Identifying Factors for Integrating Math and Music Education at Primary Schools in

Samuli Laato Romanus Shivoro Nicolas Pope Dept. of Future Technologies Faculty of Education Dept. of Future Technologies University of Turku University of Namibia University of Turku Turku, Finland Windhoek, Namibia Turku, Finland [email protected] [email protected] [email protected]

Frednard Gideon Erkki Sutinen Office of the PVC: Academic Affairs Dept. of Future Technologies University of Namibia University of Turku Windhoek, Namibia Turku, Finland [email protected] [email protected]

Abstract— school system puts little emphasis music performances is not easy [5]. To address the decline, on art subjects such as music and emphasizes STEM subjects scholars are proposing to combine music with other subjects instead. Despite heavy focus on math teaching at primary schools, like mathematics [6] or computational thinking [7]. many students are not learning. This study investigates how the Furthermore, as education is becoming more and more rich music oriented indigenous can be ubiquitous due to the availability of the internet and its offered leveraged to assist in math education by teaching math via music. resources, perhaps it’s time for education to shift more First, previous findings from literature are discussed in the towards fostering intrinsic motivation towards learning, than Namibian context. Second, three focus groups (n=12, n=2 and teaching skills which can be evaluated via tests. n=3) are interviewed and consulted in order to find the potential The aim of this study is to explore the possibilities of benefits and barriers of starting to teach math and music leveraging the rich musical culture of Namibia to enhance together. The results indicate significant potential in cross- math education. To this end, opportunities arising from disciplinary math and music education for both learning and combining math and music education are explored. This is motivation. However, equally many barriers for implementing the done by first observing and analyzing the Namibian school new form of teaching were discovered. Currently the lack of context and then literature on combining math and music. This support from the national school curriculum and teachers is followed by an interview of three focus groups who were hesitation to adopt new teaching methods are the biggest regarded experts on . Thus, the research challenges. goal of the paper is to identify the potential benefits, barriers and challenges that integrating math and music education has Keywords—math, music, cross-disciplinary education, phenomenon-based learning, in the Namibian context. The manuscript ends with discussion and future work on the findings. I. INTRODUCTION II. PRIMARY EDUCATION IN NAMIBIA Several studies have demonstrated that achievements with a music hobby correlate with success at school and even The primary education in Namibia has improved since the academic success [1]. For example, it has been discovered that country claimed its independence in 1990. However, income students who have studied music for two years or more, score inequality is still a big issue in the country and has only on average better at math than their peers [2]. Another study slightly improved since independence [8]. The Namibian found that practicing and actively playing a musical context is unique in that there are public and private schools instrument had a positive impact on academic success, with very different learning environments. The public schools especially in language and arts, although there was a positive can have 40-50 students in the class and a single teacher correlation with math as well [3]. These kinds of statistical teaching them. With no school books or technology at their analyses have been criticized for not screening for factors such disposal, hard discipline is required for teaching to be as parents’ wealth and their investment in the education of effective. On the other hand, there are many private schools their children. Still, the discovered correlations suggest with fewer students per teacher and more diverse teaching practicing and playing music may have several benefits for materials and methods. Both public and private schools still students. In Namibia despite increased resources spent on follow the same national educational curriculum. mathematics education children still often consider math As Namibia is the home of several ethnic groups, schools uninteresting. Music can help enrich the way mathematics is are naturally multicultural. At least 10 different languages are learned. being taught at primary schools including English, Rumanyo, Despite the several benefits observed from learning music Rukwangali, Thimbukushu, Silozi, Oshindonga, at schools, a global decline in music education at all levels has Oshikwanyama, Otjiherero, Setswana and [9]. been reported due to a growing emphasis on standardized Some languages such as Subia and Oshimbalantu can also be evaluation, negative approach to music advocacy, fewer spoken in some schools, even though they are not official resources available and many educational reforms which lack languages. In order to unite the large multicultural country, the support for music [4]. Even if some reforms give more Namibian government has set English as the official language freedom for music educators to expand their teaching, the and instructed primary schools to switch all teaching to growing need to evaluate progress in all school subjects can English at the start of grade four. This sudden change in the become an issue, as objective evaluation of, for example, teaching language has been made easier by already having English classes and lessons during primary school years 1-3.

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE However, reportedly the level of English that the primary biggest disrupting factors being the mobile phone and the school teachers can speak can vary greatly. Recently internet. Simply the change mobile phones have brought to Namibians have been looking at how to preserve the unique schools has had an enormous impact [15], but the learning culture and languages of their tribes, and for this end, learning they afford outside schools can be regarded as the real technologies have been suggested as a solution. unharnessed potential [16]. A. Math Education in Namibia The formal school education can teach students something The Namibian government made primary mathematics they would not learn on their own, and for many this is a major education compulsory to everyone at the beginning of 2012, justification for the industrialized school system. The main and it is now regarded as one of the most important school argument is why pay for schools if the same content can be subjects by the government. Before then, Namibia suffered learned at homes [17]. Thus, schools have focused on teaching from poor math results especially in the rural areas. This can students basic knowledge from a wide range of subjects, be seen at the university level where Namibians have including those that are not naturally interesting for the comparatively low enrollment rates in STEM subjects [10]. students. This has substantial benefits, as students learn basic As math is often seen as the most crucial part of STEM [11], skills regardless of their motivation to do so. Students can then most focus on primary level education has been directed later after primary school choose which subjects they want to towards it. Mathematics is currently taught in Namibia all the pursue for a possible future career, while having the informed way up to the university level where it an essential part of opinion on what each subject consists of. However, the danger many degrees offered both in University of Namibia (UNAM) here is that natural learning is neglected by relying too much and Namibia University of Science and Technology (NUST). on formal educational institutions such as schools. [9] To take advantage of natural learning and new emerging National math education in Namibia needs to take into learning opportunities, for example, Finland has gone to account the large number of ethnic groups and spoken introduce a few hours of compulsory phenomenon-based languages. For example, many groups such as those speaking teaching at primary schools in their school reform in 2016 Rumanyo, Rukwangali, Thimbukushu and Oshikwanyama [18], [19]. The idea behind phenomenon-based teaching is to naturally use base 5 number system aka quinary numeral tie education into real life phenomena, scaffolding students’ system as the standard, instead of a base 10 system. In the ability to apply what they have learned in practice and quinary numeral system, for example, the digits 12 refer to the fostering an intrinsic motivation to learn more. In this case number 7. As the notation is the same as in a base 10 system music is ideal because it can be integrated into teaching other but the meaning different, this can cause problems for subjects. According to the pedagogical principle of educators and ethnic groups in understanding each other. constructivism, students can absorb new learning content Perhaps because of this, currently all primary schools have better when it relates to a phenomenon they are familiar with moved towards teaching the base 10 system. [9] [19]. Despite the theoretical benefits of phenomenon-based learning, it cannot be fully harnessed unless proper teaching B. Music Education in Namibia materials or training is provided to educators. There is also the Music education is not part of the national educational difficulty of transferring knowledge from one area to another. curriculum of Namibia. Yet, it is still being taught in many Therefore research and exploration in real life contexts is schools. Public schools usually have music lessons only in the needed in developing and creating multidisciplinary learning first three classes, even though private schools might have technologies and teaching methods which support music lessons throughout the entire primary school. Despite phenomenon-based learning. music not being taught at schools, it is a major part of students’ lives, as many like to sing and dance. IV. COMBINING MATH AND MUSIC EDUCATION AT PRIMARY SCHOOLS Arts, humanities and cultural studies can promote critical As new educational content is introduced to primary thinking, as there is a link between creative thinking and schools, educators are faced with the challenge of how and critical thinking [12]. Thus, it has been argued that these where to teach it. Instead of creating a new subject, scholars should be part of not only primary education, but also higher have proposed to teach new content such as computational education [12]. However, the lack of formal education on thinking together with existing school subjects, for example, these matters does not mean that they are not being learned. In music [7], [20]. In order for this approach to work, the a multicultural country promoting human interaction such as educational content and the subject it is integrated with, a need Namibia, these subjects are being learned also outside schools to have a natural connection. Besides computational thinking, the natural way, via informal learning [13]. another subject that is often proposed to be taught with music III. FROM SCHOOL SUBJECTS TOWARDS is mathematics [6], [21]–[24]. However, the two subjects PHENOMENON-BASED LEARNING cannot be just mashed together, and therefore several strategies and technologies for integrating math and music in The current formal education system where educational education have emerged. content is organized into subjects has so far been the most effective solution globally for providing a quality education to Even though music is filled with mathematical relations, all [14]. Arguably having separate subjects helps students sort simply listening to music while taking math tests has been new information in their minds, which can be both a blessing found to have a small positive effect at best [25]. In order to and a curse. This helps students focus on specific learning benefit from combining math and music, more complex content and specialize in it, and it also helps teachers plan their solutions are required. Scholars have argued that simple teaching more clearly. So why does this system need to be drilland-practice types of routine tasks, for example in math, changed? The main reason is that the environment are not enough for the development of further knowledge. surrounding education has dramatically changed with the Instead, strategies motivating students for reflection, conceptualization and problem solving are needed. Educators One method to make music out of mathematics is data should try to move towards teaching methods which fosters sonification, that is, creating non-speech audio out of data to students’ deliberate practice [26]. Thus, instead of simply convey information [40]. Although data sonification can playing music for students or counting beats, students should produce music [41], it does not necessarily do so. Data be taught to use mathematics to create or understand music sonification has been used in education to combine music and [27]–[29]. By engaging in activities where students think, math by, for example, sonifying graphs plotted in coordinate reflect and conceptualize music using mathematics, students grids. It is argued that providing multi-sensory experiences of can learn to think of music in mathematical terms, and, mathematics and educational content in general is useful, and whenever they then hear a song playing, they can imagine and the more diverse the ways to retrieve information are, the analyze the music they hear with mathematics. This can also better [40]. work the other way around, as musical rhythm has been proposed to be important for mathematical thinking [30]. A. What kinds of math can be taught via music A recent study investigated how fractions, equivalence, ordinance, and division can be taught via music, with promising preliminary results [22]. In addition, the popular piano roll representation common in many music software can be used to at least introduce students to the mathematical concept of a coordinate grid [31]. Besides these concrete examples, higher level thinking skills such as creative thinking and imagination could be fostered via music education [32], which are also useful in mathematics. Mazzolla et al. [33] have collected in their book ”Cool Math for Hot Music” a wide list of examples of math present in music. Many of these concepts are more advanced math than is currently taught at Fig. 1. The rhythm being presented via decimal numbers in the primary schools, however, this only shows that there are future mathematical composing software Harmony Hippo. Source: screenshot opportunities to further dive into mathematics via music [34]. taken by authors On the other hand, as math teaching without the need to Professional composing software have also been identified include music can be more focused, the effectiveness of as having affordances for teaching mathematics. Digital audio crossdisciplinary or phenomenon-based learning can be called workstations, for example, have been found to have the into question [19]. Generally studies comparing the potential to teach basic calculus as well as working with effectiveness of teaching math on its own compared to coordinate grids. The now less popular early type of teaching it with music are missing. Even though positive composing software, the tracker, has been shown to require learning outcomes on math have been demonstrated, for the users to be able to work with the 12-number base system example by An et al. [27], many studies have been focusing and logical structures [31]. The use of 5-base, 7-base and 12- on the effects that combining music and math learning has on base number systems are in fact quite common in western 12- students’ motivation to learn more [21], [22], [35]. notes per octave music theory. The good part of using professional music software or similar for teaching B. Learning technologies combining math and music mathematics is that students can use the skills they learn to A major issue in teaching mathematics, or both music and compose music themselves, and hone their skills as both math at the same time, is teachers’ limited skills and lack of musicians and mathematicians naturally on their freetime educational materials [28]. Therefore many practical tools outside classrooms. Finally, it is worth to remember that in have been developed. These can be technologies such as a addition to solutions and technologies designed specifically to mathematical music composing tool Harmony Hippo [23], a teach math via music or vice versa, other resources can be virtual game for learning fractions via music [36] and used as well. For example, An and Caparo [42] designed an Listening to Math: Kids compose with LEGO [37]. Learning entire educational curriculum focusing on combining music technologies have several benefits in comparison to and math. alternative methods. For example, they provide students instant feedback on their compositions, which has been C. Importance of Motivation identified as important in processes involving creative Even though intervention studies combining math and thinking [38]. These kinds of technologies can also be used as music education have been shown to have a positive effect on objects to think with, aka construals, allowing students to students’ math skills [27], another direction to explore is the explore the relationships between music and math on their effect these activities can have on the students’ motivation to own [34]. As an example, in the software Harmony Hippo, learn both subjects. Attitude and academic time have been students can see the relationship between audible music and found to positively correlate with mathematics and science both decimal and fractional numbers. The user interface achievement [43], which suggests that improving students’ showing the decimal number representation of the rhythm of attitude and instilling an intrinsic motivation to learn are a single melody in Harmony Hippo can be seen in Figure 1. important goals for educators. Of course motivation is not as Differences have also been reported in the learning outcomes easily studied as skills which can be measured via quantitative of different technological approach to teach math such as objective tests, and perhaps thus, it has been largely ignored fractions, highlighting the importance of rigorous testing and by many school curricula. As previously mentioned, the time validation of teaching methods [39]. spent outside schools is now highlighted for learning, and thanks to the internet, children have limitless learning resources at their disposal. It is therefore no surprise integrating learning and playtime has been a goal of several  Are there any barriers you see in teaching math via education technologists recently, with the goal of getting music at Namibian primary schools? students intrinsically motivated to learn more [44], [45].  Moving beyond, how would you leverage the rich It has also been demonstrated in previous studies that multicultural heritage of Namibia to teach integrated music and math education can have a positive mathematics? impact on students’ intrinsic motivation to learn more of the subjects [21], [22], [35]. This is further supported by, for  Do you have something else in mind? example, a study on 2nd grade primary school students, which The second focus group, consisting of primary school found that integrating music and movement into mathematics children, were interviewed about their initial conceptions of education had benefits for emotional, behavioral and cognitive music and math. They were first taught the relationships engagement [21]. Even relatively short sessions of using between math and music using exercises. Afterwards, the technology to learn math and music have been enjoyed by children were asked to draw using pen and paper how they students [35]. would teach math and music at schools. The children were Combining math, music and dance education has been also invited to test and try an educational mathematical reported to increase motivation towards the subjects for pre- composing software called Harmony Hippo [23]. The consent service teachers learning to teach the subjects [46]. Lee [47] of both the participants and their guardians was asked and argues that when exposing students to the underlying received for the study. mechanical structures of music, they can observe the The final focus group consisted of two university relationships between logic and music and through these personnel, one a music teacher educator and the other math experiences learn music theory naturally. This leads to new teacher educator. They were interviewed about the current inspirations to learn [47]. state of music and math education at Namibian primary D. Summary of Findings from Literature schools. They were also asked about potential benefits and barriers of teaching math and music together at schools and Technologies focusing on integrating music and math what they felt needed to be done in order to make combining should combine them in a natural way, leveraging the existing math and music a viable teaching method. mathematical relations in music [22]. These technologies should try to activate students’ own reflection, VI. RESULTS conceptualization and problem solving [26]. It is important today that educators ensure students also stay intrinsically A qualitative analysis was done on the open answers of the motivated to learn more on their free time, thus, this should be first focus group. Four categories of answers were identified: taken into account in math and music education [48]. The potential benefits, potential issues, how to leverage the technologies could also be designed in a way which allows Namibian culture and challenges in implementation. Each students to learn dependencies between math and music by unique suggestion in these four categories is listed in Table 1. meddling with the software [34]. Finally, students need to The focus group saw several potential benefits on combining learn how to use real math to create music to give them idea music and math education, however, there were equally many that math is useful and can be applied to create fun things such challenges in implementing it. as music.

V. INTERVIEWS WITH FOCUS GROUPS In order to investigate the strengths and possible barriers of adopting teaching methods and technologies combing music and math at primary schools in Namibia, three focus groups were consulted. The first one consisted of research personnel employed at UNAM, NUST and University of Turku (n=12), the second focus group consisted of primary school children (n=3), and the final one of a music and math educator (n=2) at UNAM. Each expert group was consulted in order to identify the potential benefits, barriers and unique challenges of the Namibian school system for combining math and music education at primary schools. The first focus group, consisting of university research personnel, was called to attend an open seminar at University of Turku overseas campus at UNAM premises in Windhoek, Fig. 2. A picture from the meeting with the second focus group Namibia. First, a presentation of a few techniques combining music and math was held, which included interaction and A. African Rhythms, Math and Music communication between participants and the presenter. The It is said rhythm has a special meaning for many of the presentation contained the same findings from literature people in Africa [49]. It was furthermore regarded by two presented in this paper. After the presentation, the interviewed experts as a large unharnessed potential, which questionnaire was distributed containing the following open could be used not only to teach mathematics, but other questions. All open answers were read and from them, each subjects as well. For example, music lyrics could be used to unique suggestion was recorded. teach subjects such as English and history. Several people are  What potential benefits do you see in teaching math via still using rhymes to teach their children things, so extending music at Namibian primary schools? the use of music to primary education and even higher TABLE I. UNIQUE SUGGESTIONS FROM THE FIRST FOCUS GROUP

The thoughts of the first focus group on combining music and math education at schools in Namibia Potential Benefits Potential Issues Challenges in implemen- How to implement in tation Namibia

Mixes the line between Students who dislike music To get teachers interested Use of local rhythms and formal and informal learning might get discouraged to do and involved melodies. (folk songs) math Can keep students Need to convince Involve dancing engaged education curriculum developers about the idea. Makes maths more inter- Lack of computers Involve entire families in or music creation. esting smartphones in education Gives a fun example where No resources or skills to do Cultural visuals of Namibia math can be applied this. could be integrated in the UI of math/music. Remove some of the Namibian school kids are Involve clapping or real intimidation from math nervous and don’t dare to instruments express themselves. Musicgets taught Teacher training does not Involve materials or and gains more value include combining subjects. objects children can relate to.

Music and math can be Lack of financial resources taught together even in public to restructure existing schools which have no access educational structures. to computers or smart devices.

national educational curricula, as well as teacher education at universities, need to be influenced. An often mentioned issue education seems natural. Namibian culture is also filled by the focus groups was that it can be difficult to convince with dance, clapping and various musical instruments, which teachers that teaching math and music together is a good idea could be also used to teach mathematics. One expert suggested and get them interested. Equally often it was mentioned that that math and music could be extended beyond being an there is a lack of support for re-training teachers who are individual activity, enhancing it via collaboration with friends currently in the working life about cross-disciplinary teaching. and families. Additionally, as many of the practical tools for combining The consultation with the second focus group, which math and music rely on smart devices or computers, many consisted of primary school students, showed that the students public schools, who do not have access to such equipment were quickly able to draw connections between fractional cannot utilize them. A similar concern was also raised citing numbers, decimal numbers and musical notes. A picture of the Namibia’s current financial trouble and lack of resources and discussions with the second focus group is shown in Figure 2. funding needed to implement new teaching methods. Exercises which involved clapping the rhythms demonstrated the students’ existing rhythmic ability and willingness to VII. DISCUSSION participate in producing music themselves. As it was also A. Key Findings suggested by the other two focus groups that music should be also actively produced by students, this opens new Currently students’ progress on school subjects is mostly opportunities for creating and testing mathematical music evaluated via what the students produce during formal tests or notations. That being said, focus groups 1 and 3 identified projects. However, the evidence in employing teaching hard discipline at schools to be a potential barrier in including methods where math and music are combined and taught things such as dancing and clapping to math class. together suggests that these improve students’ intrinsic motivation to learn both subjects [21], [22], [35]. Cultivating B. Challenges in combining math and music intrinsic motivation to learn is especially important in the 21st education in Namibia century where educational resources are constantly at users’ The Namibian ministry of education has given teachers disposal via the internet, suggesting that an increasingly large strict guidelines on what to teach and how. Therefore in order focus should be put on enhancing students’ motivation to to allow for teaching math and music simultaneously, the study on their free time. This requires joint effort from

Fig. 3. Examples of some subjects which could be integrated with music education

schools, guardians and the ministry of education. a concern was raised that not all children are interested in Furthermore, teaching students to think of music via music. Previous studies suggest the use of diverse teaching mathematics seems to help in integrating mathematics as methods in math can have a positive impact on students’ part of their daily lives. An increase in spontaneous interest [52], and thus, even if music and math could be mathematical processes has been linked to the development seamlessly integrated it should not be overdone. of further mathematical knowledge later on. For example, pre-school students spontaneous focusing on numerosity, B. Limitations subitizing and counting skills correlate with their math skills The three focus groups interviewed in the current study six or seven years later [50], [51]. For this reason it is were regarded as experts on the discussed subject. They paramount to introduce applied math early to students, to represented different age groups, genders, cultures and ensure that mathematics will be part of their intellectual positions in life. Although multiple viewpoints were development. This also supports the proposition to start included, it is possible that some important aspects did not integrating math and music education already at primary arise during the interviews. The small number of schools. participants in the second (n=3) and third (n=2) focus group will have also lead to some bias or lack of viewpoints. The The interviewed focus groups saw multiple benefits in focus groups’ lack of criticism towards the general idea of teaching math via music. Not only could it help spark an combining math and music at primary schools might be an interest to learn outside schools, but it could also leverage indicator of this. This study also explored integrating music the rich music-filled culture of Namibia for learning. and math together at an abstract level. Despite involving Existing folklore, rhymes and themes could be used not only stakeholders in the focus groups, empirical practical as audio, but also as visuals in technological solutions evidence is still required to confirm the predictions made by designed for the Namibian context. Using music to teach the current study. math was regarded as a solution to give music more value at formal education institutions. The idea of teaching math via C. Future Work music was extended by some experts to cover more subjects The results of the current study seem promising from a and it was suggested that music could act as a common pedagogical standpoint as well as from the viewpoint of unifier bringing several disciplines together. This could developing relevant educational technologies. Yet, the study even lead to music-centred learning where music is more identified several barriers and potential challenges in heavily present at schools. An example of this is shown in implementing the new teaching methods combining two Figure 3, where examples are given of how four school subjects at primary schools. The future work in this area will subjects: math, history, sports and language could be taught require intervention studies at local primary schools, both via music. Music can thus in theory act as a bridge to bring those who do not have technology at their disposal as well subjects such as history and math together. Despite all this, as those who do, to determine how well the proposed teaching methods would work in practice. In case positive school students,” Research Studies in Music Education, vol. 22, no. results emerge, next steps will have to include further 1, pp. 14–27, 2004. investigation on how to remove some of the identified [4] J. L. 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