European Journal of Physical Education and Sport Science
ISSN: 2501 - 1235
ISSN-L: 2501 - 1235
Available on-line at: www.oapub.org/edu
10.5281/zenodo.218802
Volume 2│Issue 5│2016
DEMYSTIFYING MATHEMATICAL OPERATIONS:
LEVERAGING ON THE POWER OF TRADITIONAL GAMES
Mugari Abisha1i, Matemera Nathan2
Lecturer, Department of Physical Education and Sport,
1
Zimbabwe Open University, Marondera, Zimbabwe
Mathematics Tutor, Teacher Development,
2
Zimbabwe Open University, Marondera, Zimbabwe
Abstract:
Teaching and learning mathematics as a subject has for a long time been a difficult task
to both learners and teachers. A great percentage of learners hate mathematics which
has led to a high rate of failure in this subject as compared with other subjects at Grade
seven and O level. Literature content on motivation asserts that once a task is difficult
to accomplish there will be low level of motivation and burnout often develops as a
result of not succeeding. Modern teaching and learning methods recognize interactive
methods as effective especially in science subjects like mathematics. African traditional
games are in this study regarded as interactive approaches which have relevant
inclusion of every participant in the learning process. Data transcription and thematic
coding were expressed on tables and graphs for analysis purpose. This study could
assist mathematics teachers in primary and secondary schools in their endeavour to
motivate learners into loving mathematics through harnessing the power of traditional
games in manipulating complex tasks that fall under the four basic operations i.e.
addition, subtraction, multiplication and division etc.. The study observed these
objectives: i) identifying traditional games that teach the four basic mathematical
operations, ii) explaining the advantages lying in traditional games when teaching and
learning mathematical operations at primary level, iii) identifying the mathematical
myths that demotivate learners. The study concluded that traditional games like nhodo,
tsoro, pada, and madhadha ari pamutsetse are some of the most effective and interesting
games in the teaching and learning of mathematics in the primary schools. Regarding
the use of traditional games in the teaching and learning process as primitive approach,
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Mugari Abisha, Matemera Nathan DEMYSTIFYING MATHEMATICAL OPERATIONS:
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has contributed to several mathematical myths. It has been recommended that
mathematical concepts are easily grasped by a learner who is motivated to learn and
learn new concepts through familiar activities. Mathematical teaching approaches must
include traditional games. Since traditional games are basically interactive, they should
be the cornerstone to the teaching and learning of mathematics as a subject. The
teaching of mathematical operations should not be left to teachers alone but parents
should also take part introducing to their children some traditional games found in the
community and homes.
Keywords: traditional games, mathematical operations, interactive, learner
1. Introduction
The ever growing numbers of students dropping mathematics, enrolling for
mathematics bridging course, those not studying mathematics and those who fail
mathematics is a cause of concern to parents and among the learners themselves. Smith,
in Tiris,
, argues, Mathematics is vital, it underpins research and development in
the sciences, technology and computer world, it is a key driver of economic and labour market
growth and it provides a set of key skills . The centrality of mathematics to economic and
technological development of a country is not questionable. In the history of education,
civilization in Mesopotamia and Egypt included calculations using numbers, gave birth
to calendars, angles and graphic representations is testimonial to importance of
mathematics today, but were basing their civilization on indigenous knowledge.
Therefore, growing figures of learners without this essential subject remind educators
of a great need of harnessing several forms of creativeness in the pedagogical
approaches. One of these approaches earmarked in this study is the use of traditional
games to learners in the primary and secondary school levels.
Recent researches conclude that all learners are capable of learning all of the
mathematical concepts we want them to learn, and they can learn if it make sense to
them and if they are given chance to do so, (Walle, 2004, in Nyikahadzoyi, 2012:21). The
bottom line from psychologists like Triplett, (1898, the founder of social
psychophysiology and sport psychology, in Gross, (2010, p484, Maslow in King, 2008) is
that motivation plays a key role in the learning process of the learner. This point
facilitates a better place for the learner to be interested in the learning of a concept even
it is difficult. Sport games are found to have that power to motivate a learner, but it calls
for the creativeness of the teacher to harness the power of those traditional games and
convert the activities into mathematical operations.
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Efforts by the Zimbabwean government through the Ministry of Education to
motivate every learner to pass mathematics have yielded very insignificant numbers in
schools, for instance, passing a policy that says no one should enroll as a teacher, a
nurse, and other high remunerating courses at colleges without mathematics. Recently,
the Ministry of Higher and Tertiary Education has announced free education to those
students enrolled in Mathematics, Physics, Chemistry and Biology under a Model code
named Science, Technology, Engineering, and Mathematics (STEM). Still, the numbers
are not growing. This has given this study a place to argue that there should be another
strategy that need to be explored further that motivates learners to love mathematics,
and this is the utilization of traditional games familiar to learners into which
mathematical operations are embedded and teaching and learning process become just
an extension of their usual life activities.
2. Statement of the Problem
The growing failure rate in mathematics, necessitated by learners drop outs, hating
mathematics and low enrolment in mathematics by learners both at primary and
secondary school levels is a cause of concern to parents, learners and the educators. This
scenario has negatively impacted on economic and technological development of many
nations in developing nations.
3. Research Questions
Which traditional games teach mathematical operations?
mathematical concepts?
To what extent do the traditional games helpful in the teaching and learning of
Which mathematical myths demotivate learners from pursuing maths as a
subject at school?
4. Objectives of the Study
To identify traditional games which teach the mathematical operations.
operations.
To explain the extent to which traditional games teach the basic math s
To explain the mathematical myths which demotivate learners in schools.
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5. Significance of the Study
The study provides the mathematics teachers with new trends in the teaching of maths
operations using the funniest creative approach that harness the power of traditional
games found in their communities, therefore increasing the love of wisdom through
honouring indigenous knowledge systems. Furthermore, the research findings shall be
made available to school libraries and college libraries and some mathematical coaching
clinics shall be put in place in some districts by the researchers. The study will assist to
disqualify the often perceived mathematical myths and contribute to an increased
enrolment and pass rate in mathematics.
6. Assumptions
The researcher assumed that:
There is lack of creativeness on the part of teachers when teaching maths in
schools.
activities, learners will not hate it.
Once learning and teaching process is made funny and related to everyday life
There is untapped value in the traditional games as approaches to teaching and
learning of mathematical concepts.
7. Definition of Terms
Contextualization: is the teaching of basic skills in the common understanding of the
learner s life-style.
Mathematization: is the act of expressing real world contexts mathematically.
Traditional games: these are the indigenous play activities familiar to learners which
this study envisages to have mathematical values.
Interactive teaching and learning: a process in which learners have concrete
familiarization with the learning environment, the learner being at the center of
learning manipulating objects of mathematical value.
Pedagogics: the process of learning and teaching that is conducive, learning processes
in a school environment.
Myths: these are testified legendary beliefs learners attach to mathematics as difficult
subject in schools curriculum.
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8. Summary
The continuous hate and fear of mathematics in schools has been a cause of an outcry
by parents, teachers and learners themselves and this has motivated this study to come
up with formidable ways of harnessing the power of traditional games into the teaching
and learning of four basic mathematical operations at primary school level. The
researchers have theorized that contextualizing mathematical teaching and learning
process is an approach worth trying to improve students performance.
9. Review of Related Literature
9.1 Introduction
This chapter covers some African traditional games in which mathematical skills and
concepts are embedded and how those games are played so that teachers are learners
can employ as they contextualize mathematics in their lessons. Contextualizing the
teaching of mathematics is believed to be the most effective approach that makes
learners love mathematics.
9.2 Traditional games of mathematical value
For neo-Vygotskians, play is considered to be a leading activity play provides an
important context for learning and development, (Leontiev, 1981, Oerter, 1993). From
this observation, it is imperative to identify those games that have mathematical
calculations which can be adopted by teachers of mathematics in schools especially
primary teachers.
The term traditional game is derived from the two words tradition and
game , Ituh,
, in “musa et al
. Furthermore, ”enderly,
, posits that
traditions are the conventions, norms and attitudes that have been perpetuated in any
community, and the word game , according to Leornard,
refers to a play that is
structured on the basis of rules, formal or informal, by which the players must abide.
This means traditional games, therefore are acceptable indigenous plays that are
handed down from one generation to another. Once they are community bound,
learners can fully appreciate those games and it is advantageous to the teacher to
introduce maths concepts relating them to how those games are played. Taking lifestyle activities to the classroom situation becomes an extension of the common life and
there is no break between the learning of new concepts in maths and the common life
experiences of the learner.
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9.3 Contextualizing Mathematics through Traditional Games
The modern interactive teaching and learning activists like Janassen (2009), advocate
the use of computers gadgets as mind tools that advance child interactivity with a
learning environment, but common argument is that how many schools in underdeveloped nations like Zimbabwe and its remote rural schools have access to
computers, let alone electricity availability. Therefore, this calls for the embracing of
low cost innovations like the use of traditional games in solving mathematical pass-rate
dilemma. Traditional games common in several African communities that have been
played by people of young ages as past time games include these:
a.
Nhodo game
Figure 1
This game involves digging a small hole in the ground and then placing a number of
small stones in it. The game is played by two or more children. Each player tries to
scoop all the stones out of the hole and then scooping them back into the hole one by
one, then in twos, then in threes and so on until eventually one scopes them all back
into the hole. This is done by first throwing one stone (called mudodo) into the air while
simultaneously scoping out all the stones out of the hole and catching it before it falls to
the ground. The mudodo is then thrown again while scooping back the stones into the
hole as described above and catching the mudodo before it falls to the ground.
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a.
Tsoro game, NsaIsong
Figure 2
This is a game played by two people, each with 12 children (tokens). It is often drawn
on the ground but sometimes is played as a board game. Each player aims at having 3
of his tokens in the same line, either horizontally, vertically or diagonally, while at the
same time impeding the other player from coming up with this pattern.
c.
Madhadha ari pamutsetse: this is a song game in which a player imagine having
ten ducks on a line, starting either by descending order i.e. subtraction starting with
numbers figure 1 until the player comes to zero, and one can be assigned to start in
ascending order using figure 1 until ten ducks.
d.
Pada
7
8
6
4
5
3
2
1
A
B
Figure 3
The playing field consists of a combination of rectangles and circles. The player
positions him/herself in the first two rectangles with one leg in rectangle A and the
other in rectangle B. The game is played by throwing a pebble into circle 1 through to
rectangle 8. Each time the player hops past the pebble balancing on one leg and only
lands on two legs on reaching two adjacent rectangles and picks the pebble on the
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return journey. Thus, the game is played from mamu
through to mamu
. “fter
going through all the stages the player once more positions himself with one leg in
rectangle A and the other in rectangle B, but this time facing the opposite side and
throws the pebble backwards so that it lands in one of the circles or rectangles and
becomes what is called chikoko . Thus, the player has the privilege to stand using both
legs when he gets to the chikoko .
e.
Rakaraka - free start
3
4
50
1
2
Figure 4
The game is played using a ball and is played by many players who are divided into
two groups. The game begins with one group stationed in the circle at the center while
two members of the other group would stand facing each other on either side of the
longest straight edges of the playing field throwing a ball to each other with the
intention of hitting their opponents with tithe players who are inside would run to
circle 1 and then to circle 2, 3, 4 and back to 1 counting from 1 to 49 as they do so until
they come back to the starting point when they get at number 50. Those who are hit by
the ball would pull out of the game and would only rejoin the others if one of their
members successfully comes back to the starting point. If they are all eliminated it
would be the turn of the other group.
f.
Sikuza
Figure 5
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This game is played by one to four people. This game is played by one player jumping
into the quarters of the pie-chart. Depending with grade level, watchers can chart out
words in the topic of fractions, like 1quarter! , 2 quarters!, 3 quarters!, whole circle!.
g.
Bangi-ngiria-ngiria
Figure 6
The game is played by moving step by step from the first box in the first row through to
the last box in that row before stepping forward to the next box in the next row
repeating the same process as before. Enough care should be taken to avoid stepping on
the lines drawn on the ground as this would mean losing the game.
h.
Hwishu
Figure 8
The game is played by many players who are divided into two groups each stationed in
either of the two circles. One group is said to be the serving group while the other is
the receiving group. The serving group would roll a ball towards the receiving group.
A member of this group kicks the ball as far away as possible. They would then run
from their side to the servers circle crossing a line and back to their circle and would
continue back and forth counting the number of times they reach the servers circle
before the ball is brought back into play. In this game, the players will set their game
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point
the number which they wish to reach). Once that number has been reached by
the receivers, it will be a game point.
Researchers of this study have a glowing interest in explaining how these
traditional games can be used in the teaching of mathematical concepts. According to
Berns, (2001), contextual teaching and learning is a conception of teaching and learning
that helps teachers relate subject matter to real world situations, and motivates students
to make connections between knowledge and its applications to lives of family
members, citizens and workers. Traditional games are a good example of approaches
teachers could harness these games power to motivate children to learn mathematical
concepts in a funny way.Thus, students must be equipped with knowledge and skills
that enable them to transform the society in which they live. Contextualization can be
conceived as a learner-centered teaching approach. In this regard, the instructor focuses
on what students are learning, how they are learning and they use the learning,
(Weimer, 2002). Multz, (2010) concurs by viewing contextualization as a form of
deeper learning that comes about through linking ideas and concepts across courses.
Perin (2011), asserts that in anyone programme, contextualization of basic skills
instruction contains one or more of the following components: interdisciplinary
learning, use of students informal, out-of-school knowledge, active-student-centered
learning, student collaboration, use of explicit literacy strategies, authentic, everyday
life situations. The African traditional games are undoubtedly harnessing all these
components necessary to learners of mathematics in schools.
Furthermore, Perin, (2011) brings in another observation that there are two forms
of contextualization teaching: contextualized instruction and integrated-basic skills
instruction. Contextualized instruction would be employed by mathematics teachers
when exploiting the real life experiences, like games, to teach mathematical concepts,
while integrated instruction would be employed by discipline-area instructors in
academic, career and technical areas. However, the term contextualization is used to
refer collectively to the two forms of instruction. On the other hand, integrated basic
skills instruction is the incorporation of reading, writing, or maths instruction into the
teaching of any content, (Perin, 2011). The incorporation of maths skills and other
subject language skills is a common phenomenon when children interact during
traditional games in their cultures.
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10. Mathematical Myths in schools
Teachers, students, parents and communities have fear of Mathematics, largely because
of some myths associated with the subject. According to Nyikahadzoyi (2012) some of
the myths in Mathematics include:
The belief that Maths is simply a collection of facts and procedures and doing
mathematics is simply recalling the facts and performing memorized procedures
Mathematics is perceived to be increasingly mysterious, full of symbols and no
words.
Mathematics is hard and requires a good memory
One is born with mathematical talent or not. There is no room for creativity.
Furthermore, researchers like Erickan, MacCreith and Laponte, (2010),
established factors that are associated with mathematics teaching and learning process.
They pointed out that people believe that mathematics is a hard subject not for women
but men, this is echoed by Tobias,(2013) and Panaoura and Philippour (2016).
A list of myths was identified by www.uaf Development Education:
difference)
maths and solving problems. Mathematicians always think intuitively first).
music)
Men are better in maths than women. (yet researches have failed to show any
Maths requires logic not intuition- (but intuition is the cornerstone of doing
Maths is not creative-(creativity is central to maths as it is to art, literature or
It is bad to count on your fingers
approximate answers is often more important than getting exact answers.
maths is done leads to a complete lack of self-confidence.
It is always important to get the answer exactly right-(yet the ability to get
Some people have a maths mind and some don t - (belief in myths about how
There is a magic key to doing maths. – (there is no formula, rule or general
guideline which will suddenly unlock the mysteries of maths. If there is a key to
doing maths, it is in overcoming anxiety about the subject and in using the same
skills you use to do everything else).
Maths requires a good memory - (knowing maths means that the concepts make
sense to you and rules and formulae seem natural. This kind of knowledge
cannot be gained through rote memorizing).
A more similar viewpoint was given by the MathPlus Academy, (2016) as five
most harmful maths myths:
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Some people have the math gene and others don t. – ( there is no conclusive
research that shows any genetic predisposition for excelling at maths)
Boys are better at Maths than girls
Mathematicians do problems quickly and never make mistakes-(what
distinguishes a mathematician is the ability to identify patterns, willingness
to try new ideas and their desire to persevere through failures).
and practice)
Speed is a measure of ability in mathematics - (yet it is through experience
A great memory is the key to excelling at maths
Fortunately these are mythologies which may also require further researches,
therefore, one cannot be penalized of believing in them since authors have pointed out
that they are not proven as yet, but can militate against learning of mathematics in
schools. Better methods of dispelling such myths is to bring in some creative ways of
teaching and learning maths, like harnessing the motivational power of traditional
games.
11. Research Methodology
11.1 Introduction
The researchers undertook a phenomenological perspective when generating data from
the rich informants in the teaching and learning field. This study has adopted a
qualitative approach in soliciting data, hence a case study was the design deemed most
appropriate.
11.2 Research Paradigm
The study focused on rich informants personal experiences in the teaching of
mathematics, a subject that most learners have found to be most difficult as depicted by
its lowest pass rates both at junior and senior educational levels. The personal
experiences involved perceptions, myths, beliefs, attitudes and arguments of learners,
teachers and parents on performance and teaching of mathematics as a science subject.
Therefore, the ideal research paradigm adopted to solicit these experiences was the
qualitative. The underlying rationale for choosing the qualitative route was that the
nature of the study questions calls for inductive reasoning where specific participants
were observed and interviewed in their natural settings and generalization was made,
(Welman, Kruger and Michell, 2005)
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11.3 Research Design
This study adopted case study as the deemed design for the reason that, a case study
allowed the researchers to have an in-depth study of one set of characters who were
teachers, children, and parents in a given natural setting whose perceptions, attitudes
and code of contact were governed by the same culture.
11.4 Population and Sampling
Teachers, children and parents made up the population that the study focused when
soliciting relevant data. The study had unlimited sample size as the data collection
process was governed only by when the rich information reached saturation and
satisfied the researchers as enough and authentic to answer the research questions.
Therefore, the sample size ended up to fifty (50) participants.
Purposive sampling was used in this study (Oliver, 2006, in Kaputa, 2011) to
identify the three sectors concerned in the teaching and learning of the child. This
technique was selected because it enabled the researchers to identify information-rich
participants in schools. Confidentiality and anonymity of the participants was assured,
yet it was motivating to the participants as they found themselves as experts and
creative people in the teaching and learning of mathematics in schools. However,
participation was voluntary and the decision to take part was on the basis of informed
consent, especially the children.
12. Discussion of Findings
12.1 Importance of Traditional Games
As postulated by Mosimege, (2000), this study has also found out that indigenous
games are usually viewed from the narrow perspective of play, enjoyment and
recreation, yet there is more to them than just these three aesthetic aspects. It emerged
that children are mostly likely to be creative when they use their ideas and usual
experiences; and make new connections through play.
Observations showed that only infant grades usually use contextualization
(inform of traditional games like song-game Madhadha ari pamutsetse (Ducks in a line)
when teaching subtraction concept. Environment-based pictures are frequently used in
elementary classes, but junior and senior grades abandon this approach and prefer
formulae and patterns. This scenario alienates learners from their natural concepts and
that leads to abstract thinking and to demotivation.
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12.2 Tsoro
A look at the playing field when children were introduced to this game during lessons
reveals that there are various shapes of varying sizes and hence the concept of shapes,
similarity, measurement, and area and number patterns can be addressed. The concepts
of ratio and proportion can also be addressed when children compare the number of
games won by player A as compared to those won by player B. Use of this game
inculcates such mathematical skills as reasoning, interpretation, calculations and
identification. Children conversant with this traditional game at junior and senior level
could easily play the game of chess , interviews of teachers revealed so.
12.3 Pada
It was consolidated by interviews and observations that there are some mathematical
ideas embedded in the game of pada and it is enjoyable for children to learn concepts of
shapes and their properties e.g rectangles and circles including the idea of geometric
space. The motivation came when each of the players wished to be the first to play as
he/she would have more chances of winning chikokoko as all the
spaces Fig.
would
be available to him/her, hence the concept of probability can be built from the game.
That is, if
space has been won as chikokoko the probability of the next player winning
would be / assuming that each player has an equal chance of winning. Teachers
response to the value of this game was 100% in agreement, and those who tested it
recommended it as another simpler way to teach probability, one of the most difficult
mathematical concepts. It even emerged that the game of chabuta (dices) is common
game among learners and is relevant approach to teaching and learning probability
concepts.
Secondary grades introduced to the game of Padaat one of the schools went on to
use it when teaching and learning the inverse variation . They said the more the
number of players the less the number of spaces (chikokoko) to be won.
12.4 Nhodo
This game was seen to be useful in the teaching and learning of numeracy. Each player
learns to count from 1 to higher numbers in an orderly manner. The concepts of factors
and multiples can also be learnt through playing nhodo. This game was seen to be more
common among school children and is suitable to primary children. The game also
teaches accuracy, coordination and logic and calculation skills.
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12.5 Bhangi-ngiria-ngiria
Creative teachers pointed out that they find the game important in teaching
multiplication. For example, bhangi =2 boxes, ngiria=3 boxes, ngiria=4 boxes.The first row
going to the right has 4 boxes and the last column going downwards has 4 boxes, once
two children move in these two directions the equation is 4x4=16, i.e. area. Any number
of boxes moved by two students in those different directions, when multiplied would
give area covered. That game is most suitable to grades where the concepts of area and
multiplication areintroduced.
12.6 Rakaraka and Hwishu
The gamesrakarakaand hwishuhave very little to teach in terms of mathematical skills,
but invigorate mental alertness as well as counting. However, these games are good
introductory games to cricket. Teachers confirm that these two games have no much
attachment with mathematics therefore, teachers seldom employ them.
13. Conclusion
From the discussions of the results, the researchers have made the following
conclusions:
1. Traditional games are commonly used by infants teachers, but junior and senior
grades concentrate on abstract examples and formulae, to which most children
take time to comprehend and conceptualize.
2. Children good at mathematics can demonstrate to peers easily using practical
examples, e.g. probability by playing chabuta (playing cards).
3. Once skills are embedded in games, learners tend to love and appreciate
mathematics as a subject.
4. Most mathematics text books emphasize formulae which are far from learners
conceptualization ability, making mathematics a boring subject.
5. There are too much myths attached to mathematics as a subject, and these have
also contributed to maths phobia.
6. Mathematical games, in form of traditional plays, use indigenous languages
which enable quick understanding of the mathematical concepts and skills.
14. Recommendations
This study makes these recommendations:
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1. Senior and junior classes should employ traditional games common in a
particular community when teaching and learning mathematical concepts for
easy understanding.
2. Teachers must allow peer groups to exist and teach other children using their
local languages.
3. Mathematics text books should be revised to accommodate traditional games
from ECD to higher grades.
4. Schools and communities should start to campaign against mathematical myths
attributed to this subject by most societies.
5. The teacher should make sure the game matches the mathematical objective.
6. The teacher should keep game completion time short.
7. The children should be given the games as homework.
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LEVERAGING ON THE POWER OF TRADITIONAL GAMES
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