a motivating tool in the teaching and learning of mathematics · provide an alternative means of...

International Journal of Biology, Physics & Mathematics ISSN: 2721-3757, Volume 3, Issue 2, page 102 - 113

Zambrut

Zambrut.com. Publication date: May 30, 2019.

Mpofu, G. & Mpofu, M. 2019. A Motivating Tool in the Teaching and Learning of Mathematics ............ 102

A Motivating Tool in the

Teaching and Learning of

Mathematics

(Zimbabwe Indigenous Games)

G. Mpofu1 & M. Mpofu

2

1G. Mpofu, M.Sc. &

2Dr. M. Mpofu

1Ka-Zakhali High School, P.O. Box 3229, Manzini, M200, Eswatini

2University of Eswatini, Luyengo Campus, P.O. Luyengo, M205, Eswatini

Eswatini/ Swaziland

1. Introduction

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

Abstract: 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.

https://zambrut.com/


https://zambrut.com/ke/


























International Journal of Biology, Physics & Mathematics

ISSN: 2721-3757, Volume 3, Issue 2, page 102 - 113 Zambrut



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?

2. Methodology

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.

2.2 Population

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.

2.4 Instrumentation

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.

P B Q

1, 5, 9, 13,

17, 21,

danger zone

2, 6, 10, 14,

18, 22

Free

zone

mmn

Free

zone

4, 8, 12, 16,

20, 24

danger zone

3, 7, 11, 15,

19, 23

S A R

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.

25

Game Over!

(Free Zone)

Dan

ger

zon

e





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:

Table 1: Sequence Patterns

Box Number Types Sequence/Pattern/formula

P

Odd Numbers (all)

Prime numbers (2)

Perfect squares (2)

N = 4t + 1, t , 0, 1, 2, 3, 4 and 5

Q Even Numbers (all)

Prime Numbers (1) N = 4t + 2, t , 0, 1, 2, 3, 4 and 5

R Odd numbers (all)

Prime numbers (5) N = 4t + 3, t , 0, 1, 2, 3, 4 and 5

S

Even numbers (all)

Multiples of 4(all)

Perfect squares (2)

N = 4t + 4, t , 0, 1, 2, 3, 4 and 5

N-The game level number in the box.

t -The turn

The other mathematical concept in Bhekari is the Arithmetic Progression. Animasahun and

Akinsola (2007) report that many games teach number progressions. The ideas of sum to n-terms of

arithmetic progressions (AP) of these 6 numbers in each box can be considered here (Becky and

Spivey, 2008). The numbers in Box R, for example, can be said to be an AP, where a = 3, d = 4, n = 6

and

Sn = [2a + (n – 1) d]

S6 = 3[6 + 5(4)]

= 78

In the same way the sums of the other sets of the 6 numbers in P, Q and S would give 66, 72 and

84 respectively. These four totals make another number sequence. It can be said to be an AP, with first

term (a) being 66, common difference (d) being 6 and n as 4, adding to 240.

Besides Mathematical concepts in the Bhekari game there are also other benefits associated with

this game such as memory retention and adherence to instructions. According to Burns (2003) games

have many benefits to learning such as the ability to improve memory retention.

Memory Retention

In bhekari, a player has to possess some amount of intelligence to keep the correct count up to

25, without erring. The aspects of saving time and maximizing opportunities of getting to the

solution of the problem is an integral part of the concept of intelligence, which is a requisite

attribute of a mathematician.

Instruction Adherence

Mtetwa and van Wyk, (2014), commend games for impacting positively on the players‟

behaviour. Taking instructions is one of the demands that define Mathematics. Mathematics is a

science that operates under defined rules, procedures, instructions, algorithms, axioms,

formulae, theories, premises, and yet not exhaustive. On the whole this game is rich in

Mathematical ideas which can be exploited by learners and teachers of Mathematics to boost

the attitude of learners towards the subject.

3.2 Pada Game

This game is played by one player at a time. A player stands in the starting area with either leg in

each of the two rectangles then throws the bhoga (which is a small flat stone) in Box 1, jumps over Box

1 and lands with one leg into Box 2 and then hops along each of the numbered areas, ensuring that only

one leg steps in each numbered box at a time up to Box 8. When the player gets to Box 8 they turn and

face back, returns in the same manner and when the player gets to Box 2, they pick up the bhoga in

Box 1 and then jump over the box into the starting area, then turns back and throws the bhoga into Box

2 and repeats the same procedure and until they throw into Box 8.





A player should follow the hopping rules and should not miss the throw into a box. To win the game

one must be able to get to box 8 without making a mistake, after which a player chooses any box which

other players will not be allowed to step into, which makes the game more challenging to the other

players.

Box 7 Box 8

Box 6

Box 4 Box 5

Box 3

Box 2

Box 1

Left leg at start Right leg at start

Figure 2: Pada Playing Court

3.2.1 Mathematics Concepts learnt from Pada

Sequence and Counting Pada develops the skill of understanding cumulative, commutative, associative, reflexive and

distributive properties of number operations. Mathematics requires a skill of taking correct steps

at a time (Becky & Spivey, 2008). As a player plays on, they must keep count of the next box to

throw the bhoga which is associated with memory retention. The game also helps players to

develop the skills in procedure and accuracy, for example in simultaneous and quadratic

equations.

Probability Theory

According to Nisbet and Williams (2010) probability is the measure of quantifying the

likelihood that events will occur. In this game the theory of probability is in the process of

choosing who to play first as that gives the player more chances of winning the game. All the

boxes will be at the first player‟s disposal, thus there would be high chances of winning. If a

very good player starts, they can win more than boxes before others get a chance to play.

Geometrical Constructions of Polygons

The playing court has similar and congruent shapes, pairs of parallel lines, right angles and lines

of symmetry. Children learn about rectangles from the structure of the playing court. The

playing court also reflect the properties of rectangles such as the number of sides and their sizes,

diagonals, number of angles and the sum of the angles (Cha & Noss, 2001, Githua & Mwangi,

2013).

Concet of Inverse Variation

Inverse variation is where two quantities are related in such a way that as one increases the

other decreases (Mtetwa & Van Wyk, 2014). As the number of players increase, the number of





boxes to be won as houses reduces. The number of boxes won by a player as his/her territories

varies inversely with the number of players.

Concept of Projectile Motion

The bhoga, which is thrown, is a projectile. A player considers the initial velocity, the angle of

projection, force of gravity and the range in order to throw the bhoga in the correct box. Since

each player uses their own bhoga, a player has to consider the mass, the shape and the density

of the bhoga, so that the force versus mass and acceleration are unconsciously taken into

consideration. All these vary with the level of the game.

Concept of Statistics

Children make a tally chart to record the names of players the number of boxes won, games

won, and who was first, second, third or fourth player to play the game. These records are

statistics which reduce arguments and misunderstandings.

3.3 Nhodo Game Nhodo is played by at least two players. It was mostly girls of about 5 to 13 years of age who

played this game. They would sit around a small hemispherical hole dug on the ground. They used 10

small stones or fruit seeds as play objects, which they placed in the small hole. One bigger stone or

fruit seed, like marula dry seed was used as mudodo. The mudodo was then thrown into the air and not

allowed to hit the ground. The same hand that throws the mudodo quickly takes out the nhodo stones

from the hole and quickly catches the mudodo so that it does not fall down. The mudodo is thrown into

the air again and returns the other stones into the hole, leaving one outside the hole (which is a point),

before catching the mudodo, coming down under gravity. This is repeated until all the stones are out

one by one. The player was penalised if they leave a wrong number of stones outside or if the mudodo

drops. If one misses picking and in the process drops the mudodo, she passes the chance to the next

player who also tries to win the round without dropping the mudodo.

3.3.1 Mathematical concepts in the playing of Nhodo

Counting, Addition and Subtraction Concepts

Upon losing chance to the other player, a player must have the number of stones (points) they

have scored recorded against their name at the end of the game the number of stones should

balance.

Concept of Probability

Nisbet & Williams, (2010) researched on games of chance in Mathematics. Since players sit in

a circular set up, there is no starting point and playing first gives one a statistical advantage over

the other players. So players toss to determine the first player and then agree on whether the

turns follow clockwise or anticlockwise direction. If it is „Game 16‟, for example, a player

strives to score at least 8 points, and they know the game will end in a draw or he/she wins,

depending on the number of players. If three players play at level 16 and the first player scores

8 points, then this player has very high probability of winning the game, because the two

players would share the remaining stones. If the second player manages to pick up all the

remaining ones, then there is no winner. If the first one scores more than 8, then the game is

started all over again even before the player loses the game, and the player is declared a winner.

Projectiles

Throwing mudodo vertically upwards at 900 into the air ensures that the stone comes back along

the same vertical trajectory. If the mudodo is thrown at any other angle to the ground, then the

player will have to stretch to catch it, thereby increasing the chances of losing the game. Before

the mudodo free falls back, the player would have to analyse the arrangement of the stones

fumbled out of the hole and return the rest, leaves one and catches the mudodo. The initial

velocity determines the total time of flight and the height of the trajectory

Newton’s Law of motion

One of the laws of motion states that where there is motion of a body, forces are in action. (F =

mass of a body multiplied by acceleration of that body). The law of inertia dictates the size of





the mudodo. The size of mudodo will determine the force applied to throw it up where a heavier

one will require more force hence, has less acceleration.

3.4 Tsoro Game

This game is for two players each with 3 counters, with which they take turns to move on a node

(the points of the tsoro diagram where the line intersect), to leave one empty node. The first player then

moves one counter into the empty node. Other counters may be skipped. Then the other player moves

one counter into the empty node left by the first player. The first player to make a row of three of his

counters wins. It's possible that this game can last a long time without one player being able to

complete a row of three. When same moves are repeated several times, the players unanimously

declared it a draw.

A 12-Level Tsoro Game

Figure: 3. Tsoro Board Design

3.4.1 Mathematical concepts in Tsoro

Concept of Counting

The players should be able to count nodes sequentially to avert the other player from achieving

a „straight-three‟ of counters. There should be an ingenuous decision in the choice of the

opponent‟s counter to remove from the game upon achieving a straight-three. Players declare

their counters to each other, and they are counted and ascertained that they are the right

quantity.

Critical thinking

Tsoro trains players to think critically, enabling them to tackle tough Mathematics problems

such as proofs, probability, mechanics, series, conic sections, metric spaces, for example. This

is one of the attributes of a good Mathematician.

Construction & Isometric Transformation

Mashingaidze (2012), Cha and Noss (2001), Githua and Mwangi (2013) discovered great

Mathematical ideas on construction and transformation geometry in their researches in the

Mathematics embedded in games. In this game, players draw the tsoro board with application of

construction skills, even without using construction instruments. There are parallel lines, lines

of symmetry, trapeziums and rectangles. The teacher can easily teach these concepts from the

board alone.

3.5 Hwishu Game

Hwishu is a Karanga game which is very popular these days. It is played by two teams with a

ball. The teams compete for clocking an agreed numerical value for example “Game 25” or “Game

50”. Any one member of each team (some kind of a captain) tosses to start the game and decide which

team starts with the ball and while the other will be doing the “hwishu”. One member of the team with

the ball rolls the ball from their “Ball Team Zone” ( an area within an arc of a circle) smoothly to the





“Hwishu team Zone” three times. In turn the hwishu team kicks the ball back to the other team so

softly that the ball reaches the thrower, for two times. When the ball is rolled the third time, the hwishu

team member kicks the ball strictly in the direction of the ball thrower, with as much force as possible

so that the other team may not catch it. If none of Ball Team members catches that short, the hwishu

team does shuttle counts as fast and as many as possible between the other team‟s arc and the hwishu

line (drawn symmetrically perpendicular to the two arcs), stepping with one foot on the opponent‟s arc

and the hwishu line as they count the steps on both the arc and the hwishu line, after which the player

runs back to their zone, before the ball is brought back (Fig. 4). The counting must end with the largest

even number reached in the counts. Say, one had counted to 11 the player will shout 10, if they see that

the twelfth count would not be complete before they are hit by the ball.

Hwishu line

Shuttle/Counting areas

Figure 4: Hwishu Court

3.5.1 Mathematics Concept drawn from Hwishu

Circle geometry

In this game certain players become known for drawing what children call a “fair” hwishu

court. The fairness is centred on the counting zone. If distance from one arc to the hwishu line is

longer than the other, then one team will have an advantage of reaching the “Game‟ faster than

the other. Both teams at times actually inspect these dimensions. This means that children learn

how to determine the shortest distance from a line to an arc. Tangent, normal, chord, radius,

centre of a circle are also embedded concepts in this diagram (D‟Amboise, 2000).

Geometric transformation

In this game, is can be observed that the symmetric position of the hwishu line makes the line

some kind of a mirror line, which reflects identical images on its other side. Line symmetry is

yet another concept here (Mutema, 2012) also unearthed a lot of concepts on transformation

geometry from modern games.

Newton’s laws of motion

Ball games like soccer, basketball, volleyball, hockey and even motions in sea games,

automobiles, shooting, machines, embed Newton‟s three laws of motion. Similarly, is in

hwishu, in the first 2 rolls of the ball, if the player feels the ball has not been rolled as close to

them as they wish, they shout, “hwishu”, and the ball roller does it again to the satisfaction of

the kicker. Gauging the distance against the force one should apply calls in the issue of

acceleration-force-distance relationship. These also shade light onto projectile motion, velocity,

speed, displacement and time.

Ball Team Zone

Hwishu Team

Zone





4. Conclusion

It can be concluded that Zimbabwe indigenous games are rich in Mathematical concepts. All the

games observed by the researchers started with the Mathematical concept of Geometrical

Constructions, with a wide range of shapes drawn for the different games. All the playing courts are

drawn by players, thereby developing geometrical construction and polygons concepts in the process.

Critical thinking and memory retention are critical in problem solving in Mathematics, while physical

exercise helps to develop coordination of the body and the mind healthy. All of these games have their

unique rules to be followed. Abiding by the rules of the game develops virtues like fair play,

appreciating outcomes of the matches, honesty, teamwork and hard working through competing to win

fairly. These games also possess other concepts which are more pronounced in other subjects other than

in Mathematics. The different games had their own strengths in imparting Mathematical concept

unawares to the players.

The study concludes that the bhekari game concentrates much on counting, sequences, series

progressions and particularly memory retention as the key Mathematical attribute possessed by this

game, as the players have to remember their count all the time.

Pada game also teaches counting, projectile motions with the concept of probability theory

strongly embedded in this game. Statistics and probability combined concept is observed in this game

in the number of players and the chances of winning are correlated. The concept in inverse variation is

also hidden in this game, in that the more the players, the less the possible number of wins.

Nhodo is yet another game in which projectile motion concept comes into play. The higher the

mudodo is thrown, the more the time to select play back the pebbles into the whole. Counting, addition

and subtraction concepts are seen in a player having to keep count of the pebbles collected.

Hwishu is known for critical thinking in decision making, a trait that is very critical in

Mathematics. Players count to three kicks before the stronger is done.

Tsoro is another game rich in critical thinking, counting, and probability and arithmetic that is

used by tsoro players during the game. There are many other Zimbabwean indigenous games not

mentioned here, which when time permitted, would have been dealt with too.

5. Recommendations

a. The learning and teaching of Mathematics should be more practical than theoretical;

b. Teachers should uphold and respect learners‟ culture and also be familiar with the learner‟s

language, games and environment and use them appropriately in teaching and learning.

6. References 1 Atebe, H. U. (2008), Students' Van Hiele Levels of Geometry Thought and Conception in Plane

Geometry: A collective case study of Nigeria and South Africa. Doctoral Dissertation Volume 1.

Grahams Town: Rhodes University printers.

2 Atkinson, R. and Flint, J. (2012), Spatial Distribution and Experience of Social Exclusion.

Scotland: University of Glasgow publishers.

3 Burns, M. (2003), Win-Win Math Games. San Marino:The Instructor.

4 Chacko, I. (2004), Mathematics As Seen By Pupils and Teachers: A Way Forward. Africa

University, Mutare, Zimbabwe.

5 Sunzuma, G., Ndemo Z., Zinyeka, G. and Zezekwa, N. (2012), The Challenges of

Implementing Student-Centred Instruction In The Teaching And Learning of Secondary School

Mathematics In A Selected District In Zimbabwe. Int. Journal

of Current Research. Bindura. Zimbabwe, BUSE. 6 Colgan L. (2014), Making Math Children Will Love: Building Positive Mathitudes to Improve

Student Achievement in Mathematics. Queen‟s University

7 Creswell, J. W. (2009): Research Design: Research Methodology: Qualitative and Quantitative,

and Mixed Methods Approaches. (Third edition).London: Sage Publishers.

8 Gerdes, P. (2001): On EthnoMathematics and the Transmission of Mathematical Knowledge In

And Outside Schools In Africa South of The Sahara. Maputo:Universidade Pedagógica,























9 Khupe, C. (2014): Indigenous Knowledge And School Science: Possibilities For Integration.

Johannesburg, University of Witwatersrand, , South Africa

10 Kothari, C.R (1990). Research Methodology, Methods and Techniques (2nd

edition).

New Delhi, India New International (PVT) Publishers.

11 Kusure, L.P. and Basira, K. (2012): Instruction in Science and Mathematics for the 21st Century

Proceedings of The First National Science and Mathematics Teachers Conference, Bindura

University of Science Education (BUSE), Bindura.

12 Merriam, S. B. (2009). Qualitative Research: A guide to design and implementation.

SanFrancisco, Jossey-Bass Publishers.

13 Mutema, F. (2014), Shona Traditional Children’s Games and Songs as a Form of Indigenous

Knowledge: An Endangered Genre. Gweru: Zimbabwe, Midlands State University.

14 Skemp, R. R. (2008). The Psychology of Learning Mathematics. Hillside: Lawrence Eribaum

Associates.

15 Tshabalala, T. and Champion, A. N. (2012). Causes of Poor Performance inOrdinary Level

Mathematics. Nova Journal of Medical and Biological Sciences,PII: Vol.(1), 2012:1-6. Nova

Explore Publications

Zambrut Journal, Link Access;

https://zambrut.com


© Copyright International Journal of Zambrut | Zambrut, Inc.




















a motivating tool in the teaching and learning of mathematics · provide an alternative means of...

Documents