Doing mathematics with music – Creating epistemic environments

Ana Cristina Azevedo da Silva; Maria Cecília Costa; Joaquim Bernardino Lopes

doi:10.29333/ejmste/12034

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Ana Cristina Azevedo da Silva ¹ ^* , Maria Cecília Costa ² ³ , Joaquim Bernardino Lopes ² ³

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¹ Celorico de Basto School Group, PORTUGAL² UTAD, University of Trás-os-Montes and Alto Douro, Vila Real, PORTUGAL³ CIDTFF–Research Center in Didactics and Technology in Training of Trainers, Aveiro, PORTUGAL^* Corresponding Author

Abstract

It is rare to turn music into a mathematical object in an educational context, although the benefit of the articulation between mathematics and music is recognized. The present study focuses on the epistemic environment created for students to do maths with music. The methodological approach had two components: an exploratory one to study the relationships between the epistemic environment experienced by students and the epistemic levels at which they do mathematics, and a quasi-experimental one to assess the effectiveness of intervention in student learning. Three groups took part in the study. The “doing maths with music” approach is more effective than conventional ones whether, or not, students have in-depth musical knowledge. On the other hand, educational artefacts used by students allowed them to deal with music at various epistemic levels, with relevant relationships between the quality of students’ epistemic activity and the profile of epistemic levels.

Keywords

artefacts
epistemic levels
instrumental orchestration
learning
performance
teaching

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2022, Volume 18, Issue 5, Article No: em2111

https://doi.org/10.29333/ejmste/12034

Publication date: 20 Apr 2022

Article Views: 1380

Article Downloads: 1170

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

An, S. A., Kulm, G. O., & Ma, T. (2008). The effects of a music composition activity on Chinese students’ attitudes and beliefs towards mathematics: An exploratory study. Journal of Mathematics Education, 1(1), 91-108.
Asterhan, C. S., & Schwarz, B. B. (2016). Argumentation for learning: Well-trodden paths and unexplored territories. Educational Psychologist, 51(2), 164-187. https://doi.org/10.1080/00461520.2016.1155458
Branchetti, L., & Morselli, F. (2019). The interplay of rationality and identity in a mathematical group work. In M. S. Hannula, G. C. Leder, F. Morselli, M. Vollstedt, & Q. Zhang (Eds.), Affect and mathematics education (pp. 323-344). Springer. https://doi.org/10.1007/978-3-030-13761-8_15
Cartiff, B. M., Duke, R. F., & Greene, J. A. (2021). The effect of epistemic cognition interventions on academic achievement: A meta-analysis. Journal of Educational Psychology, 113(3), 477-498. https://doi.org/10.1037/edu0000490
Chao-Fernández, R., Román-García, S., & Chao-Fernández, A. (2017). Art, science and magic: Music and math the classroom. In Proceedings of the 5^th International Conference on Technological Ecosystems for Enhancing Multiculturality (p. 77). ACM. https://doi.org/10.1145/3144826.3145427
Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213-234.
Drijvers, P., Grauwin, S., & Trouche, L. (2020). When bibliometrics met mathematics education research: the case of instrumental orchestration. ZDM Mathematics Education, 52, 1455-1469. https://doi.org/10.1007/s11858-020-01169-3
Edelson, R. J., & Johnson, G. (2003). Music makes math meaningful. Childhood Education, 80(2), 65-70. https://doi.org/10.1080/00094056.2004.10521259
Elofsson, J., Englund Bohm, A., Jeppsson, C., & Samuelsson, J. (2018). Physical activity and music to support pre-school children’s mathematics learning. Education 3-13, 46(5), 483-493. https://doi.org/10.1080/03004279.2016.1273250
Gardiner, M. F., Fox, A., Knowles, F., & Jeffrey, D. (1996). Learning improved by arts training. Nature, 381(6580), 284. https://doi.org/10.1038/381284a0
Goizueta, M. (2019). Epistemic issues in classroom mathematical activity: There is more to students’ conversations than meets the teacher’s ear. The Journal of Mathematical Behavior, 55, 100691. https://doi.org/10.1016/j.jmathb.2019.01.007
Graziano, A. B., Peterson, M., & Shaw, G. L. (1999). Enhanced learning of proportional math through music training and spatial-temporal training. Neurological Research, 21(2), 139-152. https://doi.org/10.1080/01616412.1999.11740910
Guin, D., & Trouche, L. (2002). Mastering by the teacher of the instrumental genesis in CAS environments: Necessity of instrumental orchestrations. Zentralblatt für Didaktik der Mathematik [Central Journal for Didactics of Mathematics], 34(5), 204-211. https://doi.org/10.1007/BF02655823
Hadamard, J. (1945). The psychology of invention in the mathematical field. Dover Publications.
Hallam, S., & Price, J. (1998). Research section: Can the use of background music improve the behaviour and academic performance of children with emotional and behavioural difficulties? British Journal of Special Education, 25(2), 88-91. https://doi.org/10.1111/1467-8527.t01-1-00063
Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32(2), 195-222. https://doi.org/10.2307/749673
Hodges, D. A. (2005). Why study music? International Journal of Music Education, 23(2), 111-115. https://doi.org/10.1177/0255761405052403
Hudson, B. (2019). Epistemic quality for equitable access to quality education in school mathematics. Journal of Curriculum Studies, 51(4), 437-456. https://doi.org/10.1080/00220272.2019.1618917
Kämäräinen, A., Björn, P., Eronen, L., & Kärnä, E. (2019). Managing epistemic imbalances in peer interaction during mathematics lessons. Discourse Studies, 21(3), 280-299. https://doi.org/10.1177/1461445619829236
Kelly, G. J., & Takao, A. (2002). Epistemic levels in argument: An analysis of university oceanography students’ use of evidence in writing. Science Education, 86(3), 314-342. https://doi.org/10.1002/sce.10024
Lee, S. W. Y., Wu, H. K., & Chang, H. Y. (2021). Examining secondary school students’ views of model evaluation through an integrated framework of personal epistemology. Instructional Science, 49, 223-248. https://doi.org/10.1007/s11251-021-09534-9
Lerman, S. (2001). Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics, 46(1), 87-113. https://doi.org/10.1023/A:1014031004832
Lopes, J. B. (2019). Visual representation Artefacts used as epistemic tools to improve the quality of mathematics and science teaching practices. In B. Vogler (Ed.), Teaching practices - Implementation, challenges and outcomes (pp. 45-74). Nova Science Publishers.
Lopes, J. B., & Costa, C. (2019). Digital resources in science, mathematics and technology teaching how to convert them into tools to learn. In International Conference on Technology and Innovation in Learning, Teaching and Education (pp. 243-255). Springer, Cham.
Lopes, J. B., Branco, J., & Jimenez-Aleixandre, M. P. (2011). 'Learning experience' provided by science teaching practice in a classroom and the development of students' competences. Research in Science Education, 41(5), 787-809.
Lopes, J. B., Silva, A. A., Cravino, J. P., Santos, C. A., Cunha, A., Pinto, A., Silva, A., Viegas, C., Saraiva, E., & Branco, M. J. (2014). Constructing and using multimodal narratives to research in science education: contributions based on practical classroom. Research in Science Education, 44(3), 415-438.
Mannone, M. (2019). Have fun with math and music! In Proceedings of the International Conference on Mathematics and Computation in Music (pp. 379-382). Springer. https://doi.org/10.1007/978-3-030-21392-3_33
McLaughlan, R., & Lodge, J. M. (2019). Facilitating epistemic fluency through design thinking: A strategy for the broader application of studio pedagogy within higher education. Teaching in Higher Education, 24(1), 81-97. https://doi.org/10.1080/13562517.2018.1461621
Mersenne, F. (1637). Harmonie universelle, contenant la theorie et la pratique de musique [Universal harmony, containing the theory and practice of music]. Editions du Centre National de la Recherche Scientifique [Editions of the National Center for Scientific Research].
Mishiwo, M. (2021). Effect of mathematics method course on pre-service teachers’ knowledge of content and teaching fractions. British Journal of Education, 9(7), 1-13.
Monaghan, J., Trouche, L., & Borwein, J. M. (2016). Tools and mathematics. Springer. https://doi.org/10.1007/978-3-319-02396-0
Muis, K. R., & Duffy, M. C. (2013). Epistemic climate and epistemic change: Instruction designed to change students’ beliefs and learning strategies and improve achievement. Journal of Educational Psychology, 105(1), 213-225. https://doi.org/10.1037/a0029690
Mun, R. U., Hertzog, N. B. (2018). Teaching and learning in STEM enrichment spaces: From doing math to thinking mathematically. Roeper Review, 40(2), 121-129. https://doi.org/10.1080/02783193.2018.1434713
Ndemo, Z., & Mtetwa, D. (2021). Mathematics education undergraduates’ personal definitions of the notion of angle of contiguity in Kinematics. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(2), 111-127. https://doi.org/10.23917/jramathedu.v6i2.11130
Peterson, I. (1985). Some labs are alive with...: The sound of data. Science News, 127(22), 348-350. https://doi.org/10.2307/3969629
Quinn, C. M., Smith, D. K., Chappell, M. F., Carver, S. D., Duffy, S., Holcomb, J. P., Jackson, D. & Resnick, A. (2019). Music as math waves: Exploring trigonometry through sound. Journal of Mathematics and the Arts, 13(1-2), 173-184, https://doi.org/10.1080/17513472.2018.1552822
Root-Bernstein, R. S. (2001). Music, creativity and scientific thinking. Leonardo, 34(1), 63-68. https://doi.org/10.1162/002409401300052532
Schwarz, B. B., Prusak, N., Swidan, O., Livny, A., Gal, K., & Segal, A. (2018). Orchestrating the emergence of conceptual learning: A case study in a geometry class. International Journal of Computer-Supported Collaborative Learning, 13(2), 189-211. https://doi.org/10.1007/s11412-018-9276-z
Sezen‐Barrie, A., Stapleton, M. K., & Marbach‐Ad, G. (2020). Science teachers’ sensemaking of the use of epistemic tools to scaffold students’ knowledge (re) construction in classrooms. Journal of Research in Science Teaching, 57(7), 1058-1092. https://doi.org/10.1002/tea.21621
Silva A., Bernardino Lopes J., Costa C. (2021) Doing math with music - Instrumental orchestration. In A. Reis, J. Barroso, J. B. Lopes, T. Mikropoulos, & C. W. Fan (Eds.), Technology and innovation in learning, teaching and education. TECH-EDU 2020. Communications in Computer and Information Science, vol 1384. Springer, Cham. https://doi.org/10.1007/978-3-030-73988-1_8
Stroupe, D., Moon, J., & Michaels, S. (2019). Introduction to special issue: Epistemic tools in science education. Science Education, 103, 948-951. https://doi.org/10.1002/sce.21512
Svahn, J., & Bowden, H. M. (2021). Interactional and epistemic challenges in students’ help-seeking in sessions of mathematical homework support: presenting the problem. Classroom Discourse, 12(3), 193-213. https://doi.org/10.1080/19463014.2019.1686998
Švaříček, R. (2019). The role of the teacher in supporting students’ epistemic thinking in dialogic argumentation. A case study. Studia Paedagogica [Studies in Pedagogy], 24(4), 143-171. https://doi.org/10.5817/SP2019-4-7
Sylvester, J. J. (1864). XVII algebraical researches, containing a disquisition on Newton’s rule for the discovery of imaginary roots. Philosophical Transactions of the Royal Society of London, 154, 579-666. https://doi.org/10.1098/rstl.1864.0017
Thayer-Morel, T., Venegas-Thayer, M. A., & Tejada-Giménez, J. (2018). Recursos informáticos para el aprendizaje de las matemáticas mediante metáforas musicales: El proceso de creación y evaluación de PicaLab [Computer resources for learning mathematics through musical metaphors: The PicaLab creation and evaluation process]. Estudios Pedagógicos [Pedagogical Studies], 44(1), 351-376. https://doi.org/10.4067/S0718-07052018000100351
Turkka, J., Haatainen, O., Aksela, M. (2017). Integrating art into science education: A survey of science teachers’ practices. International Journal of Science Education, 39(10), 1403-1419. https://doi.org/10.1080/09500693.2017.1333656
Viladot, L., Hilton, C., Casals, A., Saunders, J., Carrillo, C., Henley, J., Gonzalez-Martin, C., Prat, M., & Welch, G. (2018). The integration of music and mathematics education in Catalonia and England: Perspectives on theory and practice. Music Education Research, 20(1), 71-82. https://doi.org/10.1080/14613808.2017.1290595
Wilhelmi, M. R., & Montiel, M. (2019, June). Integrated music and math projects in secondary education. In Proceedings of the International Conference on Mathematics and Computation in Music (pp. 390-393). Springer. https://doi.org/10.1007/978-3-030-21392-3_35

How to cite this article

APA

Silva, A. C. A. D., Costa, M. C., & Lopes, J. B. (2022). Doing mathematics with music – Creating epistemic environments. Eurasia Journal of Mathematics, Science and Technology Education, 18(5), em2111. https://doi.org/10.29333/ejmste/12034

Vancouver

Silva ACAD, Costa MC, Lopes JB. Doing mathematics with music – Creating epistemic environments. EURASIA J Math Sci Tech Ed. 2022;18(5):em2111. https://doi.org/10.29333/ejmste/12034

AMA

Silva ACAD, Costa MC, Lopes JB. Doing mathematics with music – Creating epistemic environments. EURASIA J Math Sci Tech Ed. 2022;18(5), em2111. https://doi.org/10.29333/ejmste/12034

Chicago

Silva, Ana Cristina Azevedo da, Maria Cecília Costa, and Joaquim Bernardino Lopes. "Doing mathematics with music – Creating epistemic environments". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 5 (2022): em2111. https://doi.org/10.29333/ejmste/12034

Harvard

Silva, A. C. A. D., Costa, M. C., and Lopes, J. B. (2022). Doing mathematics with music – Creating epistemic environments. Eurasia Journal of Mathematics, Science and Technology Education, 18(5), em2111. https://doi.org/10.29333/ejmste/12034

MLA

Silva, Ana Cristina Azevedo da et al. "Doing mathematics with music – Creating epistemic environments". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 5, 2022, em2111. https://doi.org/10.29333/ejmste/12034