apps/doc/A99618634/AONE?u=anon~80f1fa43&sid=googleScholar&xid=8489d361
  • LOMLOE. (2022). Spanishc Organic Law 3/2020, of December 29, which modifies Organic Law 2/2006, of May 3, on Education.
  • Lovemore, T., Robertson, S. A., & Graven, M. (2022). Task design grapplings in integrating music and fraction representations. In K.R. Langenhoven & C.H. Stevenson-Milln (Eds.) Book of Proceedings of the 30th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education (pp. 49–61). SAARMSTE.
  • Malet, O. (2010). Los significados de las fracciones: una perspectiva fenomenológica. Revista Mendom@tica, 21, 1-10.
  • Mall, P., Spychiger, M., Vogel, R., & Zerlik, J. (2016). European Music Portfolio (EMP)Maths:’Sounding Ways into Mathematics’: A Manual for Teachers. Frankfurt University of Music and Performing Arts. http://maths.emportfolio.eu/images/deliverables/ Teacher_Handbook_Spanish_Version.pdf
  • Maza, C. (1999). Equivalencia y orden: la enseñanza de la comparación de fracciones. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, 31, 87-95.
  • Maza, C. & Arce, C. (1991). Ordenar y clasificar. Sínstesis. Mata, L. E. & Porcel, E. A. (2006). Análisis de los errores cometidos en el algoritmo de la Suma de Fracciones por ingresantes a la Fa.C.E.N.A . Universidad Nacional del Nordeste.
  • McDonel, J. S. (2015). Exploring learning connections between music and mathematics in early childhood. Bulletin of the Council for Research in Music Education, (203), 45-62. https://doi.org/10.5406/bulcouresmusedu.203.0045
  • Meneses, J. & Rodrıíguez-Gómez, D. (2011). El cuestionario y la entrevista. Universitat Oberta de Catalunya. https://femrecerca.cat/meneses/publication/cuestionario-entrevista/cuestionario-entrevista.pdf
  • Morales, Z. (2014). Analysis of students’ misconceptions and error patterns in mathematics: The case of fractions. South Florida Education Research Conference, 32, 1-10. https://digitalcommons.fiu.edu/cgi/viewcontent.cgi?article=1350&context=sferc
  • NAEP] (2013). National Assessment of Educational Progress. Retrieved March 1, 2020, from https://nces.ed.gov/NationsReportCard/nqt/Search
  • Oshanova, N. T., Shekerbekova, S. T., Sagimbaeva, A. E., Arynova, G. C., & Kazhiakparova, Z. S. (2022). Methods and techniques of formation of arithmetic musical competence in students. International Journal of Learning and Change, 14(1), 46-56. https://doi. org/10.1504/IJLC.2022.119530
  • Piaget, J. (1962). The stages of the intellectual development of the child. Bulletin of the Menninger Clinic , 26(3), 120–128.
  • Rau, M. A., Aleven, V., & Rummel, N. (2015). Successful learning with multiple graphical representations and self-explanation prompts. Journal of Educational Psychology, 107(1), 30-46. https://doi.org/10.1037/a0037211
  • Ribeiro, F. S., & Santos, F. H. (2017). Enhancement of numeric cognition in children with low achievement in mathematic after a non-instrumental musical training. Research in Developmental Disabilities, 62(January), 26–39. https://doi.org/10.1016/j. ridd.2016.11.008
  • Rico, L. (1997). Mathematics education in secondary education. Horsori. Sidney, P. G., Thompson, C. A., & Rivera, F. D. (2019). Number lines, but not area models, support children’s accuracy and conceptual models of fraction division. Contemporary Educational Psychology, 58, 288–298. https://doi.org/10.1016/j.cedpsych.2019.03.011
  • Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE #2010-4039). National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, US Department of Education. Retrieved from whatworks.ed.gov/publications/practiceguides.
  • Siegler, R., Fazio, L., Bailey, D., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in cognitive sciences, 17(1), 13–19.
  • UE. (2011). The Lifelong Learning Programme: education and training opportunities for all [Access: 02/15/2023]. https://eur-lex.europa.eu/EN/legal-content/summary/lifelong-learning-programme-2007-13.html
  • van Beethoven, L. (1824). Sinfonía n.° 9, la Oda a la alegría. Viena.
  • Veraksa, N., Colliver, Y., & Sukhikh, V. (2022). Piaget and Vygotsky’s Play Theories: The Profile of Twenty-First-Century Evidence. In N. Veraksa & I. P. Samuelsson (Eds.) Piaget and Vygotsky in the XXI century. Discourse in early childhood education (pp. 165–190). Springer.
  • Vinner, S., Hershkowitz, R., & Bruckheimer, M. (1981). A Forum for Researchers: Some Cognitive Factors as Causes of Mistakes in the Addition of Fractions. Journal for Research in Mathematics Education, 12(1), 70-76. https://doi.org/10.5951/jresematheduc.12.1.0070
  • Wilson, R. J., Flood, R., & Fauvel, J. (2003). Music and mathematics: From Pythagoras to fractals. Oxford University Press.
Fuente de los datos: Dialnet