Estudio de fracciones en contextos sonoros

  1. Alexander Conde
  2. Sandra Parada
  3. Vicente Liern
Journal:
Actualidades Investigativas en Educación

ISSN: 1409-4703

Year of publication: 2016

Volume: 16

Issue: 2

Type: Article

DOI: 10.15517/AIE.V16I2.23933 DIALNET GOOGLE SCHOLAR

More publications in: Actualidades Investigativas en Educación

Abstract

Abstract: In this essay we highlight the cognitive links between mathematics and music, which can facilitate teaching and learning processes of fractions in school mathematics. The displayed activities come from a research that promotes sensory experiences in the rhythmic field to favor the construction of mathematical notions. These activities enable a harmonic gear between mathematics and music converging in time and sound as common objects of study between these disciplines. The analysis of the research reported here is the result of the implementation of activities in different teachers' training programs of Mexico and France, related to teaching and learning of mathematics in interdisciplinary contexts. This analysis was developed from three categories concerning the notions of relative unit, part-part relationship, and equipartition, which are fundamental notions for the study of fractions in school mathematics. We found that teaching with unifying approach requires not only specialized knowledge, but a change of beliefs about teachers' opinions on the organization of the curriculum, its teaching and the way in which students learn. A contribution of this experience is providing teachers theoretical and didactic elements for the study of fractions in interdisciplinary contexts.

Bibliographic References

  • Artigue, Michael.. (2002). Learning mathematics in a CAS environment: The genesis of a Reflection about instrumentation and the Dialectics between Technical and Conceptual Work.. International Journal of Computers for Mathematical Learning. 7. 245
  • Conde, Alexander.. (2009). Las fracciones al ritmo de la música.. Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional. México D.F., México.
  • Conde, Alexander.. (2013). Las unidad relativa como vínculo cognitivo entre el tiempo musical y las fracciones.. Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional. México D.F., México.
  • Conde, Alexander, Figueras, Olimpia, Pluvinage, François, Liern, Vicente.. (2011). El sonido de las fracciones: una propuesta interdisciplinaria de enseñanza. Revista Suma. 107
  • Freudenthal, Hans.. (1983). Fenomenología didáctica de las estructuras matemáticas. Departamento de Matemática Educativa del CINVESTAV-IPN.. México D.F..
  • Galperin, Piotr, Georgiev, L.S.. (1969). Soviet studies in the psychology of learning and teaching mathematics. The University of Chicago. Chicago, USA.
  • Gardner, Howard.. (1997). Ithaca Conference '96: Music as Intelligence. Ithaca College Press.. New York, USA.
  • Kieren, Thomas.. (1976). Number and measurement. ERIC/SMEAC. Ohio.
  • Kieren, Thomas.. (1983). Proceedings of the Fourth International Congress on Mathematical Education. Birkhäuser. Estados Unidos.
  • Liern, Vicente. (2011). Música y Matemáticas en educación primaria. 107
  • Naik, Shweta, Subramaniam, K.. (2008). Integrating the measure and quotient interpretation of fractions. International group of the psychology of mathematics education: Proceedings of the Joint Meeting of PME. 32. 17-24
  • Olive, John, Vomvoridi, Eugenia.. (2006). Making sense of instruction on fractions when a student lacks necessary fractional schemes: The case of Tim. Journal of Mathematical Behavior. 25. 18-45
  • Parada, Sandra, Pluvinage, François.. (2014). Reflexiones de profesores de matemáticas sobre aspectos relacionados con su pensamiento didáctico. Revista Latinoamericana de Investigación en Matemática Educativa. 17. 1-31
  • Parada, Sandra, Sacristán, Ana.. (2010). Teachers' reflections on the use of instruments in their mathematics lessons: a case-study.. International group of the psychology of mathematics education: Proceedings of the Joint Meeting of PME. 34. 25-32
  • Piaget, Jean.. (1978). El desarrollo de la noción de tiempo en el niño. Fondo de Cultura Económica. México D.F..
  • Prediger, Susanne, Schink, Andrea.. (2009). International group of the psychology of mathematics education: Proceedings of the Joint Meeting of PME. PME. Thessaloniki, Greece.
  • Rauscher, Frances, Shaw, Gordon, Levine, Linda, Wright, Eric, Dennis, Wendy, Newcomb, Robert.. (1997). Music training causes long-term enhancement of preschool children's spatial-temporal reasoning. Neurological research. 19. 2-8
  • Rauscher, Frances, Zupan, Mary.. (2000). Classroom keyboard instruction improves kindergarten children's spatial-temporal performance: A field experiment.. Early Childhood Research Quarterly. 15. 215
  • Sánchez, María.. (1999). Temporalidad, cronopsicología y diferencias individuales.. Centro de Estudios Ramón Areces. Madrid.
  • Shilling, Wynne.. (2002). Mathematics, music and movement: Exploring concepts and connections. Early Childhood Education Journal. 29. 179
  • Steffe, Leslie, Cobb, Paul, Glasersfeld, Ernst.. (1988). Construction of Arithmetical Meanings and Strategies. Springer-Verlag.. New York.
  • Socas, Martín.. (1997). La Educación Matemática en la Enseñanza Secundaria. Horsori. Barcelona.
  • Still, Kathryn, Bobis, Janette.. (2005). The integration of mathematics and music in the primary school classroom. Annual Conference of the Mathematics Education Research Group of Australasia. Building Connections: Theory, Research and Practice.
  • Tiburcio, Susana.. (2002). Música y matemáticas. Revista Elementos. 8. 21
  • Trouche, Luc.. (2005). The didactical challenge of symbolic calculators. Springer. New York.
  • Tzur, Ron.. (1999). An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning. Journal for Research in Mathematics Education. 30. 390-416
  • Vaughn, Kathryn.. (2000). Music and mathematics: Modest support for the oft-claimed relationship. Journal of Aesthetic Education. 149
  • Vérillon, Pierre, Rabardel, Pierre.. (1995). Cognitions and artifacts: a contribution to the study ofthought in relation to instrument activity. European Journal of Psychology of Education. 10. 77-101
  • Vygotsky, Lev.. (1988). El desarrollo de los procesos psicológicos superiores. Grijalbo. México D.F..
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