Music in Maths Pedagogy

Dr László Stachó (Liszt Academy of Music, Budapest, Department of Teacher Training) & Dr Márta Németh (Béla Bartók Secondary-Level Conservatoire of the Liszt Academy of Music)

Our pedagogical research programme investigates whether mathematical concepts taught through musical, visual-art, and dance-and-movement analogies and structural parallels can reduce mathematics anxiety and, at the same time, deepen conceptual understanding in maths. We hypothesise that training each of the three main areas of arts education — music, dance and movement, and the visual arts — has an effect on (1) the sub-components of mathematical competence, (2) academic performance in mathematics, and that it (3) reduces performance anxiety and (4) increases learning motivation with respect to mathematics. We further hypothesise that enhancing creative thinking exerts a beneficial effect on (5) mathematical competence and (6) academic performance. What follows introduces the reader to how this developmental mechanism operates in the case of music.

1. Mathematics and Music

The notion that music and mathematics are kindred disciplines dates back to the sixth century BC, to the Pythagorean tradition of southern Italy, which linked musical intervals to simple numerical ratios. Since pleasing sounds can be described by simple ratios, it was a short step to the broader claim that the orderly relationships found between all manner of things and phenomena can likewise be captured in numbers — in other words, that harmony is mathematical order. This idea was later enshrined in the classical division of the seven liberal arts, where music took its place among the higher studies: one of four equal partners, alongside arithmetic, geometry and astronomy, making up the quadrivium. On this view, each discipline studies the same underlying mathematical order from a different angle: arithmetic considers number in itself, geometry studies space, music considers ratio and harmony, and astronomy studies the ordered motion of the heavens.

This long-recognised kinship already hints at how much common ground music and mathematics share: both present phenomena in highly abstracted form, and understanding their respective theories requires the capacity to interpret a large number of abstractions. Researchers and teachers alike see this abstractness as one of the reasons mathematics is difficult: without a particular kind of thinking ability, it is all too easy to lose one’s footing in the world of numbers. Also, this is what makes it difficult to find common ground between the two domains. Among the art forms we are drawing on for this research, we expect one difference to stand out in particular: unlike the visual arts or dance, music is likely to help overcome mathematical difficulties only once the learner already has some grounding in it. Dance makes phenomena felt in the body, and the visual arts make them visible, but music, enjoyed simply for its own sake, does not “explain” itself so readily. Anyone can hear that two pitches or two durations differ — but by how much? Working that out is not something one can do without some prior training. It calls for practical skill (being able to judge by ear how far apart two pitches lie, or how much two durations differ, and so on) as well as theoretical knowledge (knowing what that interval is called, or what hierarchy of formal relationships the durations create over time).

At the same time, there is a good chance that young musicians who are seriously and genuinely committed to their instrument can be reached through individual musical examples, and that translating a phenomenon into mathematical language, together with its explanation, may bring conceptual understanding along with it.

2. Empirical Evidence

That expectation is not unfounded: a substantial body of research backs it up. Over three decades of empirical work has shown that enhancing musical ability also draws along the development of other cognitive domains (cf. Wang, 2002; Rodrigues et al., 2010). Experiments have shown that learning music supports the development of linguistic, reading and mathematical skills: children who have had musical training do better not only in music but in non-musical tasks too, including mathematics and reading (Schellenberg, 2006). A good deal of current neurological research also bears out the mechanisms behind the near and far transfer effects that arise from learning music: its effects show up not only in closely related cognitive domains but in more distant ones as well. According to one recent review (Wang, 2022), musical training has a direct effect on auditory processing (near transfer) and can indirectly improve linguistic and spatial skills too (medium-distance transfer). A more recent meta-analysis drawing on 23 experiments found a significant effect of musical interventions on mathematical attainment (Wang, Zhang & Mao, 2024). This bears out the persuasive case Bransford and Schwartz (1999) made, ahead of these studies, that the transferability of knowledge is one of the central questions facing modern educational reform.

It is worth distinguishing, however, which learning outcomes musical integration affects most strongly. The evidence for conceptual understanding is comparatively strong: wherever studies have used musical structure itself to represent a mathematical concept (rather than studying the effect of mere background music), the effect shows up consistently. Sue Courey, Endre Balogh and colleagues (2012), in their “Academic Music” programme, used note values (whole, half, quarter, eighth) to teach fractions, so that third-graders experienced the same mathematical relation in two different representations. This experimental group performed significantly better in understanding fractions than students who received conventional instruction. Later, Libby Azaryahu and colleagues (2020) arrived at a similar result within their MusiMath programme: combining rhythm, melody and mathematical representation produced knowledge transfer that held not only for the tasks practised but for new situations too.

The effect on mathematics anxiety, by contrast, is a considerably less explored area, and what evidence exists is best described as promising rather than proven. A recent questionnaire study by Tiro and colleagues (2026), for instance, found that music exposure — including how often a student listens to music, how actively they take part in musical activities, how important music is to them — significantly reduces math anxiety, but this does not necessarily translate into improved mathematical performance, whether directly or via that reduction in anxiety. Music, on their account, works more as emotional support than as a direct means of enhancing performance, a conclusion consistent with the assumption that musical representation aids understanding primarily through multi-channel (auditory, visual, kinesthetic, notational) conceptual encoding and through pattern recognition (repetition, periodicity, ratio, symmetry), whereas its effect on anxiety is more indirect and can take hold only if the musical experience simultaneously increases self-confidence and reduces the experience of failure. Teaching mathematical concepts through musical representation may therefore improve conceptual understanding, and the early signs on anxiety reduction are encouraging too, though both findings still need more empirical support.

Research carried out in Hungary — notably by the MTA–SZTE [Hungarian Academy of Sciences – University of Szeged] Research Group for Music Pedagogy and the MTA–LFZE [Hungarian Academy of Sciences – Liszt Academy of Music, Budapest] Active Music Learning Research Group — confirms these positive cognitive effects of music learning (Janurik, 2020; Lukács & Honbolygó, 2019). According to these findings, certain kinds of musical training produce not just near-transfer effects but improvements in school performance more broadly, along with benefits for social skills. Regular music education, moreover, may also foster critical thinking, attention, and memory (Janurik, 2020). It is worth noting that skills built through music learning can show up in other subjects through more distant neural pathways too: the growth of the corpus callosum, the bundle of fibres linking the two cerebral hemispheres, has been observed in musicians, and may affect performance in other subjects by way of its role in complex problem-solving (Schlaug et al., 2005). As for the relationship between musical and mathematical ability specifically: in an earlier study of our own, we found significant correlations between certain sub-skills, and concluded that “musical and mathematical ability and attainment are linked chiefly through the creativity closely bound up with musical practice, and presumably with musical ability itself, as well as through processes that can strengthen attitudinal and motivational systems — processes whose emergence and operation may be counted among the benefits of music education” (Gombás & Stachó, 2003, p. 63). Taken together, the research accumulated over recent decades and briefly summarised here suggests that learning music makes an indirect contribution to lifelong learning skills, though we should stress that how effective these transfer effects prove to be depends heavily on the quality and intensity of the learning involved (see Janurik, 2020). Music pedagogy in education, in short, serves not only aesthetic ends: alongside its transfer effects, and partly through them, it can also be understood as a tool for complex personal development. Learning music is thus a worthwhile investment in cognitive and social development, and we hope, in time, to identify the pedagogical interventions through which music can play a similar role in learning mathematics.

References

Azaryahu, L., Courey, S. J., Elkoshi, R., Adi-Japha, E. (2020). ‘MusiMath’ and ‘Academic Music’ — two music-based intervention programs for fractions learning in fourth grade students. Developmental Science, 23(6), e12882.
Bransford, J. D., Schwartz, D. L. (1999). Rethinking transfer: A simple proposal with multiple implications. Review of Research in Education, 24, 61–100.
Courey, S., Balogh, E., Siker, J., 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.
Gombás, J., Stachó, L. (2003). Matematikai és zenei képességek vizsgálata 10–14 éves gyerekeknél [An investigation of mathematical and musical abilities in 10–14-year-old children]. Tudomány és Lélek, 6, 50–65.
Janurik, M. (2020). A zenetanulás transzferhatásairól nemzetközi és hazai kutatások tükrében [On the transfer effects of music learning in light of international and Hungarian research]. Valóság, 63(7), 77–94.
Lukács, B., Honbolygó, F. (2019). Task-dependent mechanisms in the perception of music and speech: Domain-specific transfer effects of elementary school music education. Journal of Research in Music Education, 67(2), 153–170.
Rodrigues, A. C., Loureiro, M. A., Caramelli, P. (2010). Musical training, neuroplasticity, and cognition. Dementia & Neuropsychologia, 4(4), 277–286.
Schellenberg, E. G. (2006). Exposure to music: The truth about the consequences. In G. E. McPherson (Ed.), The child as musician: A handbook of musical development (pp. 111–134). Oxford University Press.
Schlaug, G., Jäncke, L., Huang, Y., Steinmetz, H. (1995). Increased corpus callosum size in musicians. Neuropsychologia, 33(8), 1047–1055.
Tiro, C. J. B., Nalzaro, K. J. P., Casan, D. J. R., Ymbol, K. S. B., Manawan, D. K. L., Gahum, S. L. (2026). The mediating role of math anxiety to the relationship of music exposure and math fluency among junior high school students. International Journal of Research and Innovation in Social Science, 10(2), 8399–8410.
Wang, L. (2022). Music aptitude, training, and cognitive transfer: A mini-review. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.903920
Wang, Y., Zhang, J., Mao, Y. (2024). Harmonizing mathematics: Unveiling the impact of music integration on academic performance — A meta-analysis. Thinking Skills and Creativity, 52, 101554.