The origin of AmaNdebele mathematical artefacts in KwaMsiza, Mabhoko community, North West Province

Abstract

African history shows that all cultures are mathematised, in that people within any culture use ideas of mathematics in their everyday life. In recent years, the use of historical and ethnomathematical research methods has aided a better understanding of the history of mathematics in Africa. Considering this, the origin of AmaNdebele mathematical artefacts in KwaMsiza, Mabhoko community, North-West province, was studied in this study. The following are the four data chapters that were used in this study: The first was to investigate the historical origin of the AmaNdebele mathematical artefacts. The second was to investigate the cosmic genesis of the AmaNdebele mathematical artefacts. The third was to explore the cultural identity from the AmaNdebele mathematical artefacts. The fourth was to explore how the AmaNdebele mathematical artefacts have been protected and preserved. This study was guided by the eZiko Sipheka Sisophula theory, Indigenous theory, and Afrocentricity theory to investigate the AmaNdebele worldview, beliefs, and knowledge about the origin of their mathematical artefacts which are used to express culture and ethnic identity. The findings of this study revealed how the AmaNdebele artefacts have both historical origin and cosmic origin. The AmaNdebele culture and identity are well expressed through the mathematical artefacts which are used in different ritual ceremonies and cultural commemorations. This study was underpinned by African philosophies which are the elements of qualitative research and are the basis on indigenous research to guide the researcher to conduct a study that represents the KwaMsiza community, respects their worldviews and adheres to customary laws. The African philosophical underpinnings of the study also assisted the researcher to use an indigenous lense when conducting the study with the KwaMsiza Mabhoko community. The total number of participants in this study was thirty-two, and they were divided into groups based on the study's objectives, which were used to create the data chapters. The first data chapter used an investigative research design whereby the researcher worked towards gathering knowledge about the AmaNdebele and certain knowledge which she was not familiar with. In order to perform an ethically correct and culturally relevant indigenous method of obtaining and distributing knowledge about the KwaMsiza Mabhoko community, the chapter employed an Indigenous-Informed Relational Approach. An indigenous research paradigm was used in order to honour

the Indigenous knowledge systems and worldviews of participants. The indigenous research paradigm allowed the researcher to see the research process as a sacred pursuit of knowledge. Both the Indigenous-Informed Relational Approach and the indigenous research paradigm informed the entire study. Eight participants were sampled using an expert purposive sampling procedure. Data was collected using focus group interviews. Data analysis was performed through a thematic analysis, where various themes and an emerging theme was identified. The results for this chapter indicate that according to the Ndebele oral history, the use of mathematical artefacts existed at the origins of the AmaNdebele and that means the artefacts are older than the 16th century instead of what has been claimed by many scholars. Over time, the AmaNdebele mathematical artefacts have been transformed and developed. The first major transition occurred in 1883 when the AmaNdebele were defeated by the Dutch Boers in a war. That does not mean the artefacts did not exist before, but they have developed and evolved tremendously. The second data chapter utilized an investigative research design for the researcher to investigate the cosmic genesis of AmaNdebele mathematical artefacts. The sampling size consisted of six participants who were selected using an expert purposive sampling procedure. The data collection tool for this chapter was semi-structured in-depth interviews. The data was also subjected to thematic data analysis to produce themes. The findings of this chapter show that the utilization of mathematical artefacts was influenced by the Ndebele spirituality, belief systems and religion. The findings indicate that the AmaNdebele received instructions from their supreme beings to use mathematical artefacts as part of their cultural expression and identity. The Supreme beings, according to the AmaNdebele worldview, guides and instructs humans on how to live. The meanings of the geometric shapes are also explained in the chapter, and it is said that the meanings are impacted by their religion, which is the foundation of AmaNdebele's ways of living, doing, and being. The third data chapter of this study used an ethnographic research design whereby the researcher spent a certain period of time with the participants and also in the environment of the AmaNdebele. As a Ndebele by birth, she has also attended activities held in surrounding areas to understand the cultural identity expressed through mathematical artefacts. The focus group interviews were conducted with ten members of the KwaMsiza Mabhoko community. As a result, the researcher was able

to employ a convenient sampling procedure. The tool for this chapter was piloted in the Mpumalanga Province and the KwaMhlanga surrounding areas, where Ndebele people who practice cultural activities live. The results of this chapter indicate that mathematical artefacts play a major role in ethnic identity and cultural expression. AmaNdebele mathematical artefacts are expressed during ritual ceremonies and during commemorations. Both men and women take part in ritual ceremonies and commemorations. However, women who are the custodians of Ndebele mathematical artefacts, express them more as compared to men. They are responsible for mural art and wear sophisticated beaded attires that reflect geometric shapes. The detailed beaded attires worn by AmaNdebele women differ according to age, status, and level. Men's attires are also worn according to status, age, and level. The fourth data chapter of this study utilized two research designs. The first was an exploratory research design that allowed the researcher to explore how AmaNdebele entrepreneurs protect and preserve mathematical artefact knowledge. The second design was the investigative research design which was used to investigate existing legal documents which advocate for the protection and preservation of Indigenous Knowledge Systems. Eight women with expertise and experience made up the sample size thus purposive sampling were utilized as a result. The tool that was utilized for this data chapter was in-depth interviews. Methods that were used in this chapter were separated into two. The first was interviews with elderly women who have mastered strategies/art of preserving and protecting the knowledge of AmaNdebele artefacts. The Second was the qualitative document analysis whereby the researcher analyzed existing documents on the protection and promotion of Ndebele crafts and other indigenous artworks. The findings of the study demonstrate that AmaNdebele entrepreneurs conserve mathematical objecobjectledge via a variety of strategies created locally. Some include selling their artefacts and painting their house to appeal to tourists. However, there have been worries voiced regarding the government's neglect of their area, which has been designated as a national heritage site. They argue that the government is not doing its utmost best to preserve IsiNdebele artistic works hence their national heritage sites are losing value and tourists. They feel that if the government continues to ignore Ndebele artefects, people will be deterred from practicing them. As a method of preservation, they advise that this knowledge becomes part of formal school content/curriculum. The documents

reviewed in this chapter demonstrate South Africa's success in preserving indigenous knowledge systems. Many communities, however, are still unsure of their rights when it comes to indigenous knowledge. This is one of the reasons the Department of Science and Technology established the National Indigenous Knowledge Office (NIKSO) to educate communities about intellectual property rights, benefit sharing agreements, and how to create wealth and employment using their indigenous knowledge.