Mathematics has been nicknamed the 'queen and servant of science' (Bell, 1961) probably because it rules over (or is more important or useful than) other subjects but at the same time 'serves' them. Therefore, it is also considered as a subject that human beings mostly use to solve their daily life challenges or as a subject that 'counts' a lot (Cockcroft, 1986). Mathematics is a subject of study whose content is the same worldwide but the way people use mathematical knowledge and innovations to solve local challenges may be different. According to Zaslavsky (1994, p. 6):
Students should recognize that mathematical practices and ideas arose out of the real needs and interests of human beings. They should know that a great deal of the mathematics that they learn in elementary and secondary school originated in Asia and Africa centuries before Europeans were aware of more than the most elementary aspects of mathematics. Why then is so much debate on whether there actually is 'African ethnomathematics' (Huylebrouck, 2006) or mathematical indigenous knowledge (MIK) for Africans? It may be because of colonialism and the rise and support of capitalism that "Most textbooks credit Europeans with the origin of mathematics and omit the contributions of non-Europeans" (Lumpkin, 1987, p. 2).
It could thus be argued that African communities possess mathematical knowledge and skills that they use to overcome challenges of shelter, food insecurity, risks to human health and the environment and shortage of recreation facilities. The mathematical operations or activities involved could be counting, measuring, drawing, constructions (building) or even more 'complex' ones like the Yoruba numeration system (Zaslavsky, 1994) or finding the length of the hypotenuse of a right angled triangle. These operations help them as they engage in activities such as hut building, clay pot making, medicine preparation and also recreational activities involving cultural riddles for mental mathematics (Chikodzi and Nyota, 2010) or proverbs and idioms used in, for example, Shona poems and stories.
According to Shona People Traditions and Culture (n.d.):
The Shona people are Zimbabwe's largest indigenous group, their language is also called Shona (Bantu) and their population is around 9 million. They are found in Zimbabwe, Botswana and southern Mozambique in Southern Africa and bordering South Africa. Representing over 80% of the population, the Shona tribe is culturally the most dominant tribe in Zimbabwe. There are five main Shona language groups: Korekore, Zezuru, Manyika, Ndau, and Karanga. The Ndebele largely absorbed the last of these groups when they moved into western Zimbabwe in the 1830s. Theoretical Framework
This paper is anchored on the theory of indigenous mathematical knowledge systems often called, among other terms, ethnomathematics (Gerdes, 1994) or sociomathematics (Zaslavsky, 1994; Wedege, 2010). According to Gerdes (1994, p. 347), "The concept of sociomathematics may be considered a forerunner of the concept of ethnomathematics. It is ethnomathematics as a discipline that studies mathematics (and mathematical education) as embedded in their cultural context." In particular, ethnomathematics includes the mathematics of different cultural groups of people as they engage in activities such as counting, locating, measuring, designing, playing, and explaining (Bishop, 1988). Sociomathematics is defined as, "... a concept addressing relationships between people, mathematics and society, which encompasses the studies of, for example, numeracy, ethnomathematics and workplace mathematics in a single term." (Wedege, 2010, p. 452). Thus one may conclude that different cultural groups possess different or similar mathematical knowledge, practices and beliefs which may have arisen out of the people's real needs or interests. It could be argued that the rich mathematical knowledge, skills and beliefs that the different ethnic and cultural groups have could be tapped, documented and shared among other people who might face similar challenges. The information could also be preserved as banks of African knowledge for African communities.
The paper is hinged on the concept or idea that, "There exists "hidden" or "frozen" mathematics" (Gerdes, 1985, p. 12) in the formerly colonised people of Africa. The hidden mathematical knowledge needs to be reconstructed or "unfreezed" (Gerdes, 1998) and then utilised. "Utilizing IK helps to increase the sustainability of development efforts because the IK integration process provides for mutual learning and adaptation, which in turn contributes to the empowerment of local communities" (Gorjestani, 2000, p. 2). From this brief conceptual framework and the theoretical framework outlined above, one may infer that rural people in Zimbabwe also posses rich mathematical knowledge, skills, attitudes, beliefs and practices which they use to solve their daily life problems and to meet their real needs and interests. What kind of mathematical knowledge, skills and beliefs do they possess? How can these 'possessions' be tapped and put to use in different cultural contexts and even in schools? This paper analyses 'what exists' and 'what works' in the mathematical indigenous knowledge systems of the Zimbabwean rural people, giving examples of the Shona speaking people living in Shurugwi county, in the Midlands Province of Zimbabwe where most of the people speak version of Shona called Karanga or Chikaranga.
It is believed that some important mathematical ideas and practices among rural people in Zimbabwe may have been lost due to colonisation or enculturation and one may, as Gerdes (1998, p.4) points out, try to reconstruct or 'unfreeze' the mathematical thinking, that is 'hidden' or 'frozen' in old techniques, like, e.g., that of basket making." MIK may also be used in the improvement of the education system, ".that is supposed to equip citizens with high quality cultural tools, skills and attitudes to keep up with the pace and innovations of cultural development" (van Oers, 2013, p. 267).
Statement of the Problem
Many western researchers and even some African people themselves have been indoctrinated to believe that Africans do not possess any (useful) mathematical knowledge. Some useful indigenous mathematical knowledge systems among the rural Shona people which could lead to community or global innovations and development initiatives have therefore been untapped and not put to maximum use.
Purpose of the Study
As pointed out by Huylebrouck (2006, p. 135), "Indeed, even in the 21st century, the prejudice persists mathematical activity was completely lacking in Africa, despite the many publications, conferences and lectures on the topic." The objective of this paper, therefore, is to investigate the type of mathematical indigenous knowledge systems that existed and still exist among the so called uneducated and primitive rural Shona people in Shurugwi County, Zimbabwe (which is in Africa). In particular the paper aims to show how these rural people use the mathematical knowledge that they possess in...