Educational Studies in Mathematics

, Volume 81, Issue 2, pp 251–278 | Cite as

Academic music: music instruction to engage third-grade students in learning basic fraction concepts

  • Susan Joan CoureyEmail author
  • Endre Balogh
  • Jody Rebecca Siker
  • Jae Paik


This study examined the effects of an academic music intervention on conceptual understanding of music notation, fraction symbols, fraction size, and equivalency of third graders from a multicultural, mixed socio-economic public school setting. Students (N = 67) were assigned by class to their general education mathematics program or to receive academic music instruction two times/week, 45 min/session, for 6 weeks. Academic music students used their conceptual understanding of music and fraction concepts to inform their solutions to fraction computation problems. Linear regression and t tests revealed statistically significant differences between experimental and comparison students’ music and fraction concepts, and fraction computation at posttest with large effect sizes. Students who came to instruction with less fraction knowledge responded well to instruction and produced posttest scores similar to their higher achieving peers.


Fraction concepts Elementary Representation Music notation Semiotics 


  1. Abrahamson, D. (2009). Embodied design: Constructing means for constructing meaning. Educational Studies in Mathematics, 70, 27–47. doi: 10.1007/s10649-008-9137-1.CrossRefGoogle Scholar
  2. Arzarello, F., & Paola, D. (2007) Semiotic games: The role of the teacher. In J. Woo, H. Lew, K. Park, & D. Seo (Eds.). In Proceedings of the 31st conference of the International Group for the Psychology of Mathematics Education, 2, 17–24. Seoul: PMEGoogle Scholar
  3. Arzarello, F., Paola, D., Robuti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70, 97–109. doi: 10.1007/s10649-008-9163-z.CrossRefGoogle Scholar
  4. Arzarello, F., & Robuti, O. (2004). Approaching functions through motion experiments. Educational Studies in Mathematics, 57, 305–308.Google Scholar
  5. Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin and Review, 14(2), 243–248.CrossRefGoogle Scholar
  6. Basurto, I. (1999). Conditions of reading comprehension which facilitate word problems for second language learners. Reading Improvement, 36, 143–148.Google Scholar
  7. Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and procedures (pp. 91–126). New York, NY: Academic Press.Google Scholar
  8. Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15, 323–341. doi: 10.2307/748423.CrossRefGoogle Scholar
  9. Brigham, J. F., Wilson, R., Jones, E., & Moisio, M. (1996). Best Practices: Teaching decimals, fractions, and percents to students with learning disabilities. LD Forum, 21, 10–15. Available from Accessed 11 August 2011.
  10. Bright, G., Behr, M., Post, T., & Wachsmuth, I. (1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19(3), 215–232. doi: 10.2307/749066.CrossRefGoogle Scholar
  11. Bruner, J. S. (1977). The process of education. Cambridge, MA: Harvard University Press.Google Scholar
  12. Butler, F. M., Miller, S. P., Crehan, K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research and Practice, 18, 99–111. doi: 10.1111/1540-5826.00066.CrossRefGoogle Scholar
  13. California Department of Education (1999). Mathematics content standards for California public school: Kindergarten through grade twelve. Available from Accessed 8 January 2012.
  14. Center on Education Policy (2005). NCLB Policy Brief 3: Is NCLB Narrowing the Curriculum? Available from Accessed 8 January 2008.
  15. Chandler, D. (1994). Semiotics for beginners. Available from Accessed 11 August 2011.
  16. Cobb, P. (2000). From representations to symbolizing: Introductory comments on semiotics and mathematical learning. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 17–36). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  17. Cook, T. D., & Campbell, D. T. (1979). Quasi-experimentation. Design and analysis issues for field settings. Chicago, IL: Rand McNally.Google Scholar
  18. Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33, 111–145. doi: 10.2307/749646.CrossRefGoogle Scholar
  19. David, J. H. (1995). The mathematics of music. Available from Accessed 6 January 2012.
  20. Ediger, M. (1999). Psychology foundations in teaching mathematics. (ERIC Document Reproduction Service No. ED431606). Accessed 14 July 2009 from ERIC database.Google Scholar
  21. Empson, S. B. (2003). Low-performing students and teaching fractions for understanding: An interactional analysis. Journal for Research in Mathematics Education, 34(4), 305–343. doi: 10.2307/30034786.CrossRefGoogle Scholar
  22. Foster, S. L., & Mash, E. J. (1999). Assessing social validity in clinical treatment research: Issues and procedures. Journal of Consulting and Clinical Psychology, 67, 308–319. doi: 10.1037/0022-006X.67.3.308.CrossRefGoogle Scholar
  23. Frykholm, J. A. (2004). Teachers' tolerance for discomfort: Implications for curriculum reform in mathematics education. Journal of Curriculum and Supervision, 19(2), 125–149.Google Scholar
  24. Furner, J. M., & Berman, B. T. (2004). Building math confidence for a high-tech world. Academic Exchange Quarterly, 8(2), 214–220.Google Scholar
  25. Gault, B. (2005). Music learning through all channels: Combining aural, visual, and kinesthetic strategies to develop musical understanding. General Music Today, 19(1), 7–9. doi: 10.1177/10483713050190010103.CrossRefGoogle Scholar
  26. Hiebert, J. (1989). The struggle to link written symbols with understandings: An update. Arithmetic Teacher, 36, 38–44.Google Scholar
  27. Hiebert, J., Wearne, D., & Taber, S. (1991). Fourth graders gradual construction of decimal fractions during instruction using different physical representations. The Elementary School Journal, 91, 321–341. doi: 10.1086/461658.CrossRefGoogle Scholar
  28. Hurwitz, I., Wolff, P. H., Bortnick, B. D., & Kokas, K. (1975). Nonmusical effects of the Kodaly music curriculum in primary grade children. Journal of Learning Disabilities, 8(3), 167–174. doi: 10.1177/002221947500800310.CrossRefGoogle Scholar
  29. Maccini, P., & Gagnon, J. C. (2002). Perceptions and application of NCTM standards by special and general education teachers. Exceptional Children, 68, 325–345.Google Scholar
  30. Mack, N. K. (1990). Long-term effects of building on informal knowledge in a complex content domain: The case of multiplication of fractions. The Journal of Mathematical Behavior, 19, 307–332. doi: 10.1016/S0732-3123(00)00050-X.CrossRefGoogle Scholar
  31. Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26, 422–441. doi: 10.2307/749431.CrossRefGoogle Scholar
  32. Mazzocco, M. M. M., & Devlin, K. T. (2008). Parts and ‘holes’: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11(5), 681–691. doi: 10.1111/j.1467-7687.2008.00717.x.CrossRefGoogle Scholar
  33. McLaughlin, M. W., Shepard, L. A., & O’Day, J. A. (1995). Improving education through standards-based reform: A report by the National Academy of Education panel on standards-based education reform. Stanford, CA: Stanford University, National Academy of Education.Google Scholar
  34. Menken, K. (2006). Teaching to the test: How No Child Left Behind impacts language policy, curriculum, and instruction for English Language Learners. Bilingual Research Journal, 30, 521–546.CrossRefGoogle Scholar
  35. Miller, S. P., & Hudson, P. J. (2007). Using evidence-based practices to build mathematics competence related to conceptual, procedural, and declarative knowledge. Learning Disabilities Research and Practice, 22, 47–57. doi: 10.1111/j.1540-5826.2007.00230.x.CrossRefGoogle Scholar
  36. Miura, I. T., Okamoto, Y., Vlahovic-Stetic, V., Kim, C. C., & Han, J. H. (1999). Language supports for children’s understanding of numerical fractions: Cross-national comparisons. Journal of Experimental Child Psychology, 74, 356–365. doi: 10.1006/jecp.1999.2519.CrossRefGoogle Scholar
  37. Moss, J., & Case, R. (1999). Developing children’s understanding of the rational numbers: A new experimental curriculum. Journal for Research in Mathematics Education, 30, 122–147. doi: 10.2307/749607.CrossRefGoogle Scholar
  38. Music for All (2005). Music Advocacy. Retrieved August 10, 2010, from
  39. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  40. National Research Council. (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.Google Scholar
  41. Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080–1111. doi: 10.3102/0002831208320851.CrossRefGoogle Scholar
  42. Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26, 400–417. doi: 10.1006/ceps.2000.1072.CrossRefGoogle Scholar
  43. Niemi, D. (1996). Assessing conceptual understanding in mathematics: Representations, problem solutions, justification, and explanations. The Journal of Educational Research, 89(6), 351–363.CrossRefGoogle Scholar
  44. No Child Left Behind Act of 2001. 20 U.S.C. § 6310 et seq. (Reauthorization of the Elementary and Secondary Education Act).Google Scholar
  45. Paik, J. H., & Mix, K. S. (2003). U.S. and Korean children’s comprehension of fraction names: A reexamination of cross-national differences. Child Development, 74, 144–154. doi: 10.1111/1467-8624.t01-1-00526.CrossRefGoogle Scholar
  46. Post, T. R., Behr, M. J., & Lesh, R. (1986). Research-based observations about children’s learning of rational number concepts. Focus on Learning Problems in Mathematics, 8(1), 39–48.Google Scholar
  47. Presmeg, N. (2006). Semiotics and the “connections” standard: Significance of semiotics for teachers of mathematics. Educational Studies in Mathematics, 61, 163–182. doi: 10.1007/s10649-006-3365-z.CrossRefGoogle Scholar
  48. Radford, L. (2003). Gestures, speech and the sprouting of signs. Mathematical Thinking and Learning, 5(1), 37–70. doi: 10.1207/S15327833MTL0501_02.CrossRefGoogle Scholar
  49. Radford, L., Bardini, C., & Sabena, C. (2007). Perceiving the general: The multi-semiotic dimension of students' algebraic activity. Journal for Research in Mathematics Education, 28, 507–530.Google Scholar
  50. Radford, L., Edwards, S., & Arzarello, F. (2009). Introduction: Beyond words. Educational Studies in Mathematics, 70, 91–95.CrossRefGoogle Scholar
  51. Radford, L., Schubring, G., & Seeger, F. (2011). Signifying and meaning-making in mathematical thinking, teaching, and learning. Educational Studies in Mathematics, 77, 149–156.CrossRefGoogle Scholar
  52. Rasmussen, C., Nemirovsky, R., Olszewski, J., Dost, K., & Johnson, J. L. (2004). PME special issue: Bodily activity and imagination in mathematics learning. Educational Studies in Mathematics, 57, 303–321.CrossRefGoogle Scholar
  53. Scarlato, M. C., & Burr, W. A. (2002). Teaching fractions to middle school students. Journal of Direct Instruction, 2, 23–38.Google Scholar
  54. Schnepp, M., & Chazan, D. (2004). Incorporating experiences of motion into a calculus classroom. Educational Studies in Mathematics, 57, 309–313.Google Scholar
  55. Shields, D. J. (2005). Teachers have the power to alleviate math anxiety. Academic Exchange Quarterly, 9(3), 326–330.Google Scholar
  56. Sood, S., & Jitendra, A. K. (2007). A comparative analysis of number sense instruction in first grade traditional and reform-based mathematics textbooks. Journal of Special Education, 41(3), 145–157. doi: 10.1177/00224669070410030101.CrossRefGoogle Scholar
  57. Vygotsky, L. (1978). Interaction between learning and development. In M. Cole, V. John Steiner, S. Scribner, & E. Souberman (Eds.), Mind in society: The development of higher psychological processes (pp. 79–91). Cambridge, MA: Harvard University Press.Google Scholar
  58. Wheeler, L. (1985). Orff and Kodaly: Adapted for the elementary school (3rd ed.). Dubuque, IA: Wm. C. Brown.Google Scholar
  59. Woodward, J., Baxter, J., & Robinson, R. (1999). Rules and reasons: Decimal instructions for academically low achieving students. Learning Disabilities Research and Practice, 14, 15–24.CrossRefGoogle Scholar
  60. Yoshida, H., & Sawano, K. (2002). Overcoming cognitive obstacles in learning fractions: Equal-partitioning and equal-whole. Japanese Psychological Research, 44(4), 183–195. doi: 10.1111/1468-5884.00021.CrossRefGoogle Scholar
  61. Yoshida, H., & Shinmachi, Y. (1999). The influence of instructional intervention on children’s understanding of fractions. Japanese Psychological Research, 41(4), 218–228. doi: 10.1111/1468-5884.00122.CrossRefGoogle Scholar
  62. Young-Loveridge, J., Taylor, M., Hawera, N., & Sharma, S. (2007). Year 7-8 students’ solution strategies for a task involving addition of unlike fractions. In Findings from the New Zealand numeracy development project 2006. Wellington, New Zealand: Ministry of Education.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Susan Joan Courey
    • 1
    Email author
  • Endre Balogh
    • 1
  • Jody Rebecca Siker
    • 1
  • Jae Paik
    • 1
  1. 1.San Francisco State UniversitySan FranciscoUSA

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