**6. Discussion**

#### **6.1 Gebeta game as a cultural funds of knowledge**

The Gebeta game is considered one of the cultural games, as evidenced in both the national document of the cultural sports federation in Ethiopia and the response from participants in a small-scale survey conducted *via* social media. Additionally, children playing the Gebeta game in Gondar, as described above, further supports its cultural significance. The survey results showed that 95% of respondents were aware of the game, and 81.2% had played it between the ages of 5 and 15. The game is predominantly played in rural areas and towns, usually on the ground, for entertainment, fun, and competition. This indicates that the Gebeta game is a prevalent form of cultural knowledge in most communities in Ethiopia. Children engage in this game at an early age, regardless of whether they live in cities or rural areas. This aligns with Moll and colleagues' definition of FoK (Funds of Knowledge) as a historically accumulated and culturally developed body of knowledge and skills within a household or community [12]. Clark demonstrated how nonschool activities that draw on children's FoK can enhance problem-solving abilities [29]. In this context, we argue that Gebeta is one of those cultural activities that can be considered as part of learners' FoK. The game incorporates various concepts and procedures of school mathematics. If adequately studied and integrated into the school curriculum and instruction in Ethiopia, it has the potential to enhance mathematical learning.

The Vygotskian perspective of learning advocates learning as participation in cultural activities [6, 13]. The Gebeta game is inherently suited for such learning since it is accessible to kids at an early age. It can be played by more than two players (if three players, they can share four homes at the start). One knowledgeable individual can train the other(s). That is to say, the more knowledgeable other (MKO), according *Creating a Culturally Responsive Mathematics Education: The Case of Gebeta Game in Ethiopia DOI: http://dx.doi.org/10.5772/intechopen.114007*

to Vygotsky, helps the novice to learn the game [6, 13]. The MKO can be a father, mother, sibling, or friend with whom the village kids frequently interact. The MKO and those learning the game communicate different strategies, which occur in the most natural context of the culture. In the video, the kids from Gondar demonstrate that others suggest the best strategies for the players. This demonstrates participation and communication of winning strategies at every level as the game can progress in various ways at any given level. Finding the best ways to optimize the chances of winning requires abstraction, pattern recognition, critical and strategic thinking, conjecturing, and convincing, which are the process aspects of MT [21, 22].

#### **6.2 Gebeta game as a cultural commognition artifact**

Commognition signifies the unity of interaction and thinking [15, 16], and a cultural artifact, such as the Gebeta game, could stimulate it. In particular, the Gondar Gebeta game presented in this work can potentially mathematically engage kids at age 5 and 6 [4, 11]. We are doing more profound research with kids in Ethiopia and Norway to see which aspects of mathematical thinking, language, and communication are visible in both contexts. In this regard, as depicted in **Figure 8**, the potential of the Gebeta game to facilitate both the mathematical thinking and the communication aspect could be investigated very well. The question could be which mathematical thinking is most pronounced. Mathematical thinking (cognition) is a cognitive process by which students come to understand mathematical concepts and procedures. The process includes problem-solving, reasoning and proof, communications, connections, and representation, according to [30]. If mathematics should be thought of as a human activity, games, such as Gebeta, can facilitate such a learning process. In the game, many mathematical activities are embedded. These are presented as follows:

#### *6.2.1 Gebeta and early numerical thinking (ENT)*

*Counting*: For starters, it is basically a counting activity. One has to count how many seeds a home has to play the game till the end of the game. A home can have 1, 2, 3, 4, …, 11, or more seeds. It can be empty also, representing the concept of zero. As counting is the basis of numerical thinking [11, 23], playing this game at an early age repeatedly could boost skills in early numeracy.

#### **Figure 8.**

*Gebeta game as an artifact for commognition in mathematics.*

*One-to-one corresponding*: During playing, one first counts how many seeds each home holds and decides to start at one of the homes. Then the players grab the seeds in one home and distribute the seeds to consecutive homes (holes). This is done using the one-to-one corresponding principle: For each home, you put one seed. Of course, this is a subtraction activity too. From the number of seeds in the hand, you reduce one each step forward. At the same time, it is an additional activity to the number of seeds in each hole/home.

*Concept of zero*: While at the start, one grabs all four seeds (see **Figure 1**). That home now has 4–4 = 0 seeds, and the following four homes gain one more seed, 4 + 1 = 5. Then, one empties the fifth hole/home and adds one seed for the next five holes. Making homes empty is an integral part of the game. In doing that, one communicates the concept of zero several times in a single game round. Hence, the concept of zero is visibly demonstrated *via* an empty hole/home so that preschoolers understand its meaning.

*Subitizing, cardinal, and ordinal numbers*: These skills are highly involved if one intends to win more homes in the game. Each player continuously engages in subitizing (perceptual or conceptual) activity from the start. For example, a home can have 5, 6, or 7 seeds. Then one has to update as the game proceeds instantly. For instance, in strategy 2 (see **Figure 2**), Player 2 begins at that house with six seeds, intending to annul the potential of being a home for the opponent player. It means that by counting the number of seeds to reach that home, Player 2 can instantly recognize the six seeds and use the one-to-one correspondence principle with the order of the homes to reach that particular home of Player 1. In addition, the concept of the ordinal number, the sixth home, is embedded in the thinking process.

The 12-home Gondar's Gebeta game involves a maximum of 48 seeds, which is 12 times 4. Repeated addition of four represents multiplication. Each player has six homes in this game, so 6 x 4 = 24 seeds. When you win a home, you have 1 x 4 = 4 seeds. If you have two homes, you have 2 x 4 = 8 seeds, and so on. One can also think that if there are two players, they divide the 12 homes by two, so 12 ÷ 2 = 6 homes each. The 48 seeds are divided into 12 homes, so 48 ÷ 12 = 4. To win a home, the players must first empty the hole (zero seed) and then put in four seeds to build it. This game uses a base-five counting system in addition to the base-ten counting system. Different arithmetic operations are embedded from the outset. If played many times with a grown-up person, kids can develop advanced numerical thinking even before they start formal school.

#### *6.2.2 Gebeta and algorithmic thinking*

Adopting NCTM's definition of AT [24], we can say that the Gebeta game is inherently algorithmic. It is a game in which one has to decide where to start and where to land for many rounds, following step-by-step procedures, and requires a strategy to win using the game's rules. According to Bishop, playing is considered one of the mathematical activities [2]. This game challenges players to be creative to win homes. One should have good counting strategies for repeatedly determining where to start and finish. The game can even be programmed using block programming tools, such as Scratch (See **Figure 9**) or text programing, such as Python. **Figure 8** shows the adoption of the Mancala game, which one can find through a Google search, to a Gebeta game used in this study.

There are two different activities here. First, it is possible to create a programing activity that simulates the game. Another, it is possible to make applications that can *Creating a Culturally Responsive Mathematics Education: The Case of Gebeta Game in Ethiopia DOI: http://dx.doi.org/10.5772/intechopen.114007*

**Figure 9.**

*Example of block programming to Gebeta game to foster algorithmic thinking.*

help play the game on computers and mobile applications. That makes the game to be available virtually, and kids can access it on their mobile or PC.

### **6.3 Conclusion and implications**

The Gebeta game is played in towns and rural areas and is integrated nationally as a cultural sports competition, as evidenced above. However, there needs to be clear evidence that it is used as part of the mathematics curriculum in the country. Gebeta games can be played without a proper game board, as shown in **Figure 6**. The availability and accessibility of the Gebeta game for everyone could be considered an advantage in considering it as part of the resources for mathematics education. The variations of the game, from simple to complex (such as the Gondar Gebeta game, 1-kinchibosh, 2-kinchibosh, 3-kinchibosh, and 4-kinchibosh), allow for learning the different mathematical concepts embedded in the game, as discussed above. Hence, the Gebeta game can be used as a CFoK (Cultural Form of Knowledge) and for cultural cognition. What is left is to design activities and tasks that can be integrated into the mathematics curriculum and syllabus in the country. This demands those who are engaged in designing tasks, instructional materials, and textbooks to search, for example, the Gebeta game and others, such as the 293 cultural games mentioned in the National Cultural Sports Federation document and embed the activities and tasks that can foster mathematical cognition and communication across the school mathematics curriculum. There has been a movement among education stakeholders that indigenous knowledge and practices have to be part of the formal school system, as evidenced in the new curriculum of the country [31]. However, implementing it is challenging, and this work provides one particular example within mathematics education.
