Published on International Journal of Biology, Physics & Mathematics
Publication Date: May 30, 2019
G. Mpofu & M. Mpofu
Ka-Zakhali High School, P.O. Box 3229, Manzini, M200, Eswatini
University of Eswatini, Luyengo Campus, P.O. Luyengo, M205, Eswatini
Journal Full Text PDF: A Motivating Tool in the Teaching and Learning of Mathematics (Zimbabwe Indigenous Games).
This survey study explored the Mathematics embedded in the indigenous games of the Karanga people of Zvishavane District, in Zimbabwe, so as to bridge the gap that exists between school Mathematics instruction and the learners’ home life. The Karanga games such as nhodo, tsoro, pada, bhekari, hwishu are rich in Mathematical concepts. When tapped, this Ethno-Mathematics can mitigate in the Mathematics phobia existing amongst learners. Number systems and sequences, geometry, transformations and constructions, for instance, were seen to be embedded in these Karanga games and even artefacts. Eight secondary schools, 15 Mathematics teachers, 65 secondary school Mathematics learners, were selected to participate in the study. Quota sampling technique was employed to select the samples. From the study, it emerged that 86.7% of the learners and 80% of Mathematics teachers affirmed that cultural games can be used to improve the learning and teaching of Mathematics. It was also found that learners and Mathematics teachers under study agreed to the integration of Karanga ethnic games into the Mathematics curriculum to inculcate interest for Mathematics in the learners. One other finding was that the games will help in improving positive attitude in learners towards Mathematics. These games were also found to be a powerful tool in removing stigma generally associated with Mathematics that it is abstract, difficult, and monstrous and a reserve for the gifted learners only. This study is expected to finally inform the Mathematics classroom practice, to reduce the dreaded fear and stigma associated with the Mathematics.
Keywords: Ethno-Mathematics, Embed, Karanga, Indigenous Games.
Learners in general, ostensibly shun Mathematics for being difficult. Skemp (2006) reveals that the failure rate in Mathematics in Zimbabwe schools, especially in less resourced rural schools, is unacceptably high. The primary and secondary school system is falling short in supplying enough students into tertiary training institutions for those programmes that require Mathematics as a pre-requisite. The Ordinary (“O”) and Advanced (“A”) Level examination results analysis shows, generally, that very few students are passing Science and Mathematics (Kusure and Basira, 2012). Chacko (2004) concurs with Kusure and Basira (2012) that the national pass rate oscillates between 17% and 25%, against a policy that set Mathematics pass grade a prerequisite for admission to most tertiary institutions as well for employment.
This being the case, one wonders why learners have negative attitude towards Mathematics and fail it so badly. One of Chacko (2004)’s research findings was that entry into most jobs in Zimbabwe is based on a good pass in Mathematics, yet at secondary school level, learners seem to drift away from the subject. Chacko (2004) stressed that negative attitude towards Mathematics is not innate in the learners, but is deliberately developed over a period of time and affects achievement in the subject and vice versa. Chauraya (2010), in his study, established that attitude towards a subject is positively correlated to performance in that particular subject.
Chauraya (2010) and Chacko (2004) point towards the fact that all children have an innate desire to learn, but it is how this learning process is presented to them that will make them like or dislike Mathematics. Colgan (2014) says similar ideas, when she stated that teachers are well placed to improve student achievement and attitude by re-orienting their attention to resource creativity utilisation and strategic methodologies that “pique students’ motivation, emotion, interest and attention”. Mathematics is a common thread embedded within cultural activities. When Mathematics is linked to people’s way of life, it is called Ethno-Mathematics (Tun, 2014). Tun (2004) further defines Ethno-Mathematics as the study of mathematical ideas of non-literate people. Ethno-Mathematics is hereby seen as the study of the relationship between Mathematics and culture. It examines a diverse range of ideas including mathematical models, numeric practices, quantifiers, measurements, calculations, and patterns found in culture, as well as education policies and pedagogy regarding Mathematics education (Kusure & Basira 2012).
This state of mathematical affairs is a result of, among other factors, misconceptions, by most Mathematics learners, that Mathematics is an academic activity restricted within the four classroom walls, that the discipline is difficult and consequently taken as a frightening abstract ‘monster’. Little is known by these learners that the games they play daily at home are rich in the mathematical concepts that can be schemas onto which school Mathematics learning can be build. Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor and is a passage to understanding many other subjects (Tshabalala & Ncube, 2012). According to Mupa (2015), posits that the ability to demonstrate that Mathematics can contribute towards success, may give all pupils, before leaving school, some realization of Mathematics’ inevitable intrinsic value for this success.
Mathematics is a practical subject, where the learner physically ‘does’ Mathematics all the time they will be engaged in Mathematics (Kusure & Basira, 2012). This calls for a force that accelerates this action. Games have been found to play this part quite well, as was stated by Larson (2002) argues that Mathematics needs a lot of practice in the form of written work, mostly found in “carefully designed Mathematics games or activities that reinforce concepts and skills” Ogunniyi and Ogawa, (2008) say ‘Indigenous’ implies belonging to or originating in an area, or naturally living, growing or produced in an area. However, demographic characteristics, like migration, culture diffusion, social dynamism, globalisation as an aftermath of technological advancement, render it complex to think of indigenous knowledge as an absolute phenomenon. Urbanisation and technological advancement have seriously impacted on indigenous knowledge systems (Mutema, 2013). Mutema alludes to the World Bank’s observation that much indigenous knowledge are at risk of becoming extinct because of rapidly changing natural environments, fast pacing economic, political and cultural changes on a global scale.
This is one of the motivations for this research; to unveil the indigenous Mathematics embedded in the Karanga traditional or cultural children’s games and artefacts. Success in this unveiling will provide an alternative means of motivating learners to acknowledge the beauty and vital role of Mathematics and Science in everyday real-life problem-solving and decision-making, for sustainable development. Kuphe (2014) reiterates that although the attributes above are an important guide in identifying knowledge and practices that qualify as indigenous, the definition, however is silent on how long is ‘ancient times’. Population migration in the last half of the twenty-first century has seen massive erosion of those unique attributes that hold a people together as an indigenous entity. The writers cited above collectively express that games used in the classroom in teaching Mathematics have potential to influence paradigm shifts in the teaching and learning of Mathematics. These are some of the implications of games to the learners, teachers and other interested parties: Communication improves as learners share and play the games with family members at home. This interaction impacts on the family members to like Mathematics and then encourage those who are still in school to take Mathematics seriously, without being coerced. Thus Mathematics becomes everyone and every where’s business (SANC, 2012).Learning of Mathematics through games is made interesting, meaningful and attractive, not only to the learner, but to the Maths educator too, by considering learner-teacher relations, learner motivation techniques, learner-learner interaction, content mastery by teacher, defining relevance of maths in real life’
Research findings from numerous researchers indicate that Mathematics is an indispensable aorta of society that hinges culture and school. Culture is a kind of an informal school, where all subjects are learnt by discovery as well as trial and error methods, with Mathematics being the major. Consequently, Ethno-Mathematics has been recommended by several Mathematicians in a bid to mitigate and ameliorate deteriorating attitude towards Mathematics (Mutema, 2013). ( hence, the need to carry out this study to establish particular games and the Mathematical concepts embedded in them.
1.2 Research Questions
The research sought to answer to the following questions:
a. Which indigenous games are played by the participants in this study?
b. Which Mathematical concepts are embedded in the indigenous games identified?
The interpretative approach framework has been adopted which helped to generate data from a social practical context in a fresh way rather than controlling previous theory (Merria, 2009). In seeking the answers for research, the investigator who follows interpretive paradigm used the research participants’ experiences and perceptions to come up with own view point using gathered data. Creswell, (2009) states that an interpretative research approach is an inquiry that combines or associates both qualitative and quantitative forms of research designs. It involves the mixing of both qualitative and quantitative approaches in a study. This approach plays a role in making it easier for the researcher to understand and coin new meaning of Mathematics-culture relationship in education. This study engages in a research bordering around ethno-Mathematics, which could transcend Mathematics from the traditional monotonous classroom ‘drama’ to the appreciation of Mathematics as a life-long natural phenomenon embedded in humans’ daily activities. The Karanga people’s artefacts, games and practices are rich in ethno-Mathematics embodied informally and intuitively within them.
2.1 Research Design
This research study employed the descriptive survey research design. Locklear (2012) states that a descriptive study is usually applied to samples in the range 20% to 30% of the population from which the sample is taken. Kothari (2004) argues that a descriptive survey is concerned with describing, recording, analysing and interpreting conditions under study. He further posits that this technique resembles a laboratory research, where the scientist observes and then interprets what has been observed. The sample proportion and nature of the study qualified the researcher to apply the descriptive survey design on the 8 schools in Zvishavane, with its 16 teachers and 65 learners to enable a more in-depth study of ethno Mathematics embedded in the culture of the Karanga people.
The study population comprised 27 secondary schools, about 54 Mathematics teachers and more than 9000 students altogether in Zvishavane District. It is from this population that the research sample was taken for the study, while 16 individuals from across the Zvishavane community were involved in the Karanga cultural games observations and interviews. This district is mainly Karanga community, and is one of the regions with very poor performance in Mathematics in schools in the country.
2.3 Sampling and Sampling Techniques
The study sample for this research had 8 secondary schools, 15 Mathematics teachers and 65 Form 4 Mathematics learners sampled from the population. Simple random sampling technique was applied to select secondary schools from the schools list provided at the district education office. Quota sampling method was employed in selecting teachers and learners. The researcher was allowed access to the staff list at district education offices for the purposes of this study. There was also a list of all the district Form 4 learners which had been provided by schools for the purposes of examination electronic registration. It was from these lists that quota sampling technique was used to ensure ratio gender representation.
To capture the desired data for the study, questionnaires, interviews and observations were designed to gather information to cover a number of variables, such as the current performance in Mathematics, evidenced by the pass rates figures obtained from the statistics kept at the education offices. A questionnaire consists of a multiple choice or closed and open-ended questions, whereby the closed ones require the “Yes” or “No”, “Agree”, “Disagree” type of questions. The open-ended questions give room for the respondent to express their opinion freely (Creswell, 2009), although research subjects can abuse this freedom and give irrelevant information.
2.5 Validity and Reliability Issues
This research, as was alluded to earlier, takes a mixed method research design, with more inclination to qualitative design. Cohen (2000) posits that subjectivity of respondents’ opinions, attitudes and perspectives render the data somewhat biased, as is always the characteristics of qualitative research design. Reliability relate to whether the research results are consistent, or can be trusted in relation to the data collected (Cohen, 2000). As described by Atebe (2008), “reliability simply means dependability, stability, consistency and accuracy” of a methodology applied to gather research data, while validity, on the other hand, is based on the authenticity of the data collected. To address the issues of validity and reliability, in this study, the researcher made an attempt to record data in form of pictures, of children observed playing Karanga games and those few artefacts that were seen. The explanations, descriptions, diagrams, were generated from the participants, rather than from the researcher’s own pre-conceived ideas.
2.6 Ethical consideration
Ethics are principles that guide researchers when conducting their researches (Chiromo, 2010). These are behaviours and understandings expected as per group of people, animals, plants or professional code. These are principles that guide the researcher to determine what is right and what is wrong when carrying a study, so as to protect the participants or subjects of the study from harm. The researcher, therefore, informed the participants that there would not be direct benefit for participation and that participation was entirely voluntary and that they could decide to withdraw from the study at any time. Questionnaires assured respondents that the information they gave was to be used for this study only and treated with strictest confidentiality. Thus, they were encouraged not to give their identities. Written permission to conduct the study was sought from the Ministry of Primary and Secondary Education and was granted.
3. Findings and Discussion
The results are presented as indigenous games played in the area under study and Mathematical concepts embedded these indigenous games.
3.1 Bhekari Game
Bhekari is game which is more like cricket though cricket is apparently an advanced and modernized form of this game. This game is played by two teams with at least three players at a time, where two would be targeting to hit the player with a ball. The playing team runs round the whole box along the path shown by the arrows, in a clockwise direction, starting from Box P. The other team sets two players, one at A, the other at B, who aim to beat the players of the opposing team with a ball, as they attempt to run across the Danger Zone. If a player is hit by the ball, they are automatically eliminated from the game. A player is not supposed to be hit by the ball when in a Number Box or on a Free Zone. These numbers represent game levels.
Figure 1: The Bhekari playing court
The game aimed at players successfully evading being hit by the ball whenever they ran across the danger zones until they get to the Centre circle (Game Over Zone). The player would also keep correct count of the numbers in each of the boxes. Every time the opposite team would shout “Bhekari?” all the players would be expected to shout back the number of the box in which they are. If one says out a wrong number, they are eliminated. All players end up knowing the numbers in each set. If one of the members of the playing team catches the ball, the eliminated member comes back into the game and starts at P. If any one player manages to get to 25, then the whole team wins and they start all over again in Box P, but if they are all hit by the ball before any one player reaches the centre circle, it will be the other wins the turn to run round. While two players will be aiming at hitting the opponent team players, who attempt to cross the danger zone, the rest of the players (if any) would be scattered all around the playing field to catch stray balls. This is meant to avoid giving much time to the running players to do many rounds and also to monitor the counting down to 25 the winning box. Any cheating resulted in elimination from the game.
3.1.1 The Mathematical concepts derived from Bhekari
The bhekari game embeds much aspects of Number systems in general (Animasahun and Akinsola, 2007). The numbers in Box P are all odd numbers, which differ by 4. The first time a player gets in this box, if the opposite team player shouts “bhekari”, the player must be able to say ‘1”. The next time the player comes back to the same box, the number will be 5, after which it will be 9. These numbers must be remembered by both teams because each time the numbers are asked, both the running and ball throwing teams must be sure of the count. The set of numbers in Box Q are all even numbers. The numbers in Box R are not only odd numbers, but they are also prime numbers, except 15. Those in Box S are even numbers as well as multiples of 4. It can be observed that these numbers form a sequence as shown in the Table 1 below: