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On music production in mathematics teacher education as an aesthetic experience

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Abstract

This paper addresses the integrated use of the arts and digital technology in mathematics education—specifically involving aspects of preservice teachers’ mathematical activity while engaging in music production, in pedagogic scenarios conceived of as aesthetic mathematical experiences (AMEs). Theoretically, the research evokes notions such as digital mathematical performance, aesthetics, humans-with-media, and musical theory. Methodologically, the study presents a pedagogic model for mathematics teaching and learning through music production; the model is elaborated using qualitative case studies in which preservice teachers (education majors and mathematics majors) created mathematical songs with music software. In their songs, the education majors explored place value and the mathematics majors explored progressions. The research highlights the mathematical ideas and the narrative nature of the lyrics, as well as the digital structure of the songs created collectively. The study also emphasizes aspects of thinking-with-music-software related to musical concepts such as intervals, note values, and harmonic fields. The results reveal that the AMEs offered ways for preservice teachers to think mathematically and aesthetically through the composition of the lyrics and by the creation of virtual instruments with music software.

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Notes

  1. In Brazil, place value manipulatives are called “Golden Material”.

  2. G# (fifth), F# (fourth), E (third), C# (tonic).

References

  • Abdounur, O. J. (2003). Mathematics and music: Analogic thinking in meaning construction. Sao Paulo: Escrituras Editora.

    Google Scholar 

  • An, S. A., Ma, T., & Capraro, M. M. (2011). Preservice teachers’ beliefs and attitude about teaching and learning mathematics through music: An intervention study. School Science and Mathematics Journal, 111, 236–248.

    Google Scholar 

  • An, S. A., Tillman, D., Shaheen, A., & Boren, R. (2014). Preservice teachers’ perception about teaching mathematics through music. Journal of Interdisciplinary Teaching and Learning, 4(3), 150–171.

    Google Scholar 

  • Bicudo, M. A. V. (1993). Research in mathematics education. Pro-posições, 4(10), 18–23.

    Google Scholar 

  • Boal, A. (2006). The aesthetics of the oppressed. New York: Routledge.

    Google Scholar 

  • Borba, M. C., & Gadanidis, G. (2008). Virtual communities and networks of practising mathematics. In K. Krainer & T. Wood (Eds.), The international handbook of mathematics teachers education. Participants in mathematics teacher education. Individual, teams, communities and networks (Vol. 3, pp. 181–206). Rotterdam/Taipei: Sense Publishers.

    Google Scholar 

  • Borba, M. C., Scucuglia, R. R. S., & Gadanidis, G. (2014). Phases of digital technologies in mathematics education: The classroom and the internet in motion (1st ed.). Belo Horizonte: Autêntica.

    Google Scholar 

  • Borba, M. C., & Villarreal, M. (2005). Humans-with-media and reorganization of mathematical thinking: Information and communication technologies, modeling, experimentation and visualization. Berlin: Springer.

    Google Scholar 

  • 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(2), 251–278.

    Google Scholar 

  • Dewey, J. (2010). Art as experience. Sao Paulo, Brazil: Martins Fontes.

    Google Scholar 

  • Doxiadis, A. (2003). Embedding mathematics in the soul: Narrative as a force in mathematics education. In Opening address to the Third Mediterranean Conference of Mathematics Education, Athens, Greece.

  • Gadanidis, G., & Borba, M. C. (2006). Digital mathematical performance. https://www.edu.uwo.ca/dmp/.

  • Gadanidis, G., & Borba, M. (2008). Our lives as performance mathematicians. For the Learning of Mathematics, 28(1), 44–51.

    Google Scholar 

  • Gadanidis, G., Borba, M., Hughes, J., & Lacerda, H. (2016). Designing aesthetic experiences for young mathematicians: A model for mathematics education reform. International Journal of Research in Mathematics Education, 6(2), 225–244.

    Google Scholar 

  • Gadanidis, G., & Geiger, V. (2009). A social perspective on technology-enhanced mathematical learning: From collaboration to performance. ZDM Mathematics Education, 42(1), 91–104.

    Google Scholar 

  • Gadanidis, G., Hughes, J., & Borba, M. (2008). Students as performance mathematicians. Mathematics Teaching in the Middle School, 14(3), 168–175.

    Google Scholar 

  • Gadanidis, G., & Scucuglia, R. (2010). Windows into elementary mathematics: Alternate public images of mathematics and mathematicians. Acta Scientiae, 12(1), 8–23.

    Google Scholar 

  • Gerstberger, H. (2009). Mathematics learning and aesthetic production. ZDM Mathematics Education, 41(1–2), 61–73.

    Google Scholar 

  • Gregorutti, G. S. (2016). Digital mathematical performance and public image of mathematics: poetical enterprise in preservice teacher education. Masters’ thesis (in mathematics education). Rio Claro: Sao Paulo State University.

  • Houdement, C., & Tempier, F. (2019). Understanding place value with numeration units. ZDM Mathematics Education, 51(1), 25–37.

    Google Scholar 

  • Howe, R. (2018). Learning and using our base ten place value number system: Theoretical perspectives and twenty-first century uses. ZDM Mathematics Education, 51(1), 57–68.

    Google Scholar 

  • Leviatan, Y. (2017). Making music: The 6 stages of music production. https://www.waves.com/six-stages-of-music-production. Accessed 11 Mar 2019.

  • Levy, P. (2001). Cyberculture. Minneapoliss: University of Minnesota Press.

    Google Scholar 

  • Marshall, M. N. (1996). Sampling for qualitative research. Family Practice, 13(6), 522–526.

    Google Scholar 

  • Martínez-Planell, R., Gonzalez, A., DiCristina, G., & Acevedo, V. (2012). Students’ conception of infinite series. Educational Studies in Mathematics, 81, 235–249.

    Google Scholar 

  • Pilhofer, M., & Day, H. (2007). Music theory for dummies. New York: Wiley Publishing Inc.

    Google Scholar 

  • Powell, A., Francisco, J., & Maher, C. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405–435.

    Google Scholar 

  • Rory, P. Q. (2018, October 24). Basic music theory for beginners—the complete guide. Retrieved from https://iconcollective.com/basic-music-theory/. Accessed 10 July 2019.

  • Sao, Paulo. (2011). Curriculum of Sao Paulo State: Mathematics and its technologies. Sao Paulo: Ministry of education of State of Sao Paulo.

    Google Scholar 

  • Sao, Paulo. (2014). Mathematics curriculum: Elementary school Grades 1-5. Sao Paulo: Ministry of education of State of Sao Paulo.

    Google Scholar 

  • Scucuglia, R. (2012). On the nature of students’ digital mathematical performances. Doctoral dissertation. London: The University of Western Ontario

  • Scucuglia, R. (2014). Multimodal narratives: The image of mathematicians in digital mathematical performances. Bolema, 28(49), 950–973.

    Google Scholar 

  • Sinclair, N. (2009). Aesthetics as a liberating force in mathematics education? ZDM Mathematics Education, 41(1), 45–60.

    Google Scholar 

  • Stake, R. E. (2000). Case studies. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research (pp. 435–453). Thousand Oaks: Sage.

    Google Scholar 

  • Wright, D. (2009). Mathematics and music. Providence: American Mathematical Society.

    Google Scholar 

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Acknowledgements

CNPq—Brazilian Council for Scientific and Technological Development (428323/2018/-9).

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Correspondence to Ricardo Scucuglia Rodrigues da Silva.

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da Silva, R.S.R. On music production in mathematics teacher education as an aesthetic experience. ZDM Mathematics Education 52, 973–987 (2020). https://doi.org/10.1007/s11858-019-01107-y

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