**3. Theoretical perspectives**

The study about the availability and relevance of the Gebeta game in the culture and the opportunity embedded in the game for the teaching and learning of mathematical concepts and procedures should be grounded theoretically. For this reason, two different theoretical frameworks that complement each other for the chosen study are presented as follows.

### **3.1 Funds of knowledge (FoK)**

Moll coined the term funds of knowledge (FoK) to refer to "the historically accumulated and culturally developed bodies of knowledge and skills" ([12], p. 133). They studied household knowledge to foster a participatory pedagogy that would enable educators to facilitate the transfer of knowledge between home and school contexts. As a result, they developed a framework with broader and more diverse knowledge, including agriculture, mining, medicine, economics, religion, and others. Given that FoK emanates from a given household or community, the list can also include different plays and games embedded in that household or community.

According to Bishop, playing is one of the six mathematical activities found in almost every culture [1]. It is possible to argue that the games available at home or in their community that interest children can be counted as their FoK [2]. Games provide opportunities for community participation, which is crucial to social learning and cognitive development [13]. Chesworth indicated a FoK approach to strengthening curriculum and pedagogical decisions informed by children's play choices and interests [14]. Of course, what interests children in play is a complex matter. Chesworth argues that "FoK offers an alternative mode for understanding children's interests within the context of their participation in the activities for their homes, classrooms, and communities" ([14], p. 296). Out-of-school mathematics is another terminology that emphasizes the nonformal mathematical-related activities learners engage in daily life [10].

#### **3.2 Cultural commognition**

Commognition is another interpretation of sociocultural learning theory focused on education. It comprises two words, communication and cognition, signifying the unity of interaction and thinking [15, 16]. This means that doing mathematics in this theoretical framework includes both thinking and communicating it. In this regard, culture can serve as a mediator for forming and developing competencies, such as problem-solving and critical thinking. Radford argued for the connection of mathematical thinking (cognition) to its historical and cultural situatedness and further stated: "I will suggest that thinking in general, and mathematical thinking (MT) in particular, are forms of reflective, mediated social praxis where the organization of individuals' sensuous cognitive processes is related to the meaning of things as they become objectified in practical and theoretical activity" ([17], p. 440).

Further, it was inspired by scholars, such as Brenner, who added: "Cognition to the formula for culturally relevant instruction in mathematics" ([18], p. 214). Turner synthesizes findings that integrate children's mathematical thinking with cultural FoK (CFoK) in mathematics instruction [19]. Therefore, cultural commognition refers to the mathematical thinking and communication situated in the given cultural

#### **Figure 1.**

*Cultural commognition in mathematics education is inspired in Ref. [20] work of interconnection that involves society, cognition, and culture.*

setting and context. Inspired by those who argued that mathematical production is subsidized by an interconnection involving society, cognition, and culture, this work presents the interconnection between communication, cognition, and culture [20], as shown in **Figure 1**.

#### **3.3 Introducing Gebeta as an artifact**

Culture-specific tools are integral in how learners organize and think about mathematical concepts and procedures [11]. "Gebeta" is one of the ancient African board games. It originated from ancient Ethiopians and was discovered by archeologists in Eretria, a place called Matara, which was then part of Ethiopia (see **Figure 1a** & **d**). Generally, it is also referred to as Mancala in other locations. However, the type of game described in this article is unique to Ethiopia. Tesfamicael argued that "it is difficult to find structured literature about the Gebeta game in the country." Nevertheless, some evidence was uncovered by archeologists who searched for relics in the northern part of the country.

They found a Gebeta-playing artifact and estimated that the game was practiced in Ethiopia from the sixth to seventh BC. The game can be played in both rural areas and towns. Players can dig 12 or 18 equal-sized small half-sphere-shaped holes in the ground and collect 48 small stones, beads, or seeds, placing four in each hole. Alternatively, the game can be made on a wooden material. **Figure 2** provides examples of 12-hole (homes) Gebeta artifacts, including both old and modern versions. Additionally, a digital version created using block programing, Scratch, is included.

#### **3.4 Mathematical thinking (MT)** *via* **Gebeta game**

MT is a complex matter to deal with. If one uses ChatGPT to get an answer to the question, "What is MT"? then ChatGPT provides a comprehensive definition as follows [21]:

*Mathematical thinking is a cognitive process that involves analyzing, reasoning, problem-solving, and making connections using mathematical concepts and principles. It goes beyond simply performing calculations and involves deeper levels of understanding and manipulation of mathematical ideas.*

*Creating a Culturally Responsive Mathematics Education: The Case of Gebeta Game in Ethiopia DOI: http://dx.doi.org/10.5772/intechopen.114007*

#### **Figure 2.**

*a) Gebeta playground made on the ground b) virtual Gebeta made of scratch block programming. c) Commercial Gebeta (mancala) game boards available www.kodkod.com. d) Gebeta game board made in Zege monastery in Lake Tana.*

To highlight the process aspect further, the ChatGPT definition provides ten aspects of MT: abstraction, logical reasoning, pattern recognition, problem-solving, creativity, symbolic manipulation, critical analysis, visualization, generalization, and communication. Stacey emphasized the importance of MT as it is a goal of schooling, a way of learning, and teaching mathematics [22]. Furthermore, Stacey explained MT using two pairs of processes: specializing vs. generalizing and conjecturing vs. convincing [22]. Additionally, aside from the process aspect, there is a content-specific aspect of MT, such as numerical, algebraic, geometrical, statistical, stochastic, and computational (algorithmic) thinking. The curriculum mainly encompasses these content aspects of MT. A robust curriculum should also consider the process aspect. In connection to the Gebeta game, early numerical thinking (ENT) and algorithmic thinking (AT) are evidenced and highlighted. Therefore, this study primarily focuses on these two aspects.

According to van de Walle and colleagues, developing early number concepts and number sense involves dealing with several activities and concepts such as counting, one-to-one correspondence, cardinality, comparing and ordering quantities, subitizing, counting on and counting back, developing verbal counting skills, numeral writing, recognition, and thinking about zero [23]. Furthermore, algorithmic thinking (AT) is being embedded into curricula in STEM courses [24–26] as AT has become necessary for every child to experience twenty-first century skills [25]. Of course, the broader concept is computational thinking (CT), and in recent years, Bocconi argues that educational stakeholders have advocated CT and related concepts, such as programing and AT, as abilities for all that is as fundamental as numeracy and literacy [26]. They provided ways AT and programing can be integrated into the Nordic curriculum. Lockwood presented the construct of AT in mathematics education comprehensively and used NCTM's AT definition as follows: "AT is a method of thinking and guiding thought processes that use step-by-step procedures, require inputs and produce outputs, require decisions about the quality and appropriateness of information coming in and information going out, and monitor the thought

processes as a means of controlling and directing the thinking process. In essence, algorithmic thinking is simultaneously a method of thinking and a means for thinking about one's thinking" ([24], p. 7). In this sense, the Gebeta game can foster some aspects of AT.
