‘Music is Maths’ is a phrase musicians and mathematicians often say in one form or another. As an intermediate phase teacher and a researcher, it was my goal to find ways in which I could make use of the well-known connection between music and mathematics, in the mathematics classroom.
I started this journey with a Master of Education study in which I linked fractions to music note values. I continued this process of adjusting and refining ways in which mathematics teachers, regardless of their musical knowledge, could use music elements to support their teaching of fractions in my doctoral study. It is elements from this study which I share in this article.
The challenges in the teaching and learning of mathematics is exacerbated in South Africa by low achievement rates and reports of low teacher morale (Venkat & Graven, 2017). The state of mathematics education is not lining up with core curriculum aims such as recognising mathematics as a creative human activity, something which is beautiful, creative and elegant (DBE, 2011). I saw music as a useful context from which to promote more positive experiences of mathematics in general, and fractions in particular. This was the entrée to my doctoral study.
The difficulties in both teaching and learning fractions specifically are not unknown in literature and teachers’ experiences. These challenges arise in part from the multiple, interrelated constructs of fractions: the part-whole construct, fraction as measure, fraction as ratio, fraction as operator and fraction as quotient construct.
Lamon (1999) notes that the meaning of a fraction is dependent on the context in which it is used. While South Africa’s Mathematics CAPS document describes these multiple meanings of fractions (DBE, 2011, p. 292), it is seldom made explicit in lessons on fractions. In primary schools, the focus on fractions is predominantly on dividing an object (such as a pizza or a cake) into equal sized parts. This leaves room for exploring ways to better teach the multiple meanings of fractions.
A further motivation for connecting music and mathematics is the role that curriculum integration can play in fostering positive attitudes and increasing motivation. While many benefits are described in the literature, curriculum integration, globally and here in South Africa, has had a rather turbulent history.
This is partly due to the difficulties of navigating the demands of specific subjects while still finding ways to blur the boundaries between subjects. This takes expertise in each subject and lots of time, trialling, reflecting and adjusting. This was no different in my attempt to integrate music and fractions.
I worked across two planes, as shown in Figure 1 below (Lovemore, 2023), to plan and improve lessons which integrate fractions and music.

Firstly, in a Design-Theorising plane, I worked with two fellow mathematics education researchers, guided by the theoretical framing of Realistic Mathematics Education (RME). RME promotes providing pupils with a meaningful starting point which is experientially real for them (i.e., children are provided with a real-world scenario from which mathematical thinking is needed to solve a problem). Pupils are prompted by the scenario to use their own mathematical thinking.
Let us consider the example from my music-mathematics study. An imaginary scenario was explained to pupils, where animals were crossing a river of constant width. If they did not cross the river correctly, they would be eaten by a crocodile! Each animal had a specific number of jumps per river-crossing.
For example, kudu would take one jump to cross the river, ostrich would take two jumps, and zebra would take four jumps per river-crossing. From this starting point, teachers set up a measured distance for children to jump across. This allowed for reasoning around fraction as a ratio construct (jumps per river-crossing).
While the pupils took turns physically jumping across the distance, the rest of the class clapped a musical rhythm in time with the various animal jumps. After the experience of physically jumping and clapping along with each river-crossing, pupils were asked to represent their jumps in their own ways.
An example of a pupil’s representations is provided in Figure 2, below. In this scenario, equivalence of fractions can be visually shown and physically experienced. For example, one ostrich jump is an equivalent distance to two zebra jumps; two ostrich claps are equivalent in time to four zebra claps.

Being open to trialling new ways of teaching, Grade 4 to 6 teachers implemented this in their classrooms at Woodridge Preparatory. They formed part of the second plane of the study – the Grounded- Practice plane. This was a vital part of the study, as teachers’ experiences of and reflections on implementing tasks is necessary for adjusting and improving tasks.
Eight teachers from Woodridge Preparatory took on the challenge to implement the integrated music-mathematics lessons, becoming co-researchers in this study. Their feedback led to the next iteration of the tasks.
After informally representing the animal river- crossing jumps, pupils represented the animal claps informally with an X (or other informal symbols) on a percussion line, as shown in Figure 3.

This led to opportunities for pupils to ‘compose’ their own musical rhythms. Following on from the informal representations, pupils were then led to represent their animal jumps on a number line. This then progressed to working with fractions on a number line. Many mathematics education researchers have indicated the value of using number lines to teach and develop fraction understanding (Barbieri et al., 2020; Saxe et al., 2012; Soni & Okmoto, 2019).
Figure 4 below shows how the animal river-crossing jumps can be drawn on a number line. In this example, six zebra jumps (four jumps per river-crossing) are shown, totalling 1 1/2 river-crossing units.

A benefit of iterating animal jumps on the number line is to show that fractions can extend past one whole. For example, a Grade 6 teacher in the study shared her experience of working with fractions greater than one whole:
‘I’ve changed the way I’ve taught fractions. Today we did a table on common fractions to decimal fractions to percentages. And for the first time ever, I’ve said, “Okay, but now this common fraction is five fourths –”, because I’ve always just given them three fourths or two thirds.
But today, I gave them five fourths, because you can take an extra jump. They were fascinated, because they said, “But then you can’t get a percentage!” And I said, “You actually can. It’s 125 per cent.” And then we had a very interesting conversation because of how you would use it; you can’t get 125 per cent for a test, but you can have 125 per cent markup…
I would never have thought to do that without that jumping/clapping exercise and talking about a fraction as a measure, rather than part of a whole.’
This demonstrates the potential for considering the multiple meanings of fractions. The problem scenario of the animal river-crossing jumps created opportunities for pupils to see fractions as a ratio (jumps/claps per river-crossing), and fraction as measure (distance of jumps, iterated a number of times). The context also provided problems that related to fraction equivalence and fractions greater than one whole.
Teachers and pupils reported increased motivation and a greater willingness to participate during these ‘fun’ music-mathematics lessons. The integrated lessons demonstrated the potential to show mathematics as a creative human activity and to ‘make maths fun’.
While integration has its own challenges, it also holds many benefits in showing links within and across the curriculum. Working across the Design-Theorising Plane and the Grounded-Practice Plane, teachers can collaborate, sharing their expertise and experiences to design meaningful integrated activities. I encourage teachers to consider ways in which they can integrate other subjects and real-life experiences into their mathematics lessons.
I thank the Woodridge Preparatory teachers for stepping out of their comfort zones, taking on the challenge of trialling the music-mathematics integrated lessons. Their participation in the study was invaluable. I also thank the Headmaster, Mr Trevor von Berg, for his support in this initiative.
Resources developed from this study can be accessed here: https://mathemusic.mclach.co.za/index.php