PEDAGOGICAL APPROACHES THAT CONNECT MUSIC AND MATHEMATICS
Abstract
Summary: The starting point of the publication is considering methods of music education that potentiate an early music stimulation and the possibility of their implementation and integration in the formation and development of initial mathematical concepts. Aspiration to connect two seemingly incompatible disciplines, music and maths, opens questions whose goal is to find adequate pedagogical approaches that would be in the function of music and mathematics education and achievement, but also the overall development of children. Applying the method of theoretical analysis, a comparison was made among different conceptual approaches, the results of the conducted research and the authors’ conclusions. After considering the aforementioned questions, it was concluded that the considered methods emphasize the importance of an early development in the formation of a person and start from the premise that the potential and the environment enable the children to build themselves. Organising an environment that allows children the freedom by acting through organised and spontaneous activities in kindergarten and school can contribute to children’s musical and mathematical development. Also, connecting musical and mathematical contents with each other, as well as conecting them with everyday activities and setting learning situations in a context that is close and familiar to children, and with the contents of other areas of education and upbringing, provides the basis for successful learning of music and mathematics. Pedagogical implications are contained in aforementioned recommendations for a proper approach to connecting musical and mathematical content and creating a stimulating environment. Future research should be focused on examining and improving the competencies of professionals – teachers and nursery-school teachers, which would be in the function of music and mathematics education and achievement, but also the overall development of children.
References
Barker, A. (2007). The science of harmonics in classical Greece. New York: Cambridge University Press.
Barnett Braun, E. (1973). Montessori & music: Rhythmic activities for young children. New York City. Shocken books.
Baucal, A. (2012). Standardi za rani razvoj i učenje dece ranih uzrasta u Srbiji, Institut za psihologiju Filozofskog fakulteta i UNICEF, Beograd.
Bašić, S. (2011). Modernost pedagoške koncepcije Marije Montessori. Pedagogijska istraživanja, 8(2), 205–216
Beck, M. M.., Rune, L. R., Geertsen, S. S., Ritz, C. G., Lundbye-Jensen, J., & Wienecke, J. (2016). Motor-Enriched Learning Activities Can Improve Mathematical Performance in Preadolescent Children, Frontiers in Human Neuroscience, (10), 1–14.
Beer, M. (1998). How mathematics and music do relates to each other? Brisbone: East Coast College.
Dejić. M., i Mihajlović, A. (2014). Matematička darovitost. Beograd: Učiteljski fakultet.
Dejić, M. (2016). Predškolac u svetu matematike. Beograd: Kreativni centar.
Duh, M. (2009). Interdisciplinarni pristup učenju: put ka kvalitetnijem obrazovanju deteta. Rijeka: Grafika Zambelli.
Fauvel, J., Flood, R. & Wilson, R. J. (2006). Music and mathematics: From Pythagoras to fractals. Oxford: Oxford University Press.
Haroutounian, J. (2002). Kindling the Spark: Recogniying and Developing Musical Talent, Oxford University Press.
Hetland, L. (2000). Learning to make music enhances spatial reasoning. Journal of aesthetic education, 34(3/4), 179–238.
Ivanović, M. (2019). Sistem perceptivnih aktivnosti u unapređenju muzičke percepcije i recepcije kod dece. Doktorska disertacija, Filozofski fakultet, Univerzitet u Novom Sadu.
Kopas Vukašinović, E. (2018). Predškolski programi u Srbiji kao pretpostavka ostvarivanja kvaliteta vaspitne prakse. Unapređivanje kvaliteta i dostupnosti obrazovanja u Srbiji, 69-83.
Lopes, L., Santos, R., Pereira, B., & Lopes, V. P. (2013). Associations between gross motor coordination and academic achievement in elementary school children, Human Movement Science, 32 (1), 9–20.
Marendić, Z. (2009). Teorijski okvir razvijanja početnih matematičkih pojmova u dečjem vrtiću. Metodika 18, 10 (1), 129‒141.
Maričić, S., i Ćalić, M. (2015). Integracija razvoja matematičkih pojmova i muzičkog vaspitanja u predškolskom vaspitanju i obrazovanju posredstvom pesama za pevanje. Godišnjak Učiteljskog fakulteta u Vranju, (6), 317-326.
Martenot, M. (1993). Principios fundamentales de formación musical y su aplicación. Madrid: Rialp.
Matić, E., i Mirković, K. (1986). Muzika i predškolsko dete. Beograd: Zavod za udžbenike i nastavna sredstva.
Matijević, M., i Radovanović, D. (2011). Nastava usmjerena na učenika. Zagreb: Školske novine.
McPherson, G. & Williamon, A. (2006). Giftedness and talent. In: G. McPherson (Ed). The Child As Musician: A Handbook of Musical Development. Oxford University Press. 239–256.
Milić, I., Vukićević, N. (2011). Matematički pojmovi u funkciji upoznavanja ritmičkih trajanja u radu sa decom predškolskog uzrasta. Zbronik radova sa drugog međunarodnog naučno-stručnog skupa Metodički aspekti nastave matematike. Jagodina: Pedagoški fakultet, 289-300.
Milić, I. (2020). Metodički aspekti primene animiranih filmova u muzičkom vaspitanju. U B. Mandić i J. Atanasijević (ur.), Ekspresivnost i intimnost u muzici & Tako male stvari: intimno u umetnosti i kulturi, Knjiga III, Zbornik radova sa XIV međunarodnog naučnog skupa Srpski jezik, književnost, umetnost, 25–27. oktobar 2019, Kragujevac (97–108). Kragujevac: Filološko-umetnički fakultet.
Milinković, J., & Bogavac, D. (2011). Montessori method as a basis for integrated mathematics learning. Metodički obzori, 6(1), 135-143.
Parker, J. J. (1973). Discriminative Listening as a Basis for Problem Solving Among Four–Year–Olds. Dissertation Abstracts International, 33, 8A, 4460–4461.
Paunović, L., Rašković, B., i Gajtanović, Z. (2018). Primena muzičkih sadržaja u usvajanju pojmova o geometrijskim oblicima u predškolskom uzrastu, u. Zbornik radova sa X naučnog skupa Nauka i nastava danas, 77-95.
Popović, D., i Rašković, B. (2022). Pedagoška podrška u razvijanju muzičkih sposobnosti kod dece predškolskog uzrasta. DHS-društvene i humanističke nauke 1 (18) 509-532. DOI 10.51558/2490-3647.2022.7.1.509.
Pravilnik o osnovama programa predškolskog vaspitanja i obrazovanja – Godine uzleta, „Službeni glasnik RS”, br. 88/17 i 27/18 – dr. zakon, Beograd,.
Rajić, S. (2020). Matematika i muzika u funkciji dečjeg razvoja. Doktorska disertacija, Interdisciplinarne doktorske studije istorija i filozofija prirodnih nauka i tehnologije, Univerzitet u Beogradu.
Rauscher. F. H., Shaw, G. L., Ky, K. N. (1995). Listening to Mozart Enhances Spartal-Temporal Reasoning: Toward a Neurophysiological Basis, Neuroscience Letters, 185, 44–47.
Rauscher, F. H. & Zupan,M. A. (2000). Classroom keyboard instruction improves kindergarten children’s spatial-temporal performance: A field experiment.Early childhood research quarterly, 15, 215-228.
Radonjić, S. (1992). Psihologija učenja, Beograd: Zavod za udžbenike i nastavna sredstva.
Radoš, K. (2010). Psihologija muzike (drugo dopunjeno izdanje). Beograd: Zavod za udžbenike.
Rojko, P. (1982). Psihološke osnove intonacije i ritma. Zagreb: Muzička akademija.
Rajović. R. (2012). Kako uspešno razvijati IQ deteta kroz igru. Novi Sad: Smart production.
Savić, J. (2018): Povezanost matematičkih i muzičkih sadražaja u nižim razredima osnovne škole. Inovacije u nastavi. 31 (3), 124 – 139.
Schellenberg, G. E. (2004). Music lessons enhance IQ. Psychological science, 15, 511-514.
Senturk, U., Beyleroglu, M., Guven, F., Yılmaz, A., & Akdenız, H. (2015). Motorskills in pre-school education and effects to 5 year old children’s psychomotor development, Turkish Journal of Sport and Exercise, 17 (2), 42–47.
Slunjski, E. (2011). Kurikulum ranog odgoja-istraživanje i konstrukcija. Zagreb: Školska knjiga.
Stanković, S. (2017). Mogućnosti korelacije fizičkog vaspitanja i matematike u predškolskom uzrastu, Uzdanica, XIV, (1), 197–205.
Stanković, S., i Aleksić Veljković, A. (2021). Motoriče veštine, pokret i matematika. Zbornik radova Metodički aspekti nastave matematike IV. Fakultetu pedagoških nauka u Jagodini, 240‒253.
Tajčević, M. (1997). Osnovna teorija muzike. Beograd: Književno izdavačka zadruga Centar.
Tanasković, M. (2021). Uporedna analiza pristupa muzičkom obrazovanju i metodama Edgara Vilemsa i Morisa Martenoa. Zbornik radova Pedagoškog fakulteta u Užicu br. 23, Univerzitet u Kragujevcu.
Terzić, E. (1998). Analiza i vrednovanje udžbenika muzičke kulture u osnovnoj školi u Mađarskoj i Srbiji. Beograd: Centar za usavršavanje rukovodilaca u obrazovanju.
Vaughn, K. (2000). Music and mathematics: Modest support for the oft-claimed relationship. Journal of aesthetic education, 34(3-4), 149-166.
Wang, C. C. & McCaskill, M. E. (1989). Relating musical abilities to visual-spatial abilities, mathematic and language skills of fifth-grade children. Canadian Journal of Research in Music Education,30, 184-191.
Willems, E. (1964). El ritmo musical. Buenos Aires: Eudeba.
