MATHEMATICS EMBEDDED IN CULTURAL PRACTICES OF IGALA PEOPLE

Abstract

This study sought to identify the mathematics concepts embedded in the cultural practices of the Igalas. In particular, the purpose of the study included  identifying  the  Counting  bases  and  counting  system  of  the Igalas and how they are related to the Hindu-Arabic counting system; identifying the Major occupations and crafts of the Igalas and suggesting some mathematics concepts embedded in them; identifying the religious practices and myths of the Igalas and suggesting some mathematics concepts  embedded  or implied  in  them; identifying  the various  Igala festivals and suggesting some mathematics concepts which are embedded in them; identifying the Games and puzzles of the Igalas and suggesting some mathematic concepts which are embedded in them; identifying   the   various   Igala   attires   (dressing   modes)   and   the mathematics     concepts  embedded in them. Five hundred and sixty respondents were used for the study comprising one hundred and sixty mathematics teachers and four hundred adults of Kogi state origin and eight local government areas were randomly selected out of nine local government areas which constitute the Igala ethnic group. Six research questions were formulated to guide the study. An unstructured open- ended questionnaire and an interview schedule were used to elicit responses to generate data for the study. The data obtained were analyzed  using  frequency  counts  and  percentages.  The  following findings among others were made:

The Igalas counts in base two, five, nine, ten and twenty and these are reflected in their counting systems and these counting systems are

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basically the same in the Hindu-Arabic counting systems.

The Igalas have several occupations and crafts which various mathematics concepts are embedded. Such mathematics concepts includes  measurement  of distances, perimeters, areas  and volumes, estimation,  simple   proportion   and   variation,   simple   equation   and algebraic expression, decimal operation, loses, discounts, simple and compound interests, geometric shapes, patterns, statistics, lines, curves, bearings and distances, angle of elevation and depression.

The following recommendations among others were made:

All mathematics teachers should be using cultural and local examples which are related to the daily experiences of the learners in the mathematics class room instructions.

There should be educational policy adjustments and continuous professional development of the teachers taking the culture of the learners into consideration.

CHAPTER ONE INTRODUCTION

Background of the study

There is the growing tendency of the emergence of mathematics black out given the prevailing hatred for the subject by most students at virtually all levels of education in Nigeria. The cloud of lack of interest and poor achievement enveloping the study of mathematics in Nigeria is frightening. This trend spells doom for the development of science and technology  in  the  country.  Mathematics,  which  is  described  as  the science  of  quantity  and  space  contains  sets  of concepts,  facts  and operations, which every layman, student and scientist needs to know Umeoduagu, (2001).

Mathematics, according to Nellist and Nichel (1986) comprises sets of  precise  and  logical languages  which not only leads  to interesting activities in their own ways, but can be applied or interpreted to everyday life.  It  is  a  pivot  in  which  most  physical  sciences,  social  sciences, medical sciences and technological sciences or education rotate. Mathematics is concerned with searching for patterns and relationships among different entities, developing and expressing generalizations in mathematical  symbols.  It  involves  making  decision  in  an  axiomatic system, which requires identifying and stating assumptions within which conclusions are made.

Generally speaking, Mathematics is a creation of the human mind which is concerned with ideas, processes and reasoning.

Mathematics has been known to play vital roles in the study of Science, Technology and all other spheres of human endeavors.

It is a vehicle of language through which the scientific and technological ideals   are   communicated.   For   example,   in   physics,   a   good understanding  of  graph  works,  equations,  differential  and  integral calculus are necessary for one to succeed. The knowledge of volumes, proportions, fractions, percentages, differentiation and so on are prerequisites for good understanding of chemistry. The ideas of rates, taxation, percentages, discounts, profits and loss, simple and compound interests, differentiations and other statistical information are very useful tools in the social sciences. In farming a good knowledge of statistics, rates,  discount,  areas,  weights,  profit  and  loss,  weather  forecast, taxation, simple and compound interests, etc. are useful tools for the farmers.  The  quantities  and  doses  of  drugs  to  be  administered  to patients at intervals in medical sciences require a good mathematical understanding of hourly calculations.

Mathematics is an important prerequisite for admission into both the science and technological courses in higher institutions of learning in Nigeria and a service course to all other departments. Mathematics is

therefore given priority place in the national policy on education as a core subject in the primary and secondary schools.

Despite the obvious and numerous advantages of Mathematical Science, its teaching and learning in Nigeria has been associated with several challenges. Series of efforts has been made towards the encouragement and improvements of the teaching and learning of mathematics in the primary, secondary and tertiary institutions in the country, yet researches have shown that there is yearly constant poor performance   or   achievement   of   students   in   both   primary   and secondary  schools  mathematics  (WAEC/NECO  Examiners’  report,

2012).   This  poor performance  is  further compounded  by the poor attitude which the students show towards the learning of mathematics. Fear or trepidation, often results when students do not understand the topics or the idea of what mathematics implies or means. More often than  not,  mathematics   teachers   worsen  the  situation  (from  the students’ point of view) with a barrage of jargons which they hardly explain Offorma (2004). Thus they encourage students to merely memorize their notes.

Due to the increasing demand for mathematical knowledge in nearly all spheres of life and the high level of deficiency in mathematical knowledge of secondary and pre-secondary schools students, there is the need for a new method of teaching Mathematical Sciences which

should be based on the culture of the immediate environments of the learners. This method has to be based on a well-rooted cultural mathematical training and a teaching approach aimed at solving problems. For classroom teaching and learning implication, a child whose background cultural activities include farming, should be able to relate mathematics concepts and interactions with farming activities. For instance, the heaps made by farmers in Igala culture for planting of Yams,  Coco  yams;  Cassava, maize  etc  are  conical in  shape.  The

planting of yam sets in these heaps is at an angle of 450 approximately

and all these have implication for mathematics teaching and learning in the schools system. This implies that there should be a horizontal transfer of knowledge of mathematics concepts taught in the classroom to their farming practices. Similarly, there should be some ideas or knowledge based on his experience of farming transferred to his mathematics  classroom  which  will  aid  his  understanding  of mathematics concepts.

Ashworth (2010) opined that the poor attitudes, fear and lack of interest towards mathematics is as a result of the fact that teachers concentrate mostly on the teaching of the “ processes and tricks” of mathematics rather than making mathematics more meaningful and relating it to the students’ background experiences and culture. In fact, mathematics teachers should endeavor to relate the mathematics taught

in our classrooms to the background culture and experiences of the learners.

Ohuche   and   Ali   (2008)   observed   that   in   the   teaching   of mathematics, the cultural background of the learners has to be taken into consideration, especially when giving examples in the classroom. They emphasized the total involvement of the learners in the teaching – learning  processes. They concluded that achievements and  practical experiences are vehicles through which the teacher leads his students in pursuit  of  the  attainment  of  the  secondary  school  mathematics  in Nigeria. This is in agreement with the needs for teachers of mathematics to be deep in or verse with the cultural practical life and background experiences of his learners, especially in a particular ethnic group.

People, through mathematics are able to think about the world of objects and happenings and to communicate those thoughts in ways that reveal unity and order. The numbers, lines, angles, shapes, dimensions, averages, probabilities, ratios, operations, circles, Correlations, etc, that make up the world of mathematics enable people to make sense of a universe  that  otherwise  might  seem  to  be  hopelessly  complicated. Circles, squares, triangles, and other shapes can be found in culture and in things that people culturally build. Numbers and shapes can be used to describe many things in the world. Just as letters and words make up a language in reading and writing, numbers  and shapes make up  a

language  in  mathematics.  Numbers,  shapes,  and  the  operations  on them, help to describe and predict things about the world around us.

Thomaskutty and George in Agwagah (2008) identified seven educational values of mathematics as: practical or utilitarian values, disciplinary   values,   cultural  values,  social  values,  moral  values, Aesthetic values, and recreational values. The practical or utilitarian values of mathematics seem to have been given greater emphasis in our society and the school mathematics curricular than other values. Thus there is the need to emphasize other values such as the cultural values  of mathematics. It is  hoped  that this might  help  learners  to succeed in mathematics.

Brinkerhoff and White  in Offorma (2004) defined culture as a design for living that provides ready – made solutions to the basic problems of society. They conceived culture as a tool kit of material and non-material equipment necessary to deal with the common problems of everyday life. So both the material and non-material elements of culture respond to necessities within the society.

Culture can also be defined as everything that can be communicated, with necessary modifications from one generation to the succeeding ones. It represents peoples’ ways of life that is made up of both material and non-materials aspects such as the various artifacts, art, even techniques of food preparation and preservation,

farming techniques, how they eat, how they sleep the way they wash and    how  they  build  their  houses,  their  knowledge,  laws,  beliefs, morals,  values,  norms  and  languages.  Everything  man  made  or devised by man is a manifestation of culture.   Culture according to Offorma  (2004),  helps  to  determine  individual world  view,  their  life experiences and the way they learn. These attributes provides a link between traditional cultural practices and the school science and mathematics. The traditional cultural practice has to do with  belief, norms and values which people in non-western societies employ to make sense of their own world.

These traditional cultural practices are peculiar and significant to each ethic group and are transferred from generation to generation through informal system of education mainly by imitation and through initiation Onwuka (1984). Children learn to do what their parents; the village or the tribe and ethnic group want them to learn. Knowledge gained this way is said to be of high valued and serves to preserve the community and as a support for the prestige of the ethnic group and since the mode of learning was mostly informal, there was no written down curriculum.

The  summary  of  it  is  that  culture  is  maintained  through education, since  education  is  the  transmission  of  culture  from  one generation  to   another.  It  is   a  process   by  which   an  individual

internalizes; the mode, thought, action and feeling that constitutes culture. The case with Igala ethnic group is not different. They have a culture and some cultural practices are significant to them. This implies that the Igalas have their own language, arts, norms, religion, myths, interest and aspiration which they inculcate into the minds of the younger generations informally.

The  coming  of  the  white  missionaries  in  the  18th   century  to

Nigeria and Igala kingdom in particular, brought about the Western Culture and also the Western education into the region. The Western education came with a written down curriculum which spelt out what the learners had to learn within a given period of time. The question about the type of education to be given to the young learners therefore arose as a result of this Western education.

The common observation in our mathematics class room is that the classes are modeled after the Western style or pattern. The text books used are of Western background and are filled with examples and illustration from this same Western background. The Curriculum consists of materials drawn largely from a culture the child only faintly understands or not at all. The teachers often deal with the contents and concepts as with religion which has to be swallowed  without much questioning. The non – Western children are always seen struggling to learn enough English, Mathematics and Science to make way into the

Modern world Bimba (2010). In general, the non – Western children in the above mentioned type of class room are caught between two cultures, namely, Western culture and the traditional culture. This is also the case of the Igala ethnic group.

Achor (2006) rightly explained that we are now living, not only in the “West” but in the other parts of the world as well. That is to say that, though we live in the African environment, our lives are influenced and directed by the Western world views. According to Walder, (2005), a child  estranged  from  his  culture  is  helpless. He  finds  it  difficult  to acquire   new   concepts   which   are   complete   aliens   to   his   own environment  and  which  are  also  represented  in strange name  and language. For a child to accept and adapt to the “new science and Mathematics”, the gap between his culture and the new field of study has to be bridged. The child has no occasion in village life to use mathematics skills learnt by rote in school and has no knowledge of how to use these skills other than to please the teacher.

Therefore  the  mathematics  curriculum  should  be  based  on culture. It should reflect what is going on in the society. A society may be homogenous (i.e. a simple – singled cultural society) or heterogeneous (a multi – cultural Society), and this  affects the way the various cultures performs their mathematics i.e. the way they count, measure, relate  and classify and  the way  they  infer. The  question

is,should   emphasis   be   laid   on   “foreign   mathematics”   which   is completely imported  as a  result of interactions of other cultures or “ethnomathematics” which relates mathematics to the culture of the people?  There  are  mathematical  practices  identified  with  cultural groups which are taught, perfected and reflected upon in a non-formal educational system Ambrosio (2007). This is the thrust of ethno mathematics.

Ethnomathematics is derived from ethnology which is a branch of anthropology that divides or classifies human beings into various distinctive groups; analyze their cultures, the ethnic groups and their differences. The study of anthropology revealed that each ethnic group is different from another and has her own peculiarities. Ethno mathematics has to do with the mathematics idea that is indigenous and the mathematics practiced outside the Western system of education. It has to do with the theories, knowledge and method of cultural  practices.  Ethno  mathematics  embraces  the  study  of  the system of numbers and mathematical operations in a given cultural concept and this varies across cultures (Abonyi, 2010).

In  summary,  ethnomathematics  holds  that  mathematical ideas can be developed within the cultures. The mathematics ideas are those that involve number, logic and spatial configuration or a combination  of  these  into  a  structure  Ascher  and  Ascher  (2008).

However, from culture to culture and within any culture, mathematical idea appears in various contexts. Whatever the context, mathematical ideas and ways in which they are expressed are part of the intricate web out of which a culture is woven. Where and how the mathematical ideas  are  expressed  must  be  understood  if  mathematics  is  to  be properly appreciated. Ideas that are different to one’s cultural background may be forgotten while those that are in the ways similar to one’s culture are most likely to be remembered. That is, descriptions of mathematical ideas should and must be in one’s own culture.

The primary goals of ethno mathematics are in two ways (Ascher and Ascher in Ekpo 2000). Firstly, to broaden the thirst of mathematics by aiming a global multicultural perspectives and secondly to show pedagogical implications and possibilities  in the quest to increasing mathematics achievement in our classrooms. This study hinges on this second goal of ethno mathematics.

On counting bases and counting systems, different cultures used different  methods  to  count  and  represent  numbers.  One  of  the universal ways was to use fingers on the hands. Other cultures used the toes on their feet and other body parts to count and represent numbers. Beads and pebbles were also often used to count and keep track of things. This is also the case with the Igala ethnic group.

As cultures became more literate, they began to assign symbols to the

numbers so that they could write the numbers down.

There are two different procedures that people can use to symbolize  the  concept  of  numbers.  The  two  procedures  are  the cardinal and ordinal procedures.

The cardinal procedure involves using one symbol which represents the number one and using that symbol as often as needed. The ordinal procedure  assigns  a  different symbol  for  each  whole  number.  The problem with the cardinal approach is that it is not very efficient. It is difficult to see at a glance what the number that is written down is supposed to symbolize. The problem with the ordinal approach is that an  infinite  number  of  numerical  symbols  have  to  be  created.  The solution falls somewhere in between these two approaches where all numbers can be represented  with  relatively few symbols. This was done by creating a base number system. The most prevalent base number system today is the decimal system or base ten. It has been almost universally adopted. This is no doubt that people first learn how to count using their ten fingers. This makes base 10  automatically convenient.

In the past, there were a number of cultures, Golla, (2013) that used  a  different  base  number  system.  Instead  of  using  only  their fingers to count, some cultures used their fingers and their toes. This meant that they used a base 20 number system which is commonly

known as the vigesimal system. Other cultures use the quinary system or base 5 number system. These are also found in Igala ethnic group. There are merchants today in Igala kingdom that use the quinary system. They count using their left hand to represent single units while the finger on their left right hand marks each group of five units.

Occupations and craft include skilled trades, and professions, that is, vocational callings through which individual members can earn their living are aspect of cultures shared by members of a particular ethnic group. In every society, some individuals become more proficient in specific skills or they demonstrate special powers over other members of society in certain areas. The specialization of some groups lead to group awareness which make members develop specific patterns of behavior such as special hairstyles, trades, mat weaving, pottery, weaving and dyeing of some special kind of cloths, carving or blacksmithing, farming, etc. In some cases, outsiders may receive the vocational training depending upon interest and capability.

Another area of occupation and craft is the commercial life of the people. Before the coming of the Europeans, each society and traditional culture, like the Igala ethnic group were engaged in commercial activities. These started as trade by barter. Measurements of  quantities  were  done  using  palms  and  in  containers  such  as

calabashes, lengths were measured in foot paces or hand span, the ancient cubits, the fathoms etc. The commercial lives of any ethnic group like the Igalas yield a great deal of mathematics.

In religion and myths, there exist some beliefs in Africa that are all embedded on a number of natural phenomena.   The system of beliefs is centered on religion and the concepts of supernatural (mysticisms). These beliefs were somehow abstract and baseless, but in a way generated some taboos which are strictly observed by all in the society and were mostly based on numbers. Most ancient cultures hold that numbers have not only practical meaning but also a mystical or religious one. This is also the case with the Igala ethnic group. The Igalas has religion and myth. According to Ojoade (1981), Africans attach religious significance to numbers noting that Africans are notoriously religious. It  will be  therefore  not surprising  to  note  that numbers influence many aspects of life of the traditional Africans like the Igalas,in their rituals acts, greetings, conversations, number of participant chosen to attend a particular ceremony, number of animals sacrificed and the modes of sacrifice as well as the number of times prayed to evoke their god(s). Mysticism attached to numbers affected the counting systems of the traditional societies. For example, some

villages count in four as reflected in their market days, others count in fives, sevens, eights, nines.

On festivals, it is not surprising to note that numbers influence many aspects of life of the traditional African festivals such as the ritual acts, greetings, conversations, number of participants chosen to attend a particular festival, number of animals sacrificed and the modes of sacrifice during a particular festival, as well as the number of times prayed to evoke the god(s). The counting of days, months and years for the next festival and the hourly calculation or timing of the various events during the festival etc. has mathematics embedded in them.

Games and puzzles, according to Maxwell (1983) in Ekpo (2000) are mathematical models,   artificial but powerful representations  of reality   and   goes   a   long   way   to   getting   children   involved   in understanding language, mathematics social organization and the rest. In recent years games and puzzles have become a supplementary technique  for motivating  learning,  spurring  intellectual initiators  and organizing students’ concepts and instruction. The educational value of games and puzzles is the attention focusing quality it has because they involve the students actively rather than passively. Maxwell (1983) in support of this posited that a child’s intelligence quotient and problem solving abilities may relate directly to the number of games and puzzles

that the child has mastered at the initial sensitive stages of life development. An enormous variety of games and puzzles that can be analyzed mathematically have been played in Igala ethnic group and around the world and through history. The educational values of games and puzzles exposes one fundamental issue, that is, traditional games in general and the Igala traditional games in particular possesses the values needed to enhance all the fields of learning including mathematics if well tapped and properly channeled through educational processes.  Unfortunately, most of the traditional games in Igala ethnic group have not been studied or documented.   As a result of this, most of the rich Igala games and storytelling whose background and environmental requirements were Africans are no more to be found even during moonlight times. On this strength, Chibale (2007) warns that it is unlikely that there cannot be any meaningful development in other fields of education unless traditional games and other social and cultural aspects of African life are incorporated into our educational system.

One of the ways mathematics appears in dressing is through symmetries.  Woven  designs  in  cloth  or  sowings  (to  name  two) commonly have some kind of symmetrical and geometrical arrangements. A cylindrical/rectangular armed or legged dress often

has cylindrical/rectangular symmetry in the overall patterns. A woven cloth  according  to  Crowe  in  Ekpo  (2000), may exhibits  one of the seventeen kinds of plane symmetry groups. One can explore the mathematics embedded in the special pattern of dressing like special styles of clothing, weaving and dyeing of some special kind of cloths. One can also explore the mathematics embedded in things like traditional women’s work, such as knitting, embroidery and sewing.

Statement of the Problem

The  rate  at  which  students  fail  mathematics,  in  both  internal  and external examinations these days is very alarming. This failure deteriorates from year to years. There is yearly constant poor performance   or   achievement   of   students   in   both   primary   and secondary  schools  mathematics  (WAEC/NECO  Examiners’  report,

2012).   This  poor performance  is  further compounded  by the poor attitude which the students shows towards the learning of mathematics. Fear or trepidation, often results when students do not understand the topics or the idea of what mathematics implies or means. This is because   students   have   great   difficulty   in   understanding   and assimilating the mathematics taught to them in the classroom. They neither understood the basic computation: logic, fundamental principles nor the underlying processes that gave rise to mathematical facts. This

may be as a result of the mathematics taught in schools is foreign, euro-centric in origin and built on western cultural background. So they resort to learning by memorization, which resulted to consistent mass failure of students. This lack of understanding and consistent failure robbed the students of interest in mathematics. The problem of this study  stated  in  a  question  form  is:  are  there  some  mathematics concepts embedded in Igala cultural practices?

Purpose of the Study

This study was designed to investigate the cultural practices of

Igalas in Kogi State and identify the:

1. Counting bases and counting system of the Igalas and how they are related to the Hindu Arabic counting system.

2. Major occupations and crafts of the Igalas and some    mathematics concepts embedded in them.

3. Religious practices and myths of the Igalas and some mathematics concepts embedded or implied in them.

4. Various Igala festivals and suggest some mathematics embedded in them.

5. Games and puzzles of the Igalas and some mathematic concepts which are embedded in them.

6.  Various   Igala  attires  (dressing  modes)  and   the  mathematics concepts embedded in them.

Significance of the Study

This  work  is  significant  to  the  teachers  of  primary  and  secondary schools in Igala land as they may be acquainted with the mathematics concepts involved in Igala cultural practices and the cultural background knowledge for introducing and teaching some mathematics concepts to the learners at these levels. This may go a long way to suit their background, remove  fears  of mathematics by the  students and  also promote interest as mathematics at these levels serves as a good transmission from home to school and vice-versa. A class room teacher in this ethnic group studied may be more effective and efficient if the teacher is aware of the cultural traditional mathematics behaviour of the locality and is able to integrate it into the mathematics teachings and illustrations   in   the   formal   classroom   systems.   A   teacher   who understands the culture of the people and the mathematics embedded in these cultural practices and is able to transfer same to the mathematics classroom situation may promote more achievements or understanding of the mathematics taught in the mathematics class room.

The results of the study are also beneficial to the learners at both the Primary and secondary classes as the application of the findings may  remove  fear  of  mathematics  from  the  students  and  generate

interest and curiosity for learning mathematics. The culture and daily activities being introduced into the class room learning situation may show that mathematics is not alien to their culture and as such they may see a good transfer of mathematics to their daily life situation. Example drawn from the learner’s environment and culture is a boaster for better achievement. More mathematics learners, particularly from Igala ethnic group are now aware of the various mathematics concept which could be drawn from their environments and which may eventually reduce the abstractions  of mathematics,  eliminate  fear,  to  increase  interest and achievement among the learners.

Textbook writers also benefit from the results of this work as it points out some useful examples in some relevant areas of mathematics which could be introduced into their texts. Thus the various examples and illustrations in a text for each topic would be adapted to suit the cultural background knowledge and experience of the learners.

This   work   is   also   significant  to   the   government  and   its educational agencies especially the curriculum planners for example in the Junior Secondary School mathematics curriculum, the first topic for year one is Number and numeration, “an indigenous system of mathematics   and   of   specific   relevance   locally”,   the   government therefore has a basis for organizing seminars and workshops to equip mathematics teachers on basic cultural practices of the locality where

they serve and also point out some mathematical concepts in those cultural practices through the use of resource persons from the locality.

This  work  is  also  significant  as  it  x-rayed  the  contributions  of  the cultured-centered theory to the understanding of the Igala cultural experiences embedded in mathematics in schools. It identified and provided solutions to the shortcomings in this theory vis-à-vis Igala students and suggested possibilities for the advancement of a more detailed and otherwise robust theory that can adequately describes the sociocultural experiences of the Igalas and supports their educational development for the growth of the nation.

Scope of the Study

This study was limited to the 9 Local Government Areas which constitute the Igala ethnic group of Kogi State. The local government areas are; Ankpa, Bassa, Dekina, Ibaji, Idah, Igalamela-odolu, Ofu, Olamaboro, and Omala. The study involves some of the cultural practices  of  the  Igala  people  such  as  occupation,  crafts,  games, puzzles, Religion, myths, festivals and the counting systems of the Igala people.

Research Questions

The study was guided by the following research questions:

1.   What is the mathematics embedded in the counting systems of the

Igala people?

2.What are the major occupations of the Igalas and what

Mathematics concepts are implied in them?

3.  What are the major religious practices and myths observed by the Igalas and what mathematics concepts can be derived from the Practices according to their culture?

4.  What are the major traditional festivals observed by the Igalas and what are the Mathematics concepts embedded in them?

5.  What are the major games and puzzles of the Igalas and what

Mathematics concepts are involved in them?

6.  What are the major Igala cultural attires (dressing modes) and what

Mathematics concepts are involved in them?

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