Melody of Functions and Graphs: Improving Senior Secondary Mathematics Students’ Understanding of the Function Concept by Active Integration of Mathematics and Music

References

An, S. A., Zhang, M., Tillman, D. A., Lesser, L. M., Siemssen, A., & Tinajero, J. V. (2016). Learning to Teach Music-themed Mathematics: An Examination of Preservice Teachers’ Beliefs about Developing and Implementing Interdisciplinary Mathematics Pedagogy. Mathematics Teacher Education and Development, 18(1), 20-36. https://mted.merga.net.au/index.php/mted/article/view/273/255.

Australian Curriculum, v6.0. (2014). Senior secondary curriculum, Mathematical methods, Curriculum content, Unit 1, Functions and graphs. ACARA, Canberra. Retrieved from http://www.australiancurriculum.edu.au/SeniorSecondary/ mathemat-ics/mathematical-methods/Curriculum/SeniorSecondary.

Brown, J. P. (2009). Concept maps: implications for the teaching of function for secondary school students. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (pp. 65-72). Palmerston North, NZ: MERGA. http://www.merga.net.au/documents/BrownJ_RP09.pdf.

Clement, L. L. (2001). What do students really know about functions? Mathematics Teacher, 94(9), 745-748. http://math.buffalostate.edu/~wilsondc/med%20308/clement_functions.pdf.

Dienes, Z. P. (1987). Lessons involving music, language and mathematics. Journal of Mathematical Behaviour, 6(2), 171-181.

Dienes, Z. P. (2004). Mathematics as an art form. Retrieved from http://www.zoltandienes.com/wp-content/ up-loads/2010/05/Mathematics_as_an_art_form.pdf.

Evangelidou, A., Spyrou, P., Elia, I., & Gagatsis, A. (2004). University students’ concepts of function. In M. Johnsen Hoines and A. BeritFuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (pp. 351-358). Bergen, Norway: Bergen University College. http://www.emis.de/proceedings/ PME28/RR/RR099_Evangelidou.pdf.

Evans, J. K. (2009). How does integrating music and movement in a kindergarten classroom effect student achievement in math? Wayne State College, Wayne Nebraska. http://gothenburg.k12.ne.us/StaffInfoPg/Papers/J_Evans.pdf.

Fraser, B. J. (1981). TOSRA: Test of science-related attitudes. The Australian Council for Educational Research, Hawthorn, Victoria.

Fraser, B. J. (1998). Classroom environment instruments: development, validity and applications. Learning Environment Research, 1(1), 7-33. doi: 10.1023/A:1009932514731.

Guhn, M., Emerson, S. D., & Gouzouasis, P. (2019). A Population-Level Analysis of Associations Between School Music Participa-tion and Academic Achievement. Journal of Educational Psychology, 112(2), 308-328. http://dx.doi.org/10.1037/edu0000376.

Haese Mathematics. (2015). Mathematics for Australia—11 Mathematical Methods—First edition. Adelaide, SA, Australia: Haese & Harris Publications.

Hamilton, T. J., Doai, J., Milne, A., Saisanas, V., Calilhanna, A., Hilton, C., Goldwater, M., & Cohn, R. (2018). Teaching mathematics with music: A pilot study. doi: 10.1109/TALE.2018.8615262.

Harris, M. A. (2005). Montessori Mozart Programme. Montessori International Journal, 75(17). http://ebookbrowsee.net/montessori -mozart-programme-pdf-d325833304.

Kelstrom, J. M. (1998). The untapped power of music: Its role in the curriculum and its effect on academic achievement. NASSP Bulletin, 82(34). doi: 10.1177/019263659808259707.

Kleiman, G. M. (1991). Mathematics across the curriculum. Educational Leadership, 49(2), 48-51. http://kennytucker.cmswiki.wikispaces.net/file/view/math+across+content+article.pdf/360762558/math%20across%20content%20article.pdf.

Laverne, T. H. (1971). The concept of function. State University of New York: New York City, NY. Retrieved from http://files.eric.ed.gov/fulltext/ED049926.pdf.

Malone, J., Leong, S., & Lamb, M. (2001). Misperceptions in Mathematics and Music: An Intra- and Interdisciplinary Investigation Employing Applied Metacognition via Computer-Aided Learning. MERGA. https://www.merga.net.au/documents/ RR_MaloneEtAl.pdf.

McKeachie, W. J. (1987). Cognitive skills and their transfer: discussion. University of Michigan, Michigan, U.S.A. http://deepblue.lib.umich.edu/bitstream/handle/2027.42/26983/0000550.pdf?sequence=1.

Music Speed Changer [computer software]. (2012). Harald Meyer Mobile Software. Retrieved from http://tequnique.com/msc.

Nisbet, S. (1998). Listen to the graph: Children’s matching of melodies with their visual representations. (Unpublished Ph.D. thesis). Griffith University: Brisbane, Australia.

Op't Eynde, P., & De Corte, E. (2003). Student’s mathematics-related belief systems: Design and analysis of a questionnaire (MRBQ). Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, April 21-25, 2003.

Original Sine [computer software]. (2014). The University of Adelaide, Adelaide, Australia.

Rauscher, F. H. (2003). Can music instruction affect children’s cognitive development? ERIC Clearinghouse on Early Education and Parenting, ERIC Identifier: ED480540.

Schumacher, R., Altenmüller, E., Deutsch, W., & Vitouch, O. (2006). Macht Mozart schlau? Die FörderungkognitiverKompetenzendurchMusik. [Does Mozart make clever? Advancement of cognitive competencies through music].Bildungsforschung Band, 18(1), 113-130. Berlin, BundesministeriumfürBildung und Forschung. http://www.bmbf.de/pub/macht_mozart_schlau.pdf.

Spychiger, M. (1999a). Can music in school give stimulus to other school subjects? Music Forum, 5(6), 19-22. https://www.scribd.com/document/31244333/Can-Music-in-School-Give-Stimulus-to-Other-School-Subjects.

Spychiger, M. (1999b). MachtMusikwirklichklug? [Does music make really smart?] SchweizerMusikzeitung, 2(6), 5-9.

Spychiger, M. (2001). Music education is important - Why? Bulletin of the International Kodály Society, 26(1), 32-43. http://portal.unesco.org/culture/en/files/29054/11295455821Maria_B._Spychiger.htm/Maria%2BB.%2BSpychiger.htm.

Still, K., & Bobis, J. (2005). The integration of mathematics and music in the primary school classroom. Sydney: University of Sydney. http://www.merga.net.au/documents/RP822005.pdf.

Taylor, B. A. (2004). The influence of classroom environment on high school students’ mathematics anxiety and attitudes. Perth: Curtin University of Technology. Retrieved from http://espace.library.curtin.edu.au:80/R?func=dbin-jump -full&local_base=gen01-era02&object_id=15708.

Treagust, D. F. (2001). Using analogies in science teaching to engender students’ interest, motivation and understanding. In Clements, M. A., Tairub, H. H., & Yoong, W. K. (Eds.), Energising Science, Mathematics and Technical Education for All (pp. 10-26). University Brunei Darussalam. Retrieved from http://edocs.library.curtin.edu.au/eres_display.cgi?url=dc60206572. pdf&copyright=1.

Vaughn, K. (2000). Music and mathematics: Modest support for the oft-claimed relationship. The Journal of Aesthetic Education, 34(3/4), 149-166. http://www.jstor.org/discover/10.2307/3333641?uid=3737536&uid=2129&uid=2&uid=70&uid=4&sid= 21104141630093.

Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal for Mathematical Education in Science and Technology, 14(3), 293-305. http://www.researchgate.net/publication/245760146_Concept_ defini-tion_concept_image_and_the_notion_of_function.

Virtual Piano [computer software]. (2015). Crystal Magic Studio Ltd. http://virtual piano.net.