Affordances of music composing software for learning mathematics at primary schools
Music composing is associated with various positive learning outcomes, but in several countries, such as Finland, it is not part of the primary school music curriculum. There are several issues as to why music composing is not taught at schools, such as beliefs that composing requires extensive knowledge of music theory, lack of teachers’ confidence, lack of evidence on the method’s effectiveness and difficulty of assessment. Composing software has the potential of solving some of these issues, as they are connected to mathematics via music theory and technology, and with practical opportunities arising from adopting phenomenon-based learning at schools, the affordances of music composing technologies for learning mathematics are investigated in this study. For this purpose, 57 music composing software were categorised and reviewed. Our analysis identified eight types of music visualisations and five types of note input methods. The music visualisations were compared to the mathematics content in the Finnish primary school curriculum and the note input methods were evaluated based on their relationship to the music visualisations. The coordinate grid-based piano roll was the most common visualisation and the tracker visualisation had the most affordances for learning primary school math. Music composing software were found to have affordances for teaching mathematical concepts, notations and basic calculus skills, among others. Composing methods involving direct interaction with visualisations support the experiential learning of music theory, and consequently, the learning of mathematics. Based on the findings of this study, we concluded that music composing is a promising activity through which mathematics and music theory can be learned at primary schools.
Airy, S. & Parr, J. M. (2001) ‘MIDI, music and me: students’ perspectives on composing with MIDI’, Music Education Research, vol. 3, no. 1, pp. 41–49. https://doi.org/10.1080/14613800020029941
An, S. A. & Capraro, M. M. (2011) Music-Math Integrated Activities for Elementary and Middle School Students, Education for All, Irvine, CA.
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, vol. 3, no. 1, pp. 45–60.
Atkinson, R. (2017) ‘The pedagogy of primary music teaching: talking about not talking’, Music Education Research, pp. 1–10. https://doi.org/10.1080/14613808.2017.1327946
Bamberger, J. (2003) ‘Music as embodied mathematics: a study of a mutually informing affinity’, International Journal of Computers for Mathematical Learning, vol. 8, no. 2, pp. 123–160. https://doi.org/10.1023/B:IJCO.0000003872.84260.96
Bauer, W. I., Reese, S. & McAllister, P. A. (2003) ‘Transforming music teaching via technology: the role of professional development’, Journal of research in Music Education, vol. 51, no. 4, pp. 289–301. https://doi.org/10.2307/3345656
Beckstead, D. (2001) ‘Will technology transform music education? Although technological advances make composing easier, music educators tend to use these tools to make traditional methods more accessible rather than explore new possibilities in composing’, Music Educators Journal, vol. 87, no. 6, pp. 44–49.
Beery, L. S. (1995) ‘Teaching MIDI from an African American Angle: African American students can be taught the music of their cultural heritage with the use of MIDI’, Music Educators Journal, vol. 82, no. 3, pp. 35–38.
Berkley, R. (2004) ‘Teaching composing as creative problem solving: conceptualising composing pedagogy’, British Journal of Music Education, vol. 21, no. 3, pp. 239–263. https://doi.org/10.1017/S026505170400587X
Beynon, M. (2012) ‘Modelling with experience: construal and construction for software’, in Automation, Collaboration, & E-Services, pp. 197–228. https://doi.org/10.1007/978-3-642-25209-9_9
Bonneville-Roussy, A. & Bouffard, T. (2015) ‘When quantity is not enough: disentangling the roles of practice time, self-regulation and deliberate practice in musical achievement’, Psychology of Music, vol. 43, no. 5, pp. 686–704. https://doi.org/10.1177/0305735614534910
Bunting, R. (1987) ‘Composing music: case studies in the teaching and learning process’, British Journal of Music Education, vol. 4, no. 1, pp. 25–52.
Byo, S. J. (1999) ‘Classroom teachers’ and music specialists’ perceived ability to implement the national standards for music education’, Journal of Research in Music Education, vol. 47, no. 2, pp. 111–123.
Cambouropoulos, E. (2000, July) ‘From MIDI to traditional musical notation’, in Proceedings of the AAAI Workshop on Artificial Intelligence and Music: Towards Formal Models for Composition, Performance and Analysis, vol. 30.
Cope, D. (2015) ‘Algorithmic music composition’, in Patterns of Intuition, Springer, Dordrecht, pp. 405–416. https://doi.org/10.1007/978-94-017-9561-6_19
Edworthy, J. & Waring, H. (2006) ‘The effects of music tempo and loudness level on treadmill exercise’, Ergonomics, vol. 49, no. 15, pp. 1597–1610. https://doi.org/10.1080/00140130600899104
Ericsson, K. A., Krampe, R. T. & Tesch-Römer, C. (1993) ’The role of deliberate practice in the acquisition of expert performance’, Psychological Review, vol. 100, no. 3, p. 363.
Farbood, M. M., Pasztor, E. & Jennings, K. (2004) ‘Hyperscore: a graphical sketchpad for novice composers’, IEEE Computer Graphics and Applications, vol. 24, no. 1, pp. 50–54. https://doi.org/10.1109/MCG.2004.1255809
Finney, J. & Burnard, P. (Eds.). (2010) Music Education with Digital Technology, Bloomsbury Publishing. New York, USA.
Finnish Ministry of Education. (2014) National Education Curriculum for Elementary School 2014, pp. 142, 263–264, 422–425, [online] Available at: http://www.oph.fi/download/163777_perusopetuksen_opetussuunnitelman_perusteet_2014.pdf
Foote, J. (1999) ‘Visualizing music and audio using self-similarity’, in Proceedings of the Seventh ACM International Conference on Multimedia (Part 1), ACM, pp. 77–80.
Fourney, D. W. & Fels, D. I. (2009) ‘Creating access to music through visualization’, in Science and Technology for Humanity (TIC-STH), 2009 IEEE Toronto International Conference, IEEE, pp. 939–944. https://doi.org/10.1109/TIC-STH.2009.5444364
Fox, T. (2015) Undertale. Self-Published. Played and tested on Nintendo Switch.
Gall, M. & Breeze, N. (2005) ‘Music composition lessons: the multimodal affordances of technology’, Educational Review, vol. 57, no. 4, pp. 415–433. https://doi.org/10.1080/00131910500278314
Greeno, J. G. (1994) Gibson’s Affordances. Psychological Review, Vol 101(2), Apr 1994, 336–342. American Psychological Association. 750 First Street NE, Washington, DC.
Habibi, A. & Damasio, A. (2014) ‘Music, feelings, and the human brain’, Psychomusicology: Music, Mind, and Brain, vol. 24, no. 1, p. 92. https://doi.org/10.1037/pmu0000033
Hendradjaya, B. (2018, November) ‘A framework for development of serious game for learning musical instrument’, in 2018 5th International Conference on Data and Software Engineering (ICoDSE), IEEE, pp. 1–6. https://doi.org/10.1109/ICODSE.2018.8705885
Hiraga, R., Watanabe, F. & Fujishiro, I. (2002) ‘Music learning through visualization’, in Proceedings of the Second International Conference on Web Delivering of Music, 2002. WEDELMUSIC 2002, IEEE, pp. 101–108. https://doi.org/10.1109/WDM.2002.1176199
Holcombe, J. E. (2006) U.S. Patent No. 6,987,220, U.S. Patent and Trademark Office, Washington, DC.
Holmes, T. B. & Holmes, T. (2002) Electronic and Experimental Music: Pioneers in Technology and Composition, Psychology Press, New York, USA.
Hoos, H. H., et al., (1998) The GUIDO Notation Format – A Novel Approach for Adequately Representing Score-Level Music. [ONLINE] Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.122.1122&rep=rep1&type=pdf, checked 27.8.2019
Hope, C. (2017) ‘Electronic scores for music: the possibilities of animated notation’, Computer Music Journal, vol. 41, no. 3, pp. 21–35. https://doi.org/10.1162/comj_a_00427
Hosken, D. (2014) An Introduction to Music Technology, Routledge. New York. 2nd edition. https://doi.org/10.4324/9780203539149
Hudak, P., et al., (1996) ‘Haskore Music Notation – An Algebra of Music’, Journal of Functional Programming, vol. 6, no. 3, pp. 465–484. https://doi.org/10.1017/S0956796800001805
Indiana State. (2016) Elementary and Middle Level Subjects and Descriptions, [online] Available at: http://www.doe.in.gov/sites/default/files/ccr/elementary-and-middle-school-subjects-2016-17-12-18-15.pdf
James, W. (1976) Essays in Radical Empiricism, vol. 3, Harvard University Press. Cambridge, Oxford and Massachusetts.
Kolb, D. A. (2014) Experiential Learning: Experience as the Source of Learning and Development, Pearson education Canada Ltd, USA.
Koutsomichalis, M. (2018) ‘Ad-hoc aesthetics: context-dependent composition strategies in music and sound art’, Organised Sound, vol. 23, no. 1, pp. 12–19. https://doi.org/10.1017/S1355771817000231
Laato, S., et al., (2017, July) ’Designing a game for learning math by composing: a Finnish primary school case’, In 2017 IEEE 17th International Conference on Advanced Learning Technologies (ICALT), IEEE, pp. 136–138. https://doi.org/10.1109/ICALT.2017.45
Leider, C. N. (2004) Digital Audio Workstation, McGraw-Hill, Inc, New York, USA
Lim, T., Lee, S. & Ke, F. (2017) ‘Integrating music into math in a virtual reality game: learning fractions’, International Journal of Game-Based Learning (IJGBL), vol. 7, no. 1, pp. 57–73.
Lim, T., Lee, S. & Ke, F. (2018) ‘Integrating music into math in a virtual reality game: learning fractions’, International Journal of Game-Based Learning (IJGBL), vol. 7, no. 1, pp. 57–73. https://doi.org/10.4018/978-1-5225-5469-1.ch053
Lehtinen, E., et al., (2017) ’Cultivating mathematical skills: from drill-and-practice to deliberate practice’, ZDM, vol. 49, no. 4, pp. 625–636. https://doi.org/10.1007/s11858-017-0856-6
Lonka, K., et al., (2018) Phenomenal Learning from Finland, Edita. Helsinki, Finland.
Macgill, A. (1988) ‘Composing in the school: composing for the school’, British Journal of Music Education, vol. 5, no. 1, pp. 35–43.
Malmi, E., et al., (2016, August) ‘Dopelearning: a computational approach to rap lyrics generation’, In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM, pp. 195–204. https://doi.org/10.1145/2939672.2939679
Manaris, B. & Kohn, T. (2016, February) ‘Making music with computers: creative programming in Python’, In Proceedings of the 47th ACM Technical Symposium on Computing Science Education, ACM, p. 711. https://doi.org/10.1145/2839509.2844707
Marquez, I. (2014) ‘Playing new music with old games: the chiptune subculture’, G| A| M| E Games as Art, Media, Entertainment, vol. 1, no. 3, pp. 69–79.
Marrington, M. (2010) ‘Experiencing musical composition in the DAW: the software interface as mediator of the musical idea’, in Proceedings of the 6th Art of Record Production Conference, p. 1. Available at: http://www.arpjournal.com/asarpwp/experiencing-musical-composition-in-the-daw-the-software-interface-as-mediator-of-the-musical-idea-2/
Martin, B. (2018) ‘Soundscape composition: enhancing our understanding of changing soundscapes’, Organised Sound, vol. 23, no. 1, pp. 20–28. https://doi.org/10.1017/S1355771817000243
Mattila, P. & Silander, P. (2015) How to Create the School of the Future – Revolutionary Thinking and Design from Finland, Multiprint, Oulu.
Mazzola, G., Mannone, M. & Pang, Y. (2016) Cool Math for Hot Music, Springer International Publishing Switzerland. https://doi.org/10.1007/978-3-319-42937-3
McCoid, S., et al., (2013) ‘EarSketch: an integrated approach to teaching introductory computer music’, Organised Sound, vol. 18, no. 2, 146–160. https://doi.org/10.1017/S135577181300006X
McGrenere, J. & Ho, W. (2000, May) ‘Affordances: clarifying and evolving a concept’, in Graphics Interface, vol. 2000, 179–186. Montreal, Canada.
Melodyne. (2019) Melodyne, [online] Available at: http://www.celemony.com/en/melodyne/what-is-melodyne
Meyer, J. W., Kamens, D. & Benavot, A. (2017) School Knowledge for the Masses: World Models and National Primary Curricular Categories in the Twentieth Century, Routledge, London. https://doi.org/10.4324/9781315225173 in Press.
Miller, M., et al., (2019) Analyzing Visual Mappings of Traditional and Alternative Music Notation. arXiv preprint arXiv:1810.10814.
Moher, D., et al., (2009) ‘Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement’, Annals of Internal Medicine, vol. 151, no. 4, pp. 264–269. https://doi.org/10.7326/0003-4819-151-4-200908180-00135
Nilsson, U. (2008) ‘The anxiety-and pain-reducing effects of music interventions: a systematic review’, AORN Journal, vol. 87, no. 4, pp. 780–807. https://doi.org/10.1016/j.aorn.2007.09.013
Norman, D. A. (1988) The Psychology of EverydayThings, Basic Books, New York.
Obarski, K. (1987) Ultimate Soundtracker. (Software) released online in 1987. Self published.
Paquette, K. R. & Rieg, S. A. (2008) ’Using music to support the literacy development of young English language learners’, Early Childhood Education Journal, vol. 36, no. 3, pp. 227–232. https://doi.org/10.1007/s10643-008-0277-9
Pejrolo, A. (2012) Creative Sequencing Techniques for Music Production: A Practical Guide to Pro Tools, Logic, Digital Performer, and Cubase, Focal Press. New York, USA. https://doi.org/10.4324/9780240522173
Peters, G. D. (1992) ‘Music software and emerging technology: G. David Peters outlines the history of music software and hardware and explores the new developments and benefits of the emerging software for use in the classroom’, Music Educators Journal, vol. 79, no. 3, pp. 22–63.
Piaget, J. (1970) Piaget’s Theory in PH Mussen. London, Wiley.
Pitts, A. & Kwami, R. M. (2002) ‘Raising students’ performance in music composition through the use of information and communications technology (ICT): a survey of secondary schools in England’, British Journal of Music Education, vol. 19, no. 1, pp. 61–71.
Pitts, S. (2000) ‘Reasons to teach music: establishing a place in the contemporary curriculum’, British Journal of Music Education, vol. 17, no. 1, pp. 32–42.
Pope, S. T., et al., (1995) ‘Touched by machine?: composition and performance in the digital age’, Computer Music Journal, vol. 19, no. 3, pp. 13–17.
Rabiner, L. R. & Gold, B. (1975) Theory and Application of Digital Signal Processing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 777 p.
Rogers, G. L. (2016) ‘The music of the spheres: cross-curricular perspectives on music and Science’, Music Educators Journal, vol. 103, no. 1, pp. 41–48. https://doi.org/10.1177/0027432116654547
Runco, M. A., Ebersole, P. & Mraz, W. (1991) ‘Creativity and self-actualization’, Journal of Social Behavior and Personality, vol. 6, no. 5, pp. 147.
Ruokonen, I. & Ruismäki, H. (2016) ‘E-learning in music: a case study of learning group composing in a blended learning environment’, Procedia-Social and Behavioral Sciences, vol. 217, pp. 109–115. https://doi.org/10.1016/j.sbspro.2016.02.039
Sætre, J. H. (2011) ‘Teaching and learning music composition in primary school settings’, Music Education Research, vol. 13, no. 1, pp. 29–50. https://doi.org/10.1080/14613808.2011.553276
Savage, J. (2005) ‘Working towards a theory for music technologies in the classroom: how pupils engage with and organise sounds with new technologies’, British Journal of Music Education, vol. 22, no. 2, pp. 167–180. https://doi.org/10.1017/S0265051705006133
Selwyn, D. (1993) Living History in the Classroom: Integrative Arts Activities for Making Social Studies Meaningful, Zephyr Press, Tucson, AZ.
Shapiro, R. B., et al., (2017) ‘Tangible distributed computer music for youth’, Computer Music Journal. vol. 41, no. 2, pp. 52–68. https://doi.org/10.1162/COMJ_a_00420
Smith, S. M. & Williams, G. N. (1997, October) ‘A visualization of music’, in Proceedings. Visualization’97 (Cat. No. 97CB36155), IEEE, pp. 499–503. https://doi.org/10.1109/VISUAL.1997.663931
Song Maker. (2018) Song Maker Authored by Chrome Experiments Music Lab, [online] Available at: https://musiclab.chromeexperiments.com/Song-Maker/
Strand, K. (2006) ‘Survey of Indiana music teachers on using composition in the classroom’, Journal of Research in Music Education, vol. 54, no. 2, pp. 154–167. https://doi.org/10.1177/002242940605400206
Sylwester, R. (1995) An Educator’s Guide to the Human Brain, Association for Supervision and Curriculum Development, Alexandria, VA. (ASCD Stock No. 1-95085).
Symeonidis, V. & Schwarz, J. F. (2016) ‘Phenomenon-based teaching and learning through the pedagogical lenses of phenomenology: the recent curriculum reform in Finland’, Forum Oświatowe, vol. 28, no. 2, pp. 31–47.
Taylor, T. D. (2014) Strange Sounds: Music, Technology and Culture, Routledge. New York. https://doi.org/10.4324/9780203700235
Thompson, W. F. (2015) Music, Thought, and Feeling: Understanding the Psychology of Music, Oxford University Press, New York, USA.
Tossavainen, T. & Juvonen, A. (2015) ‘Finnish primary and secondary school students’ interest in music and mathematics relating to enjoyment of the subject and perception of the importance and usefulness of the subject’, Research Studies in Music Education, vol. 37, no. 1, pp. 107–121. https://doi.org/10.1177/1321103X15589259
Troelstra, A. S. & Van Dalen, D. (2014) Constructivism in Mathematics, vol. 2, Elsevier. Amsterdam, The Netherlands.
Truitt, F. E., et al., (1997) ‘The perceptual span and the eye-hand span in sight reading music’, Visual Cognition, vol. 4, no. 2, pp. 143–161.
UK Government, (2013) Britain Primary School Curriculum, [online] Available at: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/425601/PRIMARY_national_curriculum.pdf
Von Glasersfeld, E. (2013) Radical Constructivism, Routledge, London, UK. https://doi.org/10.4324/9780203454220
Walzer, D. A. (2016) ‘Software-based scoring and sound design: an introductory guide for music technology instruction’, Music Educators Journal, vol. 103, no. 1, pp. 19–26.
Wejam. (2018) Wejam, [online] Available at: http://wejam.com/
Wikipedia. (2018) List of Music Software, [online] Available at: https://en.wikipedia.org/wiki/List_of_music_software
Winters, M. (2012) ‘The challenges of teaching composing’, British Journal of Music Education, vol. 29, no. 1, pp. 19–24. https://doi.org/10.1017/S0265051711000489
Yatatoy. (2019) Bandimal, [online] Available at: http://www.yatatoy.com/bandimal
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