Indexed and Abstracted African Journal of Education and Technology Volume 1 Number 2 (2011), pp. 84- 92 ISSN 2045-8460 (Online) ISSN 2045-8452 (Print) www.sachajournals.com ELECHI AMADI’S “THE CONCUBINE”: ETHNOMATHEMATICS RESOURCE FOR TEACHING MATHEMATICS IN IKWERRE PRIMARY SCHOOLS Godwin Alo ODILI1 and Nchelem R OKPOBIRI1 1 Department Mathematics/Statistics Rivers State University of Education Rumuolumeni, Port Harcourt ABSTRACT The study is based on the content analysis of Elechi Amadi’s book, “the Concubine”; the book captures the cultural elements and worldview of the Ikwerre people in the upland part of Rivers state of Nigeria. This research was a quasi experimental study to appraise the existence of mathematical ideas in “The Concubine” set in Ikwerre culture and to determine the effect of using these ideas in teaching some mathematics topics to Ikwerre primary school pupils. A content analysis of the text confirmed the existence of mathematical ideas in the book. Forty primary two Ikwerre pupils (making the experimental group) were taught some mathematics topics using ethnomathematics ideas as exposed in the novel and forty (the control group) were taught the same topics using the conventional methods. The two groups were given a pre - test and post - test using an achievement test as an instrument constructed by the researcher. The result of the achievement test was analyzed to determine whether there was any significant difference in the performance of pupils in the two groups. The result shows that there is a significant difference between the experimental and control groups. This difference was in favour of the experimental group. Keywords: Elechi Amadi, Education, Pedagogy, Cultural Elements 1. INTRODUCTION Mathematics is today unarguably the most integrative subject, especially in the sciences. The National Policy on Education (FRN, 2004) states the goals of primary education to include; “...to inculcate permanent literacy and numeracy and ...lay a sound basis for scientific and reflective thinking”. In a global society which is getting profoundly digitalised, the need for numeric knowledge cannot be more felt at any other time than now. Unfortunately, Ogunkunle (2007), stresses that pupils continue to perform poorly in mathematics. The problem of integrating mathematics in its role as a veritable tool in almost all fields of study, brings to the fore the growing attention in the importance of mathematics as dependent on society- based antecedents. How can diversities in orientations be reconciled in the mathematics content to encourage a curriculum developing from activities in the learners’ surrounding. The poor performance of students in mathematics in Nigeria, according to Badmus (2002) and indeed the entire third world, as emphasised by D’Ambrosio (1985), lately has given 84 African Journal of Education and Technology, Volume 1 Number 2 (2011); pp. 84-92 great concern to educational planners and administrators. The curiosity is on the causes and remedies to this anomaly. Experts, Lachaud (1983), Shirley (1986), Kurumeh (2006) argue that mathematics phobia is borne out of the age-long eurocentric bias of the mathematics curriculum which leaves the student thinking in abstractions that are alien to his environment. Such thoughts make the student think of numbers and symbols as ending on paper with solutions that need not be applied. The solutions of many other problems are sought, found depending on the intelligence of the student, and discarded without recourse to reality. Research has gingered great responses of scholars to the emergence of mathematical thinking in the local parlance, using local examples of things that can be seen, recognised in their quantities as well as their similarities in shapes and cultural applications and remembered as many times as they need to be recalled. The teacher of mathematics will find it very useful as a means of motivation to let his pupils see the value of native history and past history of mathematics that can open the door to enrichment mathematics. According to Abatan (1981), mathematics starts very informally with the children hearing, seeing; doing and then counting even before school age. Fakaude (1981) sought to, “...remove the frustrations of a teacher who cannot associate school lessons with real life situations” As a result Kurumeh (2006) calls for ethnomathematics (a culturally based mathematics methodology) as a useful resource in the teaching of mathematics. Ubiratan D’Ambrosio (1985) defined ethnomathematics as, “a methodology to track and analyse the process of generation, transmission, diffusion and institutionalization of mathematical knowledge in diverse cultural systems”. According to Yates (1989), “Every society no matter the level of its civilisation develops a kind of mathematics which helps her members to solve life’s problems”. Bishop (1997) observed that, “ethnomathematics discusses new ideas that surfaced from the development of the social dimension of mathematics education in the quest for a more meaningful mathematics education for children”. It explores the implications of research at the cultural level (i.e., “the relationships between mathematics education and the cultural and historical context of the society”). It is expected that the application of ethnomathematics will not only expose the pupil to outside-school mathematical knowledge, but will also imperatively suggest areas that would be beneficial to mathematics curricula and teacher training. D’Ambrosio (1998) further argues that, “The incorporation of ethnomathematics in the school system is the greatest challenge for a new education”. Is it possible to conciliate academic mathematics with ethnomathematics? The academic mathematics which is taught in the schools has its roots in the Mediterranean - the Egyptians, Babylonians, Greeks, and Romans. Academic mathematics has evolved and changed over time in accordance with the needs of the dominant powers – imperialism, Christianity, colonialism. Often local knowledge is co-opted by the dominant powers. The essence of the ethnomathematics program is reflecting on the myth that rationality and logic are synonymous with Western mathematics; it questions the universality of mathematical knowledge. Kurumeh (2006) claims that : It links their past (previous) experiences to their present classroom experiences ,links home background to the classroom activities thereby making mathematics concrete and a reality due to its processes. Ethnomathematics approach has the quality of restoring self-confidence, trust and enthusiasm in solving mathematics problems among students. In it, students discover the relationship between mathematics, real world and daily life activities creating new learning environments. In studying the worldview of this people, their mathematical ideas and how they interpret life in the purview of these ideas, it is intended to use these as workable basis for the teaching of mathematics to pupils in the same cultural traits and by extension, it becomes pertinent that a thorough understanding of any cultural group’s worldview can expose elements 85 African Journal of Education and Technology, Volume 1 Number 2 (2011); pp. 84-92 of teaching within their worldview which can be applied creditably in the teaching and learning of mathematics in that group. It is against this backdrop that the researcher projects to identify the usefulness of the mathematical ideas in Elechi Amadi’s The Concubine (1966) captures the cultural elements of the Ikwerre people in the upland part of Rivers state of Nigeria with a view to spotlighting how these ideas can be used in teaching mathematics topics to primary schools in the area. 2. METHOD AND MATERIALS 2.1 THE RESEARCH PROBLEMS There exists an erroneous impression that mathematics is an imported activity from the Western bloc, which is unrelated to the pupils’ culture. The content and methodology of school mathematics seem not to reflect the cultural environment of the pupils as they are disassociated from modern reality, and fail to account for important new innovations. A few sources have been found, notably Zaslavsky (1973) who often rely on present day examples and reflecting the past or on literary sources, such as Achebe’s mathematical allusions in his novels. Occasionally, societal development comes to play, such as the two –thirds of 19 debates of 1979. According to Odili (1990), pupils’ achievement levels in mathematics have remained low for many years and their performances have also continued to deteriorate year after year. This situation affects the early educational experience of children. Uche (1990) recognises the importance of education at the primary level when he said, “education acquired at the primary level serves as a key to the success or failure of the entire educational system and is usually referred to as the foundation upon which subsequent levels of educational pursuits could effectively be built”. What is the reason behind the fear which pupils have on mathematics? Is it that the curriculum is wrong or that the teachers are not competent to impart the relevant knowledge to pupils? Primary school teachers are often not trained in the application of local resources and instructional materials which will have the pupils think originally on mathematical concepts. If mathematical knowledge is created in response to man’s need for survival and transcendence, then teachers need to base their teaching on process approach which takes mathematics as a process and not as a product cognisance of the environmental and cultural needs of the pupil( Odili 2006, 2008 ). Retraining of teachers to engage in the sourcing of ethnomathematics resources in other spheres of our social life like literature in this case presents ample grounds for research. 2.2 RESEARCH OBJECTIVES AND QUESTIONS This study is designed to: Identify the mathematics ideas and thinking of the culture of the Ikwerre people that are contained in Elechi Amadi’s The Concubine. Determine the effects of teaching Ikwerre primary school children some Mathematics topics using the mathematics ideas/thinking of the Ikwerre culture as identified in the novel. The study was guided with the following research questions. Are there identifiable ethnomathematics resources in Elechi Amadi’s, The Concubine? 86 African Journal of Education and Technology, Volume 1 Number 2 (2011); pp. 84-92 What is the effect of teaching Ikwerre pupils some identified mathematics topics using the local aids and examples identified in the novel, The Concubine? 2.3 HYPOTHESIS HO: There is no significant difference in achievement between pupils taught with ethnomathematics resources and those taught with conventional method. 2.4 RESEARCH DESIGN The design of this study is quasi – experimental. Pretest / Post test control design was adopted for this study. The design presents two different groups; the experimental group and the control group. The experimental group was subjected to treatment while the control group was totally excluded from the treatment. Both the experimental and control groups were given the same pre test and post test questions. The experimental group was treated by teaching the pupils some identified mathematics concepts using the local aids and examples identified in the novel, while the control group was taught same concepts using the conventional approach. 2.5 DATA The population comprised of all the primary two pupils in 221 primary schools in the four local government Areas of Rivers State making Ikwerre land namely, Port Harcourt city, Obio Akpor, Emohua and Ikwerre Local Government Areas. Emohua and Ikwerre Local Government Areas of were selected for the study to get pupils that are Ikwerre indigenes as those from the urban schools in Port Harcourt City and Obio Akpor may have been infiltrated by non –indigenes. One school was drawn from each local Government. From the schools sampled, two intact classes each of 20 pupils were randomly drawn by even –number and odd – number balloting. The experimental and control groups were also randomly assigned to the different intact classes by balloting. The experimental and control groups, each comprised of two intact classes making a total of four intact classes for the study. At the end of the two (2) weeks of sixteen (16) periods, the teachers administered post test to both groups. The scripts for both pre test and post test of the two groups were marked, scored in percentages and recorded; these data collected paved way for further analysis. 2.5.1 INSTRUMENTATION / VALIDATION The instruments for this study were made up of; Literature text, The Concubine in Ikwerre setting Lesson plan for the experimental and control groups. Mathematics Achievement Test on the Identified Mathematics Concepts (MATIMC). MATIMC consisted of 20 – multiple choice items with four options each constructed by the researcher to measure pupils’ performance in the identified concepts (Number and Numeration, Basic operations, Measurement and Geometrical shapes and graphs). The questions in MATIMC evaluated the cognitive (lower and higher) and psychomotor learning outcomes. 87 African Journal of Education and Technology, Volume 1 Number 2 (2011); pp. 84-92 This MATIMC was used for both pre testing and post testing of pupils’ cognitive and psychomotor achievement. Two sets of lesson plans were also prepared for teaching the concepts set out for the study. One set of the lesson plans was prepared based on the content analysis of the Mathematics ideas /thinking of the Ikwerres as indentified in the novel for the experimental group while the second set of lesson plan was prepared based on conventional teaching method for the control group. The researcher took the following into consideration: The class of the pupils, the class size, and pupils’ age, the 40 minutes duration per lesson, the specific objectives, the instructional materials and cultural background of pupils. The MATIMC and the lesson plans were validated by three research experts (two from Mathematics Education and one from Measurement and Evaluation). 2.5.2 EXPERIMENTAL PROCEDURE The researcher organised a training programme for the regular school mathematics teachers that were used as research assistants for the study. The necessary local instructional materials were made available for the study. Both experimental and control groups were administered MATIMC as a pre test by teacher. This was followed by the teacher teaching the experimental group the identified mathematics concepts using the identified local aids and examples as contained in the novel, The concubine. The control group was taught the same concepts using normal lesson plan and conventional teaching approach .The teachers were closely supervised to avoid deviation from the lesson procedure prepared by the researcher. 2.5 DATA ANALYSIS The content analysis was used to answer research question 1. The mean and standard deviation were used to answer the research question 2 while the student t-test was used to test the hypothesis at significant level of 0.05 and 78 degrees of freedom. 2.6 RESULTS The modern way of counting in base ten is consistent with the Ikwerre traditional counting technique which uses the fingers toes, pebbles. The names of the numbers came from oral tradition “...he had a temper as bad as that of a man with whitlows on his ten fingers”. (p.1) Here the number ten is presented as all or a complete bundle for counting. Other smaller divisions or factors of ten is mentioned; “...You seem to be exploring the soup with your five fingers”. (p.39). The general use of other numbers is seen in Amadi’s presentation of a collection of materials; “...Here they are; seven grains of alligator pepper, seven manilas, an old basket, three cowries, a bunch of unripe palm fruit, two cobs of maize, two cocks...”. Amadi also exposed the traditional Ikwerre concept of using a base period on which former and future periods are drawn or built; “... on the evening of the brother of tomorrow”. (p.63) Distinctions of even and odd numbers could be seen in Amadi’s use of numbers which appear in pairs; “...his biceps formed two thick knots... at last Madume got his two arms under his opponents armpits...the old men said he had the best pair of calves in the village”. (p.114) The mathematical operations of addition, subtraction, multiplication and division are usually extensions of the process of counting. Addition and subtraction may be applied to events, days, weeks months, seasons. At such times the Ikwerre pupil would make reference to an event or period from which other periods could be added or deducted to come to a specifically described point. Talking about Ihuoma’s age, Amadi wrote; “... every farmland was 88 African Journal of Education and Technology, Volume 1 Number 2 (2011); pp. 84-92 used once in seven years... the piece of land on which her father farmed in the year of her birth was farmed for the fourth time last year, so she was just about Twenty two”. (p.45) Counting in twos threes or fours would be a good prelude to the teaching of factors to Ikwerre pupils. This also goes to show addition of equal numbers as an introduction to multiplication. The operations of division and subtraction seem to be closely linked in the Ikwerre parlance. This is especially when the pupil looks at division as what is left to one after so many parts have been taken away from a given quantity. The use of the sun in telling time is well explored in the concubine. Amadi brings to mind the generally accepted parlance in Ikwerre that the sun is directly above the head at 12 noon. In another use, he takes the mind to the setting sun to portray the approach of dusk. Having established that Chiolu is in the west, he wrote, “...look at the sun, my child, we must hurry home before it gets to Chiolu”. (p.15) There are remarkable contrasts in the lengths of shadows that successfully point to different times of the day as shown in this passage; ‘... then as the sun travelled to Chiolu and the shadows grew longer, Ogbuji went off to tap palmwine”. (p.40) This suggests that the shortening of the shadows was towards midday while the increase in length of shadows must imply the coming of dusk. From times in a given day, Amadi goes on to longer periods. He established long distance sby talking about whole day journeys, then he uses market days of Afor, Nkwo, Eke and Orie to show number of days intervals. Today, these market days could be used by a teacher to aid understanding of the concepts of weeks, months and years. In describing the sizes of bars representing notes of the Oduma instrument, Amadi wrote; “...twelve unequal flat pieces of wood normally arranged in order of sizes, starting with the biggest to the left of the chief beater”. (p.26) Items of clothing were measured using arm lengths. Farmlands buildings and other constructive shapes were measured by tree spaces and paces. The foot was the unit of small measures because it was the nearest to precise measurement. There is a semblance to modern use of the standard meter rule when Ikwerre employs the use of bamboos. These bamboos were usually cut into varying lengths to produce household items; “... he dived under his bamboo bed and produced two small okwo made from Indian bamboo...he dived again and fished out a couple of drumsticks”. (p.156) It would not be difficult for the Ikwerre pupil to imagine very long lengths from the length of an average house to a long canoe and probably beyond the length of a felled Iroko tree. What may be cumbersome is the issue of money measurements. Although the concept of value is still antecedent of every monetary measurement, the practice in Ikwerre was entirely based on weights. The weight of cowries determined the quantity of money. It didn’t need to be counted. The weight was heavier when the magnitude of the exchange (goods, services, land, marriages, slaves) was bigger. However, observe the relationship between cowries and manilas and compare with kobo and naira. Amadi captured this in; “...I scarcely realised one hundred manilas... it was all I could do to feed myself, I never realised a cowry”. (p.16) The geometry in Ikwerre traditional society is mostly seen in their construction of houses, household equipment, fishing and farming techniques and the appreciation of landscapes. The construction of houses especially the thatching of the roof obeys a certain order that suggests the criss-crossing relationships of line, parallels, vertically and horizontally such that the general outlay is graphical and has small rectangles or squares in between. Thatching also exposes ideas of inclinations, made so to allow rain drops to slide off the rooftops. The yam barn is arranged in rows and columns, so also is the mat, a sheet of raffia carpet constructed by intertwining raffia ropes to make a perfect graph sheet. Other ideas of 89 African Journal of Education and Technology, Volume 1 Number 2 (2011); pp. 84-92 rectangular shapes are in the mention of graves which can be extended to capacity and volume since a grave is like a tank or opened cuboids in shapes. Table 1: Mathematics Themes and Corresponding Instructional Materials as Identified in The Concubine. THEMES Number & Numeration Basic Operation Geometrical Shapes& Graphs Measurement INSTRUCTIONAL MATERIALS IN THE CONCUBINE Fingers, toes, pebbles, countable items such as basket, manilas, cowries, grains of alligator pepper, kolanut, bunch of palm fruit, cocks, cobs of maize, market days, engagement or betrothal periods. Palm heads, okwe pebbles, events, yams, oranges, age-grades, shifting cultivation and crop rotation period, sharing of village pathway for clearing, sharing of meat in gatherings or after a general village hunt. Xylophone, construction of huts and household equipment such as bamboo beds, kitchen chair, calabashes, pots, tripod stand, fish dryer, motar and pestle, fishing and farming implements such as hoes, fishing nets, thatching of roofs, arrangement of yam barns, raffia mat, graves, bows & arrows, balls of foofoo. Weight of cowries, manilas and shell of seafood, the unequal sticks of oduma instrument, arm length, tree spaces, footpaces, drumsticks, canoe, cock crows and birds/insect chirrups, shadow length, market days, whole days journey, dry and rainy season. Analysis of the data revealed that there is significant difference in the achievement levels of the experimental group and control group after the treatment. The significant difference was to the advantage of the experimental group (See Table 2.) Table 2: Mean, Standard deviation and t- test of the achievement Scores for the two groups. GROUP N PRETEST X1 POST TEST X2 SD t-cal X Control 40 38.75 39.16 38.96 7.28 Experimental 40 39.23 51.14 45.19 1.75 2.79 The mean of the experimental group is higher than the mean of the control group showing a higher responsiveness of pupils to the ethnomathematical approach than the conventional approach to teaching math topics. The Standard deviation of the experimental group is also lower suggesting that a greater number of the pupils were tending towards the same scores which points to the effect of the treatment. Using 78 degrees of freedom at 0.05 level of significance, tabulated t is 1.96. The Tabulated t is less than the calculated t which is 2.79. The null hypothesis that there is no significant difference in achievement levels between Ikwerre pupils taught some mathematics topics with ethnomathematics concepts as contained in Elechi Amadi’s, “The Concubine” and Ikwerre pupils taught the same mathematics topics using the conventional methods is therefore rejected. 3. DISCUSSIONS Mathematics is a subject which was thought in the past to be entirely reliant on abstraction. Lately, however, in place of foreign abstractions which are difficult to structure, contemporary mathematicians and curriculum planners have placed importance on the conceptual development enhanced by local aids and examples. Elechi Amadi’s “The concubine” contains images of real life situations of the Ikwerre pupils’ livelihoods and belief systems which can be applied to the interpretation of their 90 African Journal of Education and Technology, Volume 1 Number 2 (2011); pp. 84-92 mathematical thought forms. The average Ikwerre pupil (like pupils from other culture) already has some mathematics inside of him which is used in lives quantifications, measurements, estimations, calculations of periods, recurrence of peculiar events and age even before coming to school. The problem which the pupils have becomes the formalisation and extension of these ideas or the harmonisation of out of school mathematics with formal school mathematics curricula. Obodo (1990) observed that mathematics teaching still follows the wrong pattern. The reasons for the low performance levels in Mathematics are diverse. Enukoha (1998) talked about students’ dislike of mathematics as stemming from the teaching methods, mathematics teachers and the nature of mathematics. The nature of mathematics has been erroneously perceived in the past. It has been unduly mystified. Teaching and supervision of the pupils’ development seem to be a major factor in the correction of erroneous impressions pupils have on the subject of mathematics. Teachers who speak the pupils’ language and understand their belief systems have better grounds for appealing to the sense of the pupils. Certain mathematical ideas within the African culture do not stand separately in an explicit sense. They are linked with the activities wherein they lie, like games, crafts, speech, paintings. The attributes of these mathematical ideas are not arbitrarily structured. For the mathematics curriculum to be effective, it must build upon the cultural heritage and needs of a particular people first before attempting harmonisation to universal needs. 4. RECOMMENDATION AND CONCLUSION 4.1 RECOMMENDATIONS The following recommendations were made by the authors. It is necessary to develop primary mathematics curriculum in consonance with the mathematical heritage of the people. Primary school teachers should be exposed to ethnomathematics as part of their Teacher Education program. Teachers of mathematics should recognise the special place of local in understanding the subject. A well planed curriculum integration of the Nigerian Mathematics education should be implemented to pupils’ relating it to home activities. 4.2 CONCLUSION The data revealed that there are mathematical ideas embedded in the Ikwerre culture, in the way they work at their farms, prepare their food, engage in sports and games, and construct their houses. The findings give credence to the essence of the study and the implication in the Nigerian Educational setting. The Nigerian pupil is faced with the task of grappling with Western Mathematics in school. Western Mathematics does not meet the needs of all people and is not always easily understood outside the mainstream culture. Approaches that take into account, the cultural context and the mathematical systems in use within the community are likely to be more effective. Using ethnomathematics-based curricula in Nigeria will encourage and introduce the pupil to techniques directly connected to the real life of the pupil. Thus the study implies that the application of culture – based mathematics would clarify the nature of mathematics knowledge. 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(2nd Ed) New York: Wiley Zaslavsky, C.(1973). Africa Counts. Boston: Prindle, Weber and Schmidt. © African Journal of Education and Technology (AJET) published by Sacha International Academic Journals, London, England in compliance with standards recommended by the United Kingdom Arts and Humanities Research Council AJET is internationally indexed in: Open-J Gate IndexCopernicus www.sachajournals.com 92