Mathematics education is a significant issue in the South African context. Learners’ achievement levels are markedly low as suggested by both national and international studies. The teaching and learning of fractions in particular have been identified as challenging.

The aim of this article is to share some of the outcomes derived from a series of lessons in which aspects of music (note values) were integrated into the teaching of fractions in primary school.

The study was conducted in a Grade 5 class in an independent school in the Eastern Cape, with readily available resources at hand.

The broader study was an action research case study. It employed qualitative methods of data collection, based on cycles of critical reflection and adjustment, including feedback from learners and critical peers.

Findings highlighted the value of integrating music and mathematics as a teaching and learning strategy. Learning support materials and activities that promoted curriculum integration were designed. The discussion highlights benefits of these integrated lessons.

We conclude by suggesting that teachers explore synergistic opportunities across mathematics and music as subjects. In particular, we suggest curriculum integration to support the teaching of fractions in the primary grades of schooling. Our hope is that this article will encourage teachers to develop their own integrated strategies for enriching their teaching of mathematics.

Evidence from the international comparative Trends in Mathematics and Science Study (TIMSS) supports the claims that many teachers find teaching mathematics challenging and that many South African learners face obstacles learning mathematics. The 2015 TIMSS report, for example, indicated that 61% of Grade 5 learners in South Africa could not do basic mathematics, ranking these learners as the lowest performing of the participating countries (Mlachila & Moeletsi

South Africa’s matriculation results for mathematics are also a cause for concern. Only 58% of learners taking mathematics in 2018 achieved the over 30% level (Department of Basic Education [DBE]

Our focus for this article is on the use of music in the teaching of fractions at Grade 5 level. As literature indicates, fractions form an integral part of foundational knowledge for mathematics achievement, especially the development of fractional reasoning (Cortina, Visnovska & Zuniga

A number of previous studies have suggested possible ways in which musical activities can be used to support mathematics teaching and learning. For example, research by Bresler (

Both Bresler (

The present study shares elements from the first author’s response to this call to begin addressing the gap that exists in research about the

At the time when this research was carried out, the first author taught Grade 5 mathematics. She had also taught class music and violin lessons before the study. Having noticed the mathematics found in music, she recognised an opportunity to explore how music and mathematics could be integrated to support her own teaching of fractions. Subsequently, using an action research case study, she designed various learning support materials (LSMs) and trialled a range of practical strategies with her Grade 5 mathematics class across eight weeks of teaching.

The concept of curriculum integration and Bresler’s styles of arts integration guided the first author through the broader study. Bresler’s styles of arts integration (

A key motivation for this study as well as for the present article is the aforementioned poor performance levels in mathematics in South Africa. Both the study and the article represent a response to literature, suggesting the need for innovative strategies to be explored in the teaching of fractions, that is, strategies likely to enhance learners’ attitudes towards mathematics more generally and thereby encouraging their more active participation in it.

South Africa’s CAPS (DBE

a critical awareness of how mathematical relationships are used in social, environmental, cultural and economic relations;

a spirit of curiosity and a love for Mathematics;

an appreciation for the beauty and elegance of mathematics;

recognition that mathematics is a creative part of human activity;

deep conceptual understanding in order to make sense of Mathematics;

acquisition of specific knowledge and skills necessary for … the study of related subject matter (e.g. other subjects) and further study in Mathematics. (p. 8)

Curriculum integration is explicitly encouraged in South Africa’s Department of Education (DoE) curriculum documents. Both the Revised National Curriculum Statement (DoE

This curriculum support for integration across subjects provided a strong motivation and an opportune space for the first author’s broader study. She recognised that not only did integration of music into mathematics provide an opportunity to meet these curriculum aims but also that having learners work with music note values lent itself particularly well to their simultaneous conceptual work on relative fraction sizes. She was thereby able to enrich not only her own mathematics teaching strategies but also promote her learners’ ‘acquisition of specific knowledge and skills’ (DBE

The topic of fractions forms an important part of curricula internationally. It is widely accepted as a difficult topic requiring a great deal of time not only for teaching, but also for addressing misconceptions (Cortina et al.

The term ‘fraction’, as Musser et al. (

Representation of note value names and relative durations.

A literature review and analysis of curriculum expectations around the concept of curriculum integration were integral to the first author’s broader study into the ways of integrating music into mathematics.

The broader study and this article draw on two complementary views of curriculum integration: firstly, integration as ‘a philosophy of teaching in which content is drawn from several subject areas to focus on a particular topic or theme’ (Civil

Curriculum integration of the sort described above is beneficial to the teaching and learning process because of its potential for (1) facilitating a deeper understanding of the fractional concepts (Civil

In summary, the authors, along with a number of other researchers in education and mathematics education, support integration. It is, as noted, also a promoted principle of the South African curriculum. This study contributes ways for integrating mathematics and music to meet both the

One of the assumptions that drive this research is the belief that visual, auditory and tactile-kinaesthetic representations can support learners’ conceptual understanding of mathematics and that learning is enhanced through experiences that require learners to use all their senses. Many people have argued that this is important (see, for example, Claxton & Murrel

Integration is a ‘concept whose fashion ebbs and flows sporadically’ (Bresler

As we noted in our introductory section, Bresler (

The study was conducted in an independent school in the Eastern Cape. Reddy et al. (

The Grade 5 class comprised of 16 learners, eight boys and eight girls, all within the 11-12 year age range. This group of learners had diverse learning needs and socio-economic and cultural backgrounds. Because of the first author’s prior experiences of working with this group of learners, she was aware of their different learning needs. The school’s language of learning and teaching is English. Ten learners had English as their first language, and six faced the challenge of English being only their second or third language. Some other factors contributing to the diverse needs of the group were diagnoses by educational psychologists indicating that one learner had dyslexia, two learners had attention-deficit hyperactivity disorder and one was experiencing ‘mathematics anxiety’.

Before beginning the intervention, the first author needed to ensure that her research design and conduct observed the ethical requirements both of the university and of research ethics more generally. Following the submission of a carefully considered ethics application, the university’s ethical standards committee granted ethical clearance for this study. Applying for this clearance further stimulated the first author, as the action researcher, to critically reflect upon, and question, various aspects of the study from multiple perspectives. She carefully considered influences, which her personal involvement and her dual role as the researcher and research participant may have over the other participants in the study. Core ethical aspects addressed included obtaining gatekeeper permission from the school and ensuring clear explanation of all aspects of the study to critical peers, learners’ guardians and the learners themselves. Thus, written, informed consent was secured from all participants. The first author emphasised to all participants that the focus of the action research design intentions was on her teaching strategies and LSMs, not the learners. She indicated that all participants had the right to withdraw from the study at any stage without prejudice. Learners’, colleagues’ and the school’s anonymity was preserved by using pseudonyms. Finally, she ensured that there was no disruption to the school’s normal programme. The mathematics lessons took place during school hours, according to the set timetable, and the first author remained mindful of the importance of maintaining focus on her regular teaching responsibilities.

The question guiding the first author’s action research case study was as follows:

In what ways might my teaching around the inverse order relationship in unit fractions, at the Grade 5 level, be enriched by the inclusion of musical activities?

The study was qualitative in nature, influenced by an interpretivist paradigm acknowledging that individuals’ lived experiences are shaped by their context and their perceptions about knowledge are socially constructed (Maxwell

Given that the research question focussed on ways in which the first author could enrich her teaching of fractions, she acted as both the researcher and research participant in this action research case study, reflecting throughout each of the intervention cycles on her own teaching. Her learners were also research participants, and they provided feedback based on their experiences of the lessons. In addition, two of the first author’s Grade 5 colleagues became research participants, having agreed to contribute by acting as critical peers. In this role, they viewed video recordings of critical moments from the lessons, identified by the first author, and discussed their insights on these with her. The study sample was thus both purposeful and convenient (Maxwell

The reflective nature of action research (Ferrance

The 10 intervention lessons took place over an 8-week period. As

Outline of intended goals, selection of learning support materials and challenges encountered across the 10-lesson unit.

Week | Lesson | Intended goals | LSMs | Challenges reflected on |
---|---|---|---|---|

1 | 1 | Introduction of musical note values’ names, symbols and their duration with singing and clapping examples | Posters of note values’ names and symbols; clapping and singing; memory game cards; violin to play a short song | Unsure of most accurate terminology and note value naming systems; identifying note values aurally in melody too difficult; too much teacher talk time |

2 | 2 | Demonstration of how note values can ‘fit in’ to one another (implicit link to equivalent fractions) | Paper plate cut outs (whole, halves, quarters, eighths); homemade percussion instruments (shakers, sticks) | Organising percussion orchestra; too many activities; not enough small group assistance |

3 | 3 | Ordering of note values in ascending and descending order; identifying note values in audio clip | Posters with note value names; paper plates from previous lesson; PowerPoint presentation and audio clips; bingo sheets | Metronome too fast; aural recognition of note values poor; inaccurate expected timing of activities |

4 | 4 | Addition of notes of different values to make a ‘whole note’; place note values on a ‘note value’ line | Posters with note value names; body percussion; note value mat and POP game note value dice; note value and number line worksheet | Noisy game, smaller groups better; confusion with explanation about note value number line |

5 | Addition of notes of different values to create a bar of music (whole); explicit link made to adding fractions with like and unlike denominators | Posters of note values; note value mat; violin | Noisy class; time not as planned | |

5 | 6 | Investigation with playdough: as a note value decreases, more are needed to make up a whole note (explicit link to the inverse order relationship of unit fractions) | Posters of note values; note value flash cards and PowerPoint presentation (PPt) with audio clips; playdough; homemade percussion instruments | Aural identification of note values still difficult; difficult to control groups with percussion instruments; time ran out |

6 | 7 | Labelling of the note value LSMs with their corresponding fraction, that is, a half note = one half | Note value paper plate cut outs from previous lessons; work booklets; PPt | Some individual learners’ confusion (only aware after listening to recorded lesson) |

7 | 8 | Labelling of the note value LSMs with their corresponding fraction continued, that is, a half note = one half. Explicit discussion on the link between the music notes and fractions | Note value mats from previous lesson; work booklets; PPt presentation | Some learners still not confident to verbalise understanding and thought process; POP game took longer than expected, did not complete all activities in work booklet |

8 | 9 | Use of music notes to demonstrate ‘sharing’ and using a ‘whole’ as something other than 1 | PPt; video clip; note value cut outs; colour-coded bars for different instruments; instruments: violin, guitar, drum, shaker | Explain new concept, use correct terminology |

10 | Solve problems with fractions and music notes (equivalence, ordering and comparing, adding, grouping and sharing) | All from Lessons 1 to 9; problem-solving question cards; note value and fraction mat; note value and fraction paper plates; note value cut outs | Rushed for time, would like to develop concepts over more lessons |

LSMs, learning support materials.

Multiple data collection tools from multiple sources were used to gain rich insight into this 10-lesson unit. Data sources included the first author’s reflective research journal, video and audio recordings of intervention lessons, photographs, examples of learners’ work, the learners’ self-assessment feedback forms and informal oral feedback during the lessons as well as the voice-recorded semi-structured interviews with critical peers (Mrs H and Mr K are both Grade 5 teachers. Mrs H is in her early fifties, and Mr K is in his mid-twenties). Triangulating across sources reduced the risk of bias deriving from any single source (Bush

After every second lesson, learners were asked to complete a self-assessment feedback form which asked them to indicate on a continuum on how they felt about the lesson in general, their level of understanding of the lesson content and their level of participation. Learners also had the opportunity to complete the written prompt, ‘I want my teacher to know …’. Three informal oral feedback sessions were held and voice recorded (at the beginning, middle and end of the 10-lesson intervention), where the first author invited her learners to discuss their general feelings about and experiences of the various lesson activities and the LSMs used.

Similarly, after every two lessons, the first author identified critical moments within the video recordings of the lessons and met with her Grade 5 critical peers to watch through the relevant sections with her and share their ideas about the successes and challenges in relation to the teaching strategies and LSMs. All nine (four individual and one combined) of these semi-structured interview sessions were recorded and subsequently transcribed. Through member checking (Brenner

The first author’s own reflections (on lessons, on the feedback from the research participants and on examples of learners’ work and photographs) recorded in her reflective research journal played a crucial role. Journal entries followed a template originally designed by the University of Birmingham’s Academic Skills Centre (

Representation of cycles of reflection in action research.

Representation of the cycles of reflection, from the first author’s reflective journal, exemplified through Lessons 1–4.

Some of the ways in which critical reflections informed the first author’s subsequent lesson planning and implementation are shown in

Lessons 5–10 similarly included reflections and subsequent changes to lessons that followed. Examples of these reflections and changes are summarised in

Example changes and adaptations made through the cycles of reflection.

Lesson | Changes |
---|---|

5 | Decision was made to make fractions more explicit in activities to follow; timing of activities did not go as planned because of unexpected learner discussion. |

6 | Realisation that the main focus does not need to be on aural identification of note values, but rather on the link to fractions; equal emphasis should now be placed on fractions, explicitly. |

7 | Although the link to fractions has been made explicit, learners need more opportunities to practise linking note values and fractions, in order for the note values to be useful as a resource for conceptual understanding. |

8 | Some learners are still not confident to verbalise understanding; the next two sessions should focus on the ‘whole’ as something other than 1 (sharing). |

9 | Visual examples must be used to support auditory examples; the lesson can now progress to focus on problem-solving with fractions. |

10 | Learners used a variety of strategies to solve problems; the link between note values and fractions was discussed fully; there is room for further exploration in future lessons. |

Analysis was an iterative and ongoing process throughout the study (Maxwell

This combination of analytical strategies and multiple data sources facilitated a clear and holistic interpretation of the broader study’s findings. By systematically and iteratively working through the data, major elements and emerging themes were identified. For a full discussion of these findings, see Lovemore (

From the process of data collection, presentation and analysis, the first author derived findings, which she grouped into five categories, based on repeated key phrases, as well as key elements within each category. A summary of these findings is shown in

The five categories of findings and key elements.

Category | Key elements |
---|---|

1. Teaching and learning strategies | Integration: Critical peers noticed the potential for the integration of music notes and fractions in the mathematics curriculum to be beneficial to both subject areas. |

2. Value of the LSMs | Most valuable LSMs were musical instruments, paper plates, note value and fraction mat, note value number line, PowerPoint presentations, work booklets and play dough. |

3. Activities from music based to fraction based | Problem-solving activities: The last two lessons were intended to combine the use of note values and fractions in a more balanced way, in line with Bresler’s co-equal style, where the musical activities and LSMs supported the learning and application of fractions. Mr K noted that Lesson 9 used music as a context in which fractions can be applied. |

4. Links between the music (note values) and the mathematics (fractions) | The American naming system for the note values lent itself well to compare music notes to fractions. The practical musical activities and examples as well as the LSMs led to clear links with fractions, including the notion of iteration, equivalence, comparing and ordering, adding fractions with unlike denominators and the inverse order relationship in fractions. |

5. Reflections on the action research cycles | Through the cycles of trialling, reflecting, adjusting and re-trialling strategies and LSMs, the teacher found that this intervention programme of 10 lessons had a positive effect on her teaching around the inverse order relationship in unit fractions. In the final lesson, it was interesting to see the variety of methods that the learners used to solve the problems and hear the group discussions and debates. |

LSMs, learning support materials.

The focus for the present article is, as was indicated, the value of integrating music into mathematics lessons on fractions. In the discussion which follows, we highlight three aspects of this:

opportunities for making connections across mathematics and music;

achieving a co-equal style of arts integration; and

some benefits of curriculum integration.

Because this discussion section focusses so exclusively on action research and classroom-based data, we now replace the term ‘first author’ with ‘teacher’. Whilst the research took place within the Grade 5 classroom of the teacher (in her mid-twenties), fractions are introduced in the South African curriculum in the foundation phase. The focus of the activities and the LSMs on using multiple and concrete representations invoking learners to employ multiple senses (auditory, verbal, visual, tactile and kinaesthetic) is particularly relevant to foundation phase learners. We, therefore, argue that the following themes that emerged from the research would likely similarly apply to the teaching of fractions through integration with music in foundation phase classrooms.

In line with curriculum expectations, the teacher designed various LSMs to use in teaching learners the names of the note values. On the basis of reflection and observations of learners’ discussions, she found that the fractional American note-naming convention worked more effectively (learners appeared, for example, to grasp the term ‘eighth note’ more easily than the term ‘quaver’). An early learning task involved getting learners to compare and sequence the duration of different note values (recognising, for example, that three-quarter notes represent a longer duration than one-half note).

Throughout the intervention cycle, musical activities were linked to fractions. Although, at first, no link was explicitly made by the teacher, from the first lesson some learners were quick to recognise the connection between note values and fractions. The school’s violin teacher (Mrs M) walked past the classroom and commented that ‘music

Why do you think Mrs M said that music is maths?

Because you also do fractions.

Why are we using fractions?

To count the quarters, the halves and the whole.

(Lesson 1 transcript, 06 February 2019)

As the intervention cycle lessons continued, the connection between the two subjects became ever clearer. In the second critical peer interview, after Lesson 4, Mrs H commented on how the link between the music notes and fractions had strengthened, ‘I can definitely in this lesson see more progression, and a clearer link or where you’re going to, or what your aim is here’ (Mrs H, Interview 2 of 5, 01 March 2019).

From Lesson 5, the link was made explicit by the teacher. In Lesson 3, the teacher had got the children to use paper plates to represent different note values (

Photograph of paper plate learning support materials to visually represent different note values.

Two learners demonstrating with paper plate learning support materials that three-eighth notes are longer than one-quarter note; therefore, is more than.

Another example of this overlaying procedure was in Lesson 8, when the ‘note value line’ was converted into a number line between zero and one (see

So, what’s the last fraction you have to label?

Anastasia: I think it’s gonna be close to the one?

Why do you think 15 sixteenths will be close to one whole?

Anastasia: Because if you had one more sixteenth it will be a whole.

Exactly!

Ava: So, it should be here.

Now, how are we going to find an accurate place? What strategy can we use?

Anastasia: Halve it and halve it again.

Okay, because we know that this is a quarter (points), so if you’re going to divide it into four, it will be sixteenths.

Anastasia: So, you’re gonna halve it and halve it again?

Yes, well done Anastasia!

(Lesson 8 transcript, 19 March 2019)

Example of how the ‘note value line’ was used along with the number line between zero and one.

Additionally, throughout the lesson intervention cycle, and specifically in Lesson 6, music note values were used to demonstrate the concept of the inverse order relationship of unit fractions. Learners’ participation and discussions showed that they were developing a deeper understanding of this, prompting Mr K, in the final interview, to note:

‘I think the inverse relationship came through quite strongly where they had to divide the counts between the different instruments and when they could see the counts on the board. So, if it had fewer notes, it could have been played over a longer period of time, depending on the note value. So, ja, I think the inverse relationship came through quite strongly.’ (Mr K, Interview 5 of 5, 26 March 2019)

It was encouraging that the learners and critical peers recognised that a clear connection had been made across mathematics and music, which is supported by literature, as mentioned earlier (Civil

It was challenging to find an optimal balance between using music note values and fractions, thereby staying true to the co-equal style of arts integration (Bresler

‘Mrs H was not convinced that the music is helping the maths in the [previous] interview. However, I feel that the intervention lessons should be looked at as a whole, which is possible now, after completing Lesson 8. I’ve noticed evidence of the music notes and LSMs helping support learners with the fractions. Mrs H and Mr K have now both made similar observations in this interview.’ (reflective journal entry by the teacher based on Mrs H and Mr K, Interview 4 of 5, 21 March 2019)

The following comments from the critical peer interviews further highlight the balance between the mathematics and music and act as evidence of a co-equal strategy of integration (Bresler

‘I do think they’ve helped each other, definitely … because in the beginning there was lots of emphasis on the music, now there’s more emphasis on the math … there’s definitely a link and the children can see the link between the two.’ (Mrs H, interview 4 of 5, 21 March 2019)

‘Ja, I think, you’ve definitely struck that balance now. I think, obviously you had to lay that foundation of music knowledge … I mean, I think you struck like a very healthy balance between the music and the maths.’ (Mr K, Interview 4 of 5, 21 March 2019)

Having satisfied herself that a balance had been found between the mathematics and music, the teacher analysed and reflected on the benefits that the integrated lessons appeared to have had overall.

In this subsection, we share some of the beneficial findings of this venture into cross-curricular integration.

The integration of mathematics and music provided an opportune context in which learners could see fractions being used in the real-life context of note values making up musical rhythms and melodies. The beauty of mathematics and mathematical relationships in the creation of music could also be explored, linking the activities to the broader mathematics curriculum aims, which is encouraged in the curriculum (DBE

Learners could relate to the rhythm activities and enjoyed clapping the different note values. The examples of singing a note, such as in a choir, showed a real-life context where dividing a note into equal parts would be necessary. Mr K specifically noted the real-life connections learners had made in relation to their understanding of fractions within the context of music:

‘I think it makes fractions more real world, like more real-life … So, I think children are given practical examples now about how fractions can be used in everyday life, in music for example.’ (Mr K, Interview 2 of 5, 01 March 2019)

Part of Lesson 10 focussed on solving problems involving fractional proportional reasoning, which were related to real-life examples in contexts other than music note values. The teacher’s reasoning behind this decision was to observe whether learners could apply the conceptual understanding from the previous nine lessons to other examples. One of the critical moments that both the teacher and the critical peers reflected on was the way Messi (a learner who generally was not confident to participate in mathematics activities) participated in the lesson. He was the only one in his group to recognise that 4 out of 7 days, four-sevenths (), was the same as 8 out of 14, eight-fourteenths (). Although the other learners thought that he was incorrect, he confidently argued his reasoning, showing his peers how he got to his answer through working with the proportion and recognising that the fractional representations were equivalent. This was a true ‘Aha-moment’ for him, as he often experienced mathematics anxiety (as recently diagnosed by an educational psychologist). This makes it all the more interesting that, during a critical peer interview, Mrs H specifically noted that Messi appeared ‘more comfortable to work with the numbers, because he’s learnt them as notes’ (Mrs H, Interview 4 of 5, 21 March 2019). Both the teacher and the critical peers believed that working with music note values and fractions together gave Messi this confidence.

Similar to the above example of Messi, the intervention cycle lessons helped other learners understand and gain confidence in their ability to tackle problems relating to both music note values and fractions. This relates to the advantage of curriculum integration described by Landsberg et al. (

It is better than doing normal fractions (Danny)

I hope to do other lessons like this one (Lionel)

I would like to do more music and a little bit of maths (Paige).

(Learner self-assessment feedback forms, 19 March 2019)

In an informal discussion towards the end of the intervention cycle, class opinion was divided relative to their preference of answering questions of music note values or replying with fraction names and notations. Some learners stated that they preferred ‘doing fractions’, some preferred ‘doing music’ and other learners commented that they did not have any preference, as they were the same. Examples of the variety of preferences can be seen in the following responses during Lesson 8:

Well the music notes are easier because it’s like there’s one whole. It’s easier to put them together, because if you had, uhm, eight sixteenths and then you got [four] eighths it would be a whole. But for some people it takes a long time to figure out fractions.

Fractions … Uh, it’s easier to calculate.

Uhm, they the same, like two halves make a whole.

(Lesson 8 transcript, 19 March 2019)

It seems from such comments, therefore, that the integrated strategies allowed learners additional conceptual resources and representations for working with fractions, thereby increasing opportunities to learn and make sense of fractions, thus developing deeper understanding of the fractional concepts, as suggested by Civil (

The use of music note values in representing fractions allowed for multiple representations to support learning. The lesson activities provided learners’ visual, auditory, tactile and kinaesthetic opportunities for learning, which Eisner (

‘I think because you’ve involved the different senses a lot in the way that you’ve taught these last couple of lessons.’ (Mr K, Interview 2 of 5, 01 March 2019)

Activities, such as the playdough one in Lesson 6 and the paper plate one in Lesson 3, also gave learners the opportunity to learn through practical, hands-on experiences with concrete resources. Many LSMs similarly allowed for learners to construct concrete fraction models, which they could first manipulate and then use in showing and explaining their reasoning:

Paul, how did you know what to label each piece of card?

Uhm, Chanel said that, uhm, because like it was cut into sixteen, we had sixteenths.

Okay, so you had sixteen pieces of card, sixteen notes, so there were sixteen in total. So, one of them would be …?

One sixteenth.

(Lesson 8 transcript, 19 March 2019)

Mrs H noted the benefit of comparing the relative sizes of the concrete models, such as the note value paper plates (see

‘Oh, it was nice discussion amongst the children and comparing fractions and, uhm, putting them [fraction mats] together, working out which one’s bigger, smaller, in a practical way.’ (Mrs H, Interview 4 of 5, 21 March 2019)

Mr K noticed similar value to the practical nature of the activities with the percussion orchestra and clapping:

‘I also liked the practical application, that percussion game, when the one group was clapping the half notes and that group was clapping the quarter notes. I mean, effectively, it’s the same as using the fraction mat, but now it becomes practical.’ (Mrs H and Mr K (combined), Interview 3 of 5, 12 March 2019)

Learners appeared motivated to engage in the lesson because they were intrigued by the new resources and the music examples. They seemed excited hearing the violin and participating in clapping rhythms. A student teacher (Mr W), on observing the first lesson, noted the learners’ intrigue at the novel resources:

‘Uhm, I think it was exciting for the kids, because it’s something new. Uhm, and they want to listen and they want to be involved. So, I thought they were very interactive and keen to do it.’ (Mr W, Interview 1 of 2, 06 February 2019)

Similar positive feedback came from the informal discussion with learners after the first lesson:

We found it fun and interesting.

It was not a boring maths lesson …

It was different to our normal maths lesson.

(Lesson 1 transcript, 06 February 2019)

The following journal entry by the teacher resonated with learner comments:

‘The learners were actively involved and motivated. There were many opportunities for me to identify misconceptions and to address them. I am happy that the learners were all actively involved in the group and individual activities.’ (reflective journal entry by the teacer, 19 March 2019)

The active participation was beneficial for the teacher to make observations and evaluate learners’ understanding. The critical peers shared similar observations with regard to the learner motivation and engagement. For example, they shared the following during their fourth interviews:

‘Uhm, I think I’ve noticed now that all of them seem to be very happy to be involved.’ (Mr K, Interview 4 of 5, 21 March 2019)

‘Oh yes, they loved it. You can see it. Yes, all very good and the explanation, because even a child, like Lionel, you could see he was busy and engaged.’

‘Yes, he generally doesn’t get engaged and involved in lessons as much.’ (Teacher)

‘But he knew what was going on and could ask questions.’ (Mrs H, Interview 4 of 5, 21 March 2019)

Practical activities, such as the music games and the problem-solving competition, motivated learners to engage, including those who were normally shy to participate. Commenting that learners’ involvement in the lessons was a way to assess the success of the lessons, Mr K remarked on the progress that was evident throughout the lessons:

‘I suppose one way of assessing the learners throughout these lessons and their understanding that they’ve gained would be through involvement. And I can definitely see, if you compare to Lessons 1 and 2, as opposed to now, it looked like all the learners were getting involved too.’ (Mr K, Interview 5 of 5, 26 March 2019)

The explicit design for collaborative activities enabled those learners who were taking private music lessons to assist those who had not been exposed to music theory outside of the class music lessons. The following entry from the teacher’s reflective research journal noted that ‘the small group setting allowed for the music pupils to assist the non-music pupils to recognise and name the note values’ (reflective journal entry, 06 February 2019). This collaborative space assisted in developing understanding of (1) how music note values work, (2) the concept of fractions in music note values and (3) the concept of fractions as applied to a range of abstract and applied mathematics problems.

The collaborative activities further encouraged group discussion amongst the learners and between the teacher and the learners. This increased collaboration and participation is similarly described by Landsberg et al. (

‘Yes, I learnt from them. They would mention something and I would say, I didn’t even think of that! So, I learnt a lot from that incidental learning as well, and often it helped me to think of how I would do the next lesson.’ (Mr K, Interview 5 of 5, 26 March 2019)

As noted, the teacher had knowledge and skills in both subjects. During one of the critical peer interviews, however, concern was raised, as to how

‘There’s a link between what’s going on. I mean if my children were doing that in music and then came to [mathematics] class, it would make my job so much easier.’ (Mrs H and Mr K (combined), Interview 3 of 5, 12 March 2019)

This observation from Mrs H is consistent with the arguments made by both Bresler (

As the foregoing discussion has shown, the integration of music into mathematics provided a way in which fractions could be represented other than the traditional representation of pizza or chocolate bars so commonly used in primary school lessons. Such integration, we argue, is beneficial in that it offers teachers an additional strategy to draw on in representing fractions.

This action research study was not about identifying generalised findings, but rather hoping that the findings spark interest and recognition by other teachers in other settings of the value of curriculum integration. We acknowledge that a potential limitation of this research could be that the first author was able to use her strong musical knowledge in the design and implementation of her fraction lessons. This limitation notwithstanding, we argue that integration of mathematics and music holds much potential for supporting student conceptual understanding of fractions and developing productive mathematical learning dispositions.

The question then would be to what extent these findings might be seen as useful to teachers without the necessary musical knowledge. Further research would be needed to find out whether other, non-musically trained, teachers could benefit from the use of these strategies and LSMs; for example, the use of the American note-naming convention may make it a manageable strategy for such teachers. We believe that collaborative working between music and mathematics teachers could overcome challenges that emerge for those teachers who do not have specialised knowledge of teaching both. Research can also be conducted on the use of fewer note values and lower number ranges of fractions to adapt the strategies for younger grade learners.

A key contribution of this article is that it shows curriculum integration as a means of achieving the broader curriculum aims of, for example, developing ‘an appreciation for the beauty and elegance of mathematics’ and recognising ‘that mathematics is a creative part of human activity’ (DBE

This article is a product of a number of individuals’ contributions who offered their time and insight into the various aspects of the study. The authors thank the headmaster of the school where the study was conducted as well as the guardians of the learners and the learners themselves. Two critical peers played a vital role in sharing their reflections; the authors appreciate their time.

The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.

The first author (T.S.L.) was a master of education student, supervised by the second author (S.-A.R), with the third author as co-supervisor (M.G.). This article emerged from the first author’s master of education thesis. Whilst the first author carried out the actual writing, the second and third authors made considerable contributions to the discussions around the topic, responded to earlier drafts of the article and provided constructive suggestions regarding the overall content.

The first author submitted a written research proposal for consideration by her faculty’s Higher Degrees Committee in August 2018. The University’s Ethical Standards Committee of Rhodes University granted ethical clearance for this study (06 November 2018), which was then renewed for the following year (2019; ethical clearance number: Lovemore20181023).

This research has been supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation (NRF) (Grant No. 74658). The NRF’s financial assistance towards paying for the first author’s studies is hereby acknowledged. Opinions expressed and conclusions arrived at are entirely the authors’, however, and should thus not be attributed to the NRF.

Data sharing is not applicable to this article as no new data were created or analysed in this article. Data from the first author’s master’s research work were used in the writing of this article.

Opinions expressed and conclusions arrived at are entirely the authors’, however, and should thus not be attributed to the NRF.