Ethnomathematics in Intermediate Phase: Reflections on the Morabaraba Game as Indigenous Mathematical knowledge

Abstract

Mathematics education remains a worrisome issue in the South African education system. This dilemma presents itself in the underperformance of learners in Intermediate Phase mathematics. In an effort to address this challenge and develop alternative approaches to the teaching of mathematics, a university-based project was initiated. As part of the project, this article reflects on the experiences of five project members who observed the implementation of Morabaraba, which is an Indigenous game, rich in mathematical relevance. This qualitative case study explored how mathematics teachers implemented the Morabaraba game to teach Intermediate Phase mathematics content. The method used to capture the data entailed reflections of the team that were derived from the observation of mathematics lessons in the Intermediate Phase. From these observations the researchers found that teachers invented their own rules when integrating mathematical concepts; they reinvented the game to cater for the complexity of mathematical content and experienced challenges in the playing of the game. We conclude that the Morabaraba game can be implemented, with practical adjustments, to comply with the objectives of the mathematics concept. The recommendation is that ethnomathematical games be employed as a teaching strategy as they are found to encourage active learning. Future research endeavours include exploring how ethnomathematical games can be sustained for future use.

Keywords:

• Africanisation
• ethnomathematics
• Morabaraba game
• mathematical concepts
• reinventing

1. Introduction

The poor performance of African learners in mathematics is becoming a major concern in educational circles because of its direct impact on economic growth and the creation of employment opportunities for African youth. Learners’ performance in mathematics suffered the perils of a colonial educational system that alienated learners from the knowledge content of the subject. Yet the African civilisation possesses a rich mathematical legacy, hitherto suppressed, but slowly emerging in the decolonisation of mathematics debate in the form of ethnomathematics. The need to seek African solutions to African problems, such as poor performance in mathematics, is recognised by making a conceptual connection between decolonisation, Indigenous knowledge and mathematics. The importance of decolonising education is particularly enhanced through an Africanisation perspective for African countries. Le Grange (2018) determines that Africanisation is a decolonial model as it serves to undo the oppression of colonialism rendered on the African state. Letsekha (2022) further adds that an Africanised perspective emerges from the political, social and economic injustices that were forced on African countries through colonial endeavours. Therefore, Letsekha (2022) argues, Africanisation allows for Indigenous knowledge systems that were previously stripped from Black people through colonialism.

Mathematics education upholds colonial structures in the way that it is still being taught and learnt in schools. South African mathematics teachers have not yet made the transformation to a learner-centred perspective that endorses an Africanised knowledge system (Meeran & Van Wyk, 2022). Perhaps that is the reason why learners are struggling to cope in mathematics in South Africa, as Reddy et al. (2016) verify through the pathetic results that South Africa obtained in the Trends in International Mathematics and Science Study (TIMSS). In the most recent TIMSS, South Africa was listed at the bottom of the 64 countries that participated in the study (Mullis et al., 2020).

In an endeavour to address the problem of poor mathematics performance, a team of university-based researchers introduced an ethnomathematics project to teaching mathematics in a cultural paradigm in some Intermediate Phase South African classrooms in Tongaat, Verulam and surrounding schools. Aikpitanyi and Eraikhuemen (2017) clarify the reasoning for using such a strategy by stating that mathematics can be grasped more effectively if the mathematics that is used in the daily lives of existing cultures is brought into the classroom to improve learner results. Indigenous games was the chosen platform to encourage learners to enjoy mathematics in a fun, yet relevant way in the classroom (De Beer, 2019; Ribeiro et al., 2020).

Through the various observations made by the project researchers of teachers teaching various Indigenous mathematical games, Morabaraba was the most commonly used game that was employed to teach mathematics concepts in the Intermediate Phase. However, what we did notice was that the teachers adapted the rules of the game, in innovative ways, to make it relevant and purposeful. This study therefore explored how teachers used the Morabaraba game to enhance Intermediate Phase learners’ understanding of certain operational mathematical concepts such as factorisation, addition and subtraction. This study was informed by the following research question: What are the relevant mathematical insights identified through the observations of the Morabaraba Indigenous game played in the Intermediate Phase mathematics classroom?

The sections that follow will include a literature review of the Morabaraba game and how it is used in the classroom, and the application of the Sociocultural theory with the theoretical principle of the ethnomathematics concept will be explained. Methodologically, the study was framed as a case, using observations and reflective reports to collect and analyse the data. The methodology is followed by the analysis section; thematic analysis was used to analyse the findings and discuss the relevant themes using the literature. Finally, the conclusion will summarise the main points of the article.

2. Literature Review

2.1. Using the Morabaraba Game in the Classroom

People in Africa use Indigenous games for entertainment, physical fitness, recognition and status within their communities (Dyer, 2013). Although these are the main intentions, the games also develop values such as patience and respect, and skills such as strategic thinking, communication and decision-making (Van Dijk & De Dreu, 2021; Bayeck, 2018; Jonassen & Hung, 2012). In addition, Bayeck (2018) points out that board games are worth investigating for their learning potential, particularly in a classroom setting. These explications show that values and skills could be further developed in a formal setting like a classroom. For example, strategic thinking is a skill that is needed in problem-solving activities that involve ‘unseen, non-routine problems (which are not necessarily difficult), higher order understanding and processes’ (Department of Basic Education, 2011: 296). In acknowledging the relevance of Indigenous games, Madimabe et al. (2022) recommend that the Department of Education facilitate the process of developing materials that will help teachers incorporate Indigenous knowledge into their lessons. Similarly, Amlor (2016) suggests that further investigations should be conducted to come up with African-centred school curricula for use in schools.

Several studies have been conducted on how mathematics teachers use or integrate the Morabaraba game in the classroom (Nkopodi & Mosimege, 2009; Tachie & Galawe, 2021; Tangkur et al., 2022). In their study, Tachie and Galawe (2021) recommend that a comprehensive study be conducted to enforce the use of Morabaraba to enhance teaching and learning. In other words, any study related to the use of Morabaraba should include or deal with all or nearly all of the elements or aspects of the game. Furthermore, Nkopodi and Mosimege (2009) explored integrating mathematical concepts using the cultural significance inherent in Morabaraba. In the same vein, Tangkur et al. (2022) found that the use of Indigenous languages enables a quick understanding of mathematical skills among children.

The study by Rossouw (2002) highlights the fact that the Morabaraba board game was used to teach tactical skills to empower young warriors with cattle raid and leadership skills. Tangkur et al. (2022) further advise that there is a need to associate an Indigenous game with a particular domain of mathematics. This view seems to suggest that a single Indigenous game cannot be one-size-fits-all. Because the use of Indigenous games in formal mathematics is relatively underdeveloped, research in this field should be sensitive to potential contextual factors which may influence the quality of learning and cognition at classroom level. That being said, this study reflected on how teachers used the Morabaraba game to enhance Intermediate Phase learners’ understanding of mathematical concepts.

2.2. Incorporating Cultural Heritage when Using Morabaraba in the Classroom

Although it is acknowledged that teachers decide on the modes of instruction that are most appropriate to their circumstances to enhance learners’ learning (Ramnarain & Schuster, 2014), Mosimege (2003) emphasises that the attachment of specific cultural meanings is important to have a deeper understanding of many Indigenous games. Furthermore, Nkopodi and Mosimege (2009: 389) believe that ‘leaving the socio-cultural context out when Indigenous games are used deprives the mathematics learners of the rich context that is necessary to fully understand and use such games in mathematics learning’. The key indicator from this understanding is that learning should carry social and cultural meanings (Burnett, 2006). Similarly, Mosimege and Ismael (2004) emphasise the importance of considering the game in its entire context (historical, social and cultural). Also, Hadebe-Ndlovu (2022) sees the incorporation of games as the opportunity to encourage learners to use the correct mathematical terms and highlight the mathematical concepts.

To understand the Morabaraba game better, the Indigenous knowledge of cows and the value they hold in African cultures is explored. The game is discussed in the context of how the Tswana culture values cows (Bayeck, 2018). The stones used are symbolically referred to as cows. When playing this game, players need to keep in mind the Indigenous meaning of possessing cows as a form of wealth and the enhanced status of the winner in the community.

2.3. Rules of the Morabaraba Game to Integrate Mathematical Concepts

Figure 1 shows the Morabaraba board on which the game is normally played. Two players are involved in this game, and they play against each other. They normally sit opposite each other. The game is played by placing the cow on a vacant point and moving it horizontally, vertically or diagonally (Bayeck, 2018). When the players are each left with three in their hands, they then ‘fly’ the cow. Marivate (2009: 47) explains that this means that the player is then allowed to move anywhere on the board where there is an empty node. They no longer have to move to an adjacent connected node. The aim of placing the cow is to block the opponent and prevent them from winning. If one player is left with three cows and the other is left with more, only the one with three is allowed to ‘fly’ the cow. Normally the game ends when one opponent cannot move and the other wins the game.

Figure 1. Morabaraba board

There is no consensus or agreed way in the literature on how to integrate Morabaraba in mathematics lessons. In Nkopodi and Mosimege’s study (2009), learners played the game while the researchers analysed it for mathematics concepts that were demonstrated by the learners when playing the game. Learners applied the mathematical skills pursuing explicitly stated lesson outcomes. In Moloi’s study (2015) learners played the game and identified the mathematics concepts themselves. Moloi’s approach encouraged learners to think about mathematics concepts while playing the game. Thus, the focus was on playing for fun rather than a deliberate pursuit of achieving specific mathematical learning outcomes. We argue that teachers should be guided by their lesson’s objective in using Morabaraba in their classrooms.

Rules of the games ensure fair competition among participants. Thus, they should be followed when a game is played. Following the rules of the game is in line with mathematical problem-solving, as certain rules must be followed in solving a mathematical problem. Nkopodi and Mosimege (2009: 379) remind us that ‘in a game, participants have to follow the rules of the game or come to a consensus on how the rules can be amended’. They further emphasise that playing a game according to the rules is similar to problem-solving where a solution is obtained through application of the rules. The said study also found that as learners are playing the game, they learn the mathematics vocabulary. They further advise that if games are recorded, they can still be used during the lesson because teachers can pause the video and ask more questions related to mathematics. In their study, Tachie and Galawe (2021) point out that playing the Morabaraba (a three-in-a-row type) game (Mosimege & Ismael, 2004) is in line with mathematical problem-solving in the sense that although all players aim to win the game, there is a need to follow the rules. They further indicate that players plan their moves and strategies while keeping the rules in mind, which illustrates the application of mathematical skills in a competitive way.

Mosimege (2020) found that a few learners deviated from the rules of Morabaraba, and concludes that the deviation might have been a result of an agreement between the players. However, he makes no mention of the roles of the rules of Morabaraba in enhancing mathematics teaching and learning. Spangenberg (2021) studied the affordances of cultural artefacts in mathematics and found that four out of 10 participants used Morabaraba as their cultural artefact to teach mathematics. One of the participants explained the rules of the game but did not explain how the rules of the game assisted learners in understanding mathematics concepts better. From this literature review, it can be concluded that there is an awareness of the game Morabaraba, but its hidden mathematical value is yet unexplored and latent. This study intended to explore the mathematical knowledge hidden in the Indigenous game, by adopting ethnomathematics and the Sociocultural theory as the theoretical lens to make a conceptual link between Indigenous knowledge and modern mathematics teaching.

3. Theoretical Framework

The Sociocultural theory was initiated by Vygotsky (1997) and deals with peers working together where the more knowledgeable learner informs the other learner in the interaction but also what the learner himself/herself brings to the interaction through their culture which shapes the interaction. Hence, this theory works well as through the collaborative nature of the Morabaraba game, which is a culturally based Indigenous game the learners play together to understand the tenets of mathematical concepts. Furthermore, the theory blends with the concept of ethnomathematics.

The term ethnomathematics was coined by D’Ambrosio (1978) at an annual meeting of the American Association for the Advancement of Science (Tutak et al., 2011) and the theoretical principle relevant for this study is the connection between culture and mathematics. Mania and Alam (2021) categorise those aspects of mathematics that relate to culture as arithmetic, classifying, ordering and modelling. The relationship between culture and mathematics allows for mathematical learning to become relevant because by integrating culture into the lesson, the teacher is bringing contextual significance to the classroom. This relevance of using what learners are familiar with is believed to have a positive effect on the learners’ cognitive levels in mathematics (Widada et al., 2020) through the development of a curriculum that includes cultural values and makes mathematics more accessible to all learners.

The rich knowledge that ethnomathematics provides for learners of diverse languages and cultures in South Africa has prodigious implications for mathematics learning. Machaba and Dhlamini (2021) describe the rich cultural heritage from Indigenous games and cultural artefacts (round huts, wire cars, beadwork, woven baskets), the South African flag, architecture and Ndebele mural art. The implications for learning mathematics through the cognitively stimulating tactics in the Indigenous games provide a resource for homing in on learners’ mathematical skills (Chahine, 2020). Ethnomathematics as a strategy is therefore regarded as a means to meet the needs of learners in the classroom. The section that follows deals with how this study was carried out.

4. Methodology

A qualitative approach was used, as the nature of the data to answer the research question warranted an understanding of experiences (Cohen et al., 2018). There was a need to gain a deeper understanding of the experiences of a team of researchers through their observations of ethnomathematics lessons based on the Morabaraba board game.

4.1. Sampling and Participants

The study focused on the observation of lessons in ten schools in a rural and semi-rural area in KwaZulu–Natal, South Africa. The observations took place in the Intermediate Phase (Grades 4–6) mathematics classrooms with 10 teachers. These teachers were purposively sampled (Cohen et al., 2018) because they taught mathematics in the Intermediate Phase in schools that were regarded as disadvantaged. The team of five researchers observed the lessons based on the Indigenous game of Morabaraba. They then reflected on what they had observed. The Intermediate Phase was chosen as ethnomathematical games is a fun and relevant way for learners to learn mathematics in this phase. Moreover, as was stated in the introduction, the project was undertaken to improve mathematics performance. We felt that if learners improved their performance in the Intermediate Phase, they were more likely to be motivated to learn mathematics in the Senior Phase (Grades 7–9) and the Further Education and Training Phase (Grades 10–12).

4.2. Background

Ethnomathematical games as an Indigenous tool to teach mathematics was introduced through an Intervention Programme as part of the project. The data for the games and how to play them was derived from community elders. Teachers were skilled in playing the games and implementing the games by integrating the mathematics concepts used in the Curriculum Assessment Policy Statement (CAPS) curriculum, which is the curriculum used by all South African public schools. Thereafter, the observations were conducted of how the teachers implemented the Indigenous games. Interestingly, the teacher participants chose to use the Morabaraba game most often in their classrooms. The teachers planned their lessons on a particular topic they were teaching from the CAPS curriculum in conjunction with the Morabaraba game.

4.3. Methods of Data Collection

Data were collected through observations made during the span of a week by research team members. In the form of reflective reports and in a focus group format, experiences were shared and recorded. The observations were based on an unstructured observation schedule so that the team members could gauge how Morabaraba was implemented in the classroom. Ten schools, two schools per day, were visited to observe how the Morabaraba game was implemented in the Intermediate Phase. The observations were audio-recorded. After the visits to the classrooms, the team of five researchers sat together and shared their findings using the unstructured observation schedules and the audio-recordings. A reflective discussion took place each day of the week using the notes from the unstructured observation schedule. The reflection meeting lasted two hours and was audio-recorded. The question used to start the conversation was ‘What did you observe during the observation of the ethnomathematics lesson using the Morabaraba game?’ In response to this question team members shared their reflections of what they had observed in each school. Their reflections were recorded and transcribed. Therefore, there are five recordings and five transcriptions.

We observed the teacher participants implementing the Morabaraba game in their classrooms. Learners were provided with the necessary resources such as created Morabaraba game boards with beads as well as worksheets to fill in as they played the game. The role of the learners was to follow the instructions of the teacher on how to play the game, to play the game and to fill in the worksheet. The rules of the game were on the worksheet and the teacher went through the rules verbally.

4.4. Analysis of Data

The reflection session was transcribed verbatim for the purpose of analysis. The transcribed session was checked by the research team members for accuracy. The transcripts were read and reread to help make the content more familiar. Colour-coding was applied in order to identify frequently used words, concepts and expressions, and this assisted in the detection of patterns and categories. These were later used to constitute emerging themes (Cohen et al., 2018). To ensure the trustworthiness of the study, the authors used the member-checking and participant confirmation techniques. The observations that were audio-recorded served to triangulate the reflections made by the research team members. As part of a broader project, ethical clearance for the fieldwork was applied for and granted by the institutional ethics authority (reference no. 2020/09/09/90441435/10/AM). For ethical reasons, pseudonyms (Desmond, Sarah, Somi, Vino and Mary) are used for the research team members and for the schools. Based on the data from the reflections by the research team members, the findings and discussion section follows.

5. Findings and Discussion

There were four findings derived from this study. Even though teachers were able to identify most mathematical concepts in the CAPS curriculum that related to the Morabaraba game board, the findings below identify and discuss addition, subtraction and factorisation.

5.1. Finding 1: Uncovering of Hidden Mathematical Knowledge in Morabaraba

Each researcher had a short time to report on their observations, as was discussed in the methodology section. The discussion was generated through the following question: ‘The manner in which the game was played, or the manner in which the problems were solved, was it in relation to how the game should be played?’ Desmond responded as follows:

if you mean that the game is a means to an end, the game has got certain rules for this game, but for the application, it goes beyond that.

This explanation was supported by Sarah when she said:

If it can be used even though it is not according to how it should be played, but if it can be used to apply that maths, even in a different way, and the children understand it that way, you can achieve the aim of what the teacher wants to achieve, then it is fine.

The core idea, as seen in these responses, is for the learners to learn new rules for uncovering certain mathematics concepts and become innovative in applying what they have learnt in class. While this became the understanding, as researchers proceeded with the debate on what the rules of the game meant for the teachers, Somi asked for further explanation and justification and said:

So, meaning that when you explore a concept, using the game, you don’t consider the rules that much, is that what you are saying?

Somi’s question was clarified by Vino when she said:

No, I understand it. She wants to know as to whether the rules of the game are not important because we gave rules.

In responding to the two questions Desmond said:

Ja, because there is something like a game which they know, Morabaraba and we explore it the mathematical potential that they already know but they don’t know it. In other words, it is the hidden knowledge in the game that we are making them aware off, but if it is not relevant and you can use it, the game in a different way and they went to set up their own rules.

Desmond clarified his argument to the other team members, declaring that the Morabaraba game actually allows the learners to find the hidden mathematics knowledge in the game.

To further justify his argument, Desmond argued:

The board is just a notion, an ethno-maths bringing to the classroom something new. Something new as a method, as a checkerboard game, but the content as you can see is still the same. The objective of teaching him the basic operations remain the same.

Sarah’s explanation was illustrated and confirmed through the following extract:

To add on, if the number is 5 plus 19, just say okay, already we have 5, let’s just put in 19 and we will get the sum (Teacher A) in the Morabaraba game. This example has nothing to do with the rules of the game as learnt but conveys the mathematical ideas.

Somi further clarified:

So, the comment that I made, there were no rules there. That is the rule that she invented for the board. Yes, that is why I said to her, I even commented to Sarah to say I understand what the lady is saying, the lady was excellent in everything that she tackled, but I was worried because the rules of the game were not applied as I was discussing it, but after having talked about that, after having explained to me then it says you can bring the rules but the teachers can also come up with their own rules and it is not as if it is the end. Learners will understand the rules.

From the active debate of whether to use rules or not in playing the Morabaraba game, it is evident that the researchers agreed that the rules of the game are not necessary when playing it in the classroom. Teachers were able to invent their own rules in line with the specific content area they were teaching. In this way, not only the teachers but also the learners were able to relate to and understand the mathematical knowledge inherent in the game. It was also evident during the observations that most of the learners were able to play the Morabaraba game and were aware of the known rules. However, they were able to actively play the games with the new rules, which allowed them to detect and understand the mathematical knowledge used in the CAPS document. The participants did diverge from the rules of the game and Mosimege (2020) agrees that when there is a deviation from the rules of the game, there should be agreement between the players. They were able to deviate from the rules as they were able to detect mathematical knowledge in the games which did not warrant the playing of the game in the normal way. The learners did have fun playing and learning at the same time, as was observed, so sticking to the rules of the Morabaraba game was not compulsory. As also pointed out in the study done by Spangenberg (2021), even though the rules of the game were explained, there was no explanation of whether the rules assisted learners in understanding the mathematics concept better. On the other hand, Tachie and Galawe (2021) as well as Mosimege and Ismael (2004) argue that following the rules of the game does allow for problem-solving as there need to be rules if there has to be a winner. However, the teachers in this current study had their own rules, as was observed by Desmond, ‘but if it is not relevant and you can use the game in a different way and they want to set up their own rules’. While the teachers may have not followed the rules of how the Morabaraba game is originally played, they did have their own rules which allowed them to implement the mathematical concepts in a different way. In keeping with the ethnomathematics theoretical principles of the study and as the team agreed, the Morabaraba game does have cultural significance and relevance to the lives of the learners and therefore has a potential for positive cognitive effect on mathematics learning (Widada et al., 2020). The evidence is shown in the way the game was played and engaged with in relation to mathematical concepts and what literature says.

5.2. Finding 2: Identifying Complex Mathematics in Morabaraba

The Morabaraba game has a total of 24 tokens used by both players. During the reflection of the observed lessons, the researchers indicated that they observed a teacher using Morabaraba to operate large numbers. This teacher was creative in extending the game to include numbers that were greater than 24.

Desmond:

She could show the factors of 12, the factors of 24, of 60 also, but she never, the children had to be creative to then getting 60 cows. Because she prepared them beyond the 24, because she used example a bottle top, so she had about four packs of bottle tops but then it goes at the end to 60, there weren’t enough, She is very creative, she was not using the pairs, …  because in the pairs there were not enough cows, so she combined various groups.

This teacher used the learners’ knowledge of Morabaraba to extend the learners’ understanding of operating numbers greater than 24 and using factors which were complex. The learners’ understanding was observed during their response to the teacher’s questions. This was confirmed by Mary when she said,

Even when they do not have sufficient numbers, … they were able to answer when she asked questions, you will see them raising up their hands.

Figure 2 shows how the game was played. When learners were in groups of three, each group member placed a token on the same spot. All the tokens of the group had the same colour. If the group chose a1 as their spot, there will be three tokens of the same colour on a1. Thus, one token was extended to three tokens.

The teacher showed agency by reinventing the Morabaraba game so that she could implement factors using numbers greater than 24. So, to get the higher numbers, rather than using two players with 24 tokens, she combined groups so that more tokens could be used. Moreover, she brought in the aspects of culture by identifying the bottle caps as cows to create cultural relevance to her mathematics instruction. Nkopodi and Mosimege (2009) explain that this contributes to learners being able to understand the relevant mathematics concepts, thereby leading to mathematics learning. As Burnett (2006) emphasises, learning carries social and cultural meaning and contributes to learner understanding. Therefore, the teacher was able to use learners’ cultural knowledge to make the teaching of factorisation (a difficult mathematics concept to teach) familiar to learners and at the same time, through the games, create interest and motivation to learn. She showed that she was able to reinvent the Morabaraba game by creatively using the board game to include complex numbers. Interestingly, learners were able to grasp the concept of factorisation even when using other numbers, as was identified by Mary, because they understood the concept through playing the Indigenous game of Morabaraba. Hence, as the Sociocultural theory advises, the learners’ cultural knowledge informed the understanding of the abstract concept of factorisation.

Figure 2. Morabaraba game board showing factorisation

5.3. Finding 3: Integrating Morabaraba into CAPS Addition and Subtraction

This theme deals with how a teacher used the Morabaraba board game to teach addition and subtraction. He showed innovation in making the mathematical concepts that he taught easier to understand by using the game. Below Somi reflects on how a lesson on addition was taught:

So, what the teacher in School C did; he used the combination of numbers, he will give two numbers and request the learners to add the third one to maybe a given, let’s say you want the numbers, I mean the learners to add the numbers to 100, he will give the learners the 60 and the 40, then the learner is supposed to put the third one to add to 100. So, he cut the pieces and wrote the numbers on these pieces. So that is how he made the game, to me it was very relevant, it was also according to the rules of the game to say either on a straight line, vertical, horizontal or diagonally then he can use any combination of numbers to it.

Sarah added to what she observed of the teacher in School C.

He also showed learners how we get numbers to match through addition and subtraction. He had numbers cut into pieces, so it was different numbers, so if I put a 60 there, right, so he put a 40 there, right, it was my turn to either find a 100 to match that or find the 20 to show I subtracted to get the value.

A representation of how the game was played is given in Figure 3. Looking at the figure, Each learner was provided with six number tags. Moving horizontally from point A to point C, Learner 1 starts by putting the number tag, 10, on point A. Learner 2 decides to put the number tag 21 on point B. To put the correct number tag on point C, Learner 1 must either add 10 and 21 = 31 or subtract 10 from 21 = 11. Learner 1 will therefore put down the number tag 31.

During the reflection, the researchers indicated how the teacher allocated numbers to tokens, which is a deviation from how the game is played. Learners played with those tokens; however, they were to follow the instructions given to them by their teacher. The instructions included, among others, adding and subtracting the numbers allocated to the token while playing the game. In this way learners were playing not only to get tokens from their opponents, but also to operate numbers correctly. Learners were provided with different ways of addition, as indicated by Somi (get numbers to add to 100 by following the rules of the game) and by Sarah (use values provided by the teacher to either add or subtract depending on what value/token the learner has).

Figure 3. Addition and subtraction of two-digit numbers

It was found in the literature that there are no standard ways of implementing mathematical concepts using the Morabaraba game (Moloi, 2015; Nkopodi & Mosimege, 2009). This was evident in the way the teacher referred to addition and subtraction using the Morabaraba game. He followed the rules where numbers had to add up to 100. However, he made his own rules when learners had to find a value either by adding or subtracting which did not have to match. Nkopodi and Mosimege (2009: 379) stress that ‘in a game, participants have to follow the rules of the game or come to a consensus on how the rules can be amended’. Therefore, the teacher reinvented the Morabaraba game rules to implement addition and subtraction, which led to better understanding for learners.

5.4. Finding 4: Rethinking the Morabaraba Game for Formal Teaching

Challenges were noted as significant to make sense of what transpired during the lessons when playing the Morabaraba game. The first issue that was identified from School A was the fact that although the teacher handed out copies of the Morabaraba game to the learners, it was observed that the use of the game did not achieve the intended outcomes. This view is confirmed by Sarah:

The teacher now is busy. So, with the three masks she has on and the noise of the fan which we had to have because of the heat, the children could not hear her. And then the children start getting a little bit, they don’t understand what is happening, the teacher is telling them, okay I am giving you this page cut this, but they are all just looking at her, what is she talking about?

It became apparent that the learners were confused as they did not have any direction on what to do. The extract below illustrates how Sarah tried to check if learners followed the teacher’s instructions:

So, and then she (Teacher) is cutting, I then spoke to a learner, I said, you know this game. He said, ja, I know this game. I asked him if he could cut the game beads and he said he could, then he started, but they couldn’t understand the teacher, and then there is this teacher cutting this and the other children are starting to talk now in the back. So, what we noticed is she’s got a worksheet on the board, she’s got one group on that side, working on what she had on the board, this one she is trying to cut up, but the lesson itself was totally unrelated to the Morabaraba game. It was that they were just playing it for fun, cutting, but that side they were doing the addition, it was addition. They were doing it there, so it was very disappointing. There was not much we could observe.

In response to what was highlighted, it is obvious that the teacher needed assistance. The aim of using the Morabaraba game to integrate the mathematical concepts being taught was not achieved. The game was played, but it was not related to the mathematical concept being taught, which was addition. From what was observed, the learners were confused, so the use of the Morabaraba game to implement the mathematical concepts in a fun and relevant way was not achieved.

Desmond clarified the teacher’s situation by remarking:

Very difficult to expect that school and the teacher and I mean the whole project although it mustn’t be an excuse for us to pull out or for her, but we must maximise our support for her.

Desmond was able to find a way to resolve the issue. The reflections assisted the researchers in finding ways of helping the participants to implement the Morabaraba game with the integration of mathematical concepts in ways that were conducive to learning.

The engagement with learners in School B continued as follows:

Mary: She used the game while they were playing to show them addition, to show them whilst the learners were playing the games, there were the addition, the multiplication or counting in threes, counting in twos and counting in fours. Grade 4s. they were moving and when they were, the stones in that way they were counting, two, four six. The only challenge was that she used one board. So, learners had to come play one team at a time, instead of having different boards games so that learners could play at the same time. So, it was a bit of a challenge in terms of classroom management. So, she finds it quite difficult, yes in that matter but they enjoyed the game.

The challenge that this teacher had was a lack of resources. She was observed relating the mathematics concepts to the game and making addition and multiplication easier for the learners to understand using the Morabaraba game board. She also showed that she reinvented how the Morabaraba game was played by using it to integrate the basic operation that was being taught in the classroom. However, she needed to have more resources to engage all the learners in the game and to integrate the concepts being taught. It is also evident from what Mary said that the learners did enjoy the lesson, so at least the goal of making mathematics more interesting for learners was achieved.

From the challenge that the first participant from School A experienced, it became apparent that she was unable to integrate the mathematics concept of addition with the Morabaraba game. Tangkur et al. (2022) advise that for the ethnomathematical game to be effective, it has to be associated with one or more mathematics concepts. However, the authors also found that the way the game is implemented is influenced by contextual factors. The crowded classroom in School A, COVID-19 conditions and the extreme heat were attributed to her not being able to clarify how the game was to be played. The contextual challenge of not having enough resources was also experienced at School B. Madimabe et al. (2022) and Amlor (2016) agree that the Department of Education needs to assist teachers in implementing ethnomathematics in the classroom.

6. Conclusion

In response to the research question, ‘What were the relevant mathematical insights identified through the observations of the Morabaraba Indigenous game played in the Intermediate mathematics classroom?’, it was found that the Morabaraba game allowed for the emergence of mathematical knowledge, created the identification of specific mathematical concepts, permitted conducive integration of Morabaraba into CAPS-related mathematical knowledge in the Intermediate Phase and showed that teachers are innovative and creative in incorporating Indigenous knowledge systems into the formal curriculum by adapting the rules of the games. A case can therefore be made that based on the experiences of the researchers (observations and discussions), Morabaraba offers tangible evidence that ethnomathematics can make a significant contribution to decolonisation of mathematics teaching in contemporary mathematics classes. We therefore suggest that the use of ethnomathematical games such as Morabaraba is a worthwhile strategy to improve mathematics learning and promotes cognitive development in learners. Future research endeavours include sustaining the use of Indigenous games in mathematics and discovering how other Indigenous games establish resourcefulness in the way mathematics is taught.

Acknowledgment

We acknowledge the funding provided by the National Research Funding (NRF), grant number 129765. The views expressed in this article are not those of the NRF.

Disclosure Statement

No potential conflict of interest was reported by the author(s).