Building Web-based Farm Information System Using 3D Visualization Technology: A Case Study of Jigawa State

 

ABSTRACT

Better developments in farming have been achieved when the information required by farmers on agricultural technologies are made available as accessing latest information of agricultural activities will produce a sustainable farming improvement.

The research is aimed at the dissemination of information to farmers through 3D visualization technology for the development of agriculture to improve the life of citizen. The thesis examines the basic 3D form of visualization technology of major plants found in the farms of Jigawa State farming environment.

The methods used in the research provided a reviewed of the related work in order to make a clear understanding of two dimensional works. Next, it made designed of the farm information model using Sketch up with Ruby for three dimensional farms.

It started with observing some works previously done on disseminating information to farmers including organization and surveyed project based on how to improve the flow of agricultural information through modern channels for sustainable farming development where the works are not 3D enabled form of disseminating information The research continues with design of Web-based farm information technology which is a 3D form of information dissemination.

To address none 3D limitation identified, we designed, implemented and evaluated a 3D farm information system. Results obtained showed that our 3D information system provided enhanced information dissemination to farmers in Jigawa State. Our 3D farm information system can be adapted and used in other environments to achieve better information dissemination.

TABLE OF CONTENTS

DECLARATION …………………………………………………………………………………………………………………… iii
CERTIFICATION …………………………………………………………………………………………………………………. iv
DEDICATION ………………………………………………………………………………………………………………………. v
ACKNOWLEDGEMENT ………………………………………………………………………………………………………. vi
ABSTRACT ………………………………………………………………………………………………………………………… vii
LIST OF TABLE …………………………………………………………………………………………………………………… xi
LIST OF FIGURES ………………………………………………………………………………………………………………. xii
ABREVIATIONS ………………………………………………………………………………………………………………… xiii
CHAPTER ONE …………………………………………………………………………………………………………………….. 1
INTRODUCTION ………………………………………………………………………………………………………………….. 1
1.0. Background of the study ……………………………………………………………………………………………….. 1
1.1. Statement of the Research Problem ………………………………………………………………………………… 4
1.2. Motivation ………………………………………………………………………………………………………………….. 5
1.3. Aim and Objectives of the Thesis …………………………………………………………………………………… 6
1.4. Methodology ……………………………………………………………………………………………………………….. 6
1.5. Organization of the Thesis …………………………………………………………………………………………….. 7
CHAPTER TWO ……………………………………………………………………………………………………………………. 9
LITERATURE REVIEW ………………………………………………………………………………………………………… 9
2.1 Introduction ……………………………………………………………………………………………………………………… 9
2.2 3D form of Visualization ……………………………………………………………………………………………………. 9
2.3. Why 3D? ……………………………………………………………………………………………………………………….. 11
2.4 Geographic Information System (GIS) ……………………………………………………………………………….. 13
2.5 Google Earth …………………………………………………………………………………………………………………… 14
2.6 Description of the study Area. …………………………………………………………………………………………… 14
2.7. Review of farm management software. ……………………………………………………………………………… 16
2.8. Review of related literature ……………………………………………………………………………………………… 17
2.9. Limitation of the existing work ………………………………………………………………………………………… 30
CHAPTER THREE ………………………………………………………………………………………………………………. 32
DESIGN OF WEB BASED FARM INFORMATION SYSTEM. ………………………………………………. 32
ix
3.1. Introduction …………………………………………………………………………………………………………………… 32
3.2. System Requirement ……………………………………………………………………………………………………….. 32
3.3. System Architecture ……………………………………………………………………………………………………….. 33
3.3.1. GIS map layer ………………………………………………………………………………………………………….. 34
3.3.2. Data layer ………………………………………………………………………………………………………………… 35
3.3.3. Interface layer ………………………………………………………………………………………………………….. 37
3.4 Dataflow ………………………………………………………………………………………………………………………… 38
3.5. Design of GIS map …………………………………………………………………………………………………………. 40
3.6. Designing 3D Farm model ………………………………………………………………………………………………. 40
3.6.1 Tools ……………………………………………………………………………………………………………………….. 41
3.7 3D farm on Google Earth ………………………………………………………………………………………………… 41
CHAPTER FOUR ………………………………………………………………………………………………………………… 43
IMPLEMENTATION AND DISCUSSIONS …………………………………………………………………………… 43
4.1. Introduction …………………………………………………………………………………………………………………… 43
4.2. Tools and Platform. ………………………………………………………………………………………………………… 43
4.2.1. Google Earth ……………………………………………………………………………………………………………. 43
4.2.2. Keyhole Markup Language (KML) …………………………………………………………………………….. 43
4.2.3. ArcGIS ……………………………………………………………………………………………………………………. 44
4.2.4. Ruby Programming Language ……………………………………………………………………………………. 44
4.2.5. Google Sketchup ………………………………………………………………………………………………………. 45
4.2.6. COLLADA ……………………………………………………………………………………………………………… 45
4.2.7. HTML …………………………………………………………………………………………………………………….. 45
4.2.8. Geodabase ……………………………………………………………………………………………………………….. 45
4.3 Code Implementation ………………………………………………………………………………………………………. 45
4.3.1 User Search Interface code. ………………………………………………………………………………………… 46
4.3.2 Zone Searching …………………………………………………………………………………………………………. 46
4.3.3 Accessing the Google Earth………………………………………………………………………………………… 47
4.3.4 3D model …………………………………………………………………………………………………………………. 49
4.4. Testing ………………………………………………………………………………………………………………………….. 49
4.4.1. User Interface Level …………………………………………………………………………………………………. 49
4.4 2. GIS Maps Level ……………………………………………………………………………………………………….. 51
4.4.3. Data level ………………………………………………………………………………………………………………… 52
4.4.4. Modeling the 3D effect ……………………………………………………………………………………………… 53
x
4.5 Results and Discussion …………………………………………………………………………………………………….. 56
4.5.1 Comparison of reviewed and proposed research ……………………………………………………………….. 61
CHAPTER FIVE ………………………………………………………………………………………………………………….. 64
SUMMARY, CONCLUSION AND RECOMMENDATION …………………………………………………….. 64
5.1 Summary …………………………………………………………………………………………………………………….. 64
5.2. Conclusion …………………………………………………………………………………………………………………. 65
5.3. Recommendation ………………………………………………………………………………………………………… 66
5.4. Future Work. ………………………………………………………………………………………………………………. 67
References. ………………………………………………………………………………………………………………………. 69
Appendix …………………………………………………………………………………………………………………………. 77

CHAPTER ONE

INTRODUCTION

1.0. Background of the study

Computer technology has improved many aspects of the oldest occupations, which is Agriculture. In Agriculture, these improvements include automated milk collection that comprises the robotic milking machine and the use of Geographic Information System (GIS) and Remote Sensing in Agriculture, automated Weather station, Geographic Positioning System (GPS)in agriculture and computerized farmland assessment.

With this, it is believed that computers have transformed farming activities. Advanced disseminating agricultural information technology has brought about strong changes in farming practices such as Information and Communication Technology application in agriculture, Mobile phone application of Agriculture and internet application of Agriculture.

With this application, it results in wonderful increase in production capacity of Agriculture. Most common use of computers in today’s agriculture has been in replacing human work and involvement in oldest farming machinery and other farming tools.

The automatic forms of farming such as use of machines and application of fertilizers are in use. With all these we can say computers have changed farming system while Internet has also doubled that change toward agricultural information dissemination.

Agricultural information dissemination is an important stage of agricultural technology development. It is essential because if it is not done properly and through the appropriate channels it will not serve the purpose it is intended for. The importance of information in agricultural development can never be over emphasized. Information generally is considered as being an essential production factor in Agricultural and rural development (Zijp, 2002).

Agricultural information is needed for overall development of Agriculture in order to improve the living standard of farmers. Adefuye and Adedoyin (1993) suggest that for a steady flow of accurate understandable and factual Agricultural progress, farmers must know, and act in accordance with Agricultural information.

Therefore, how far people progress in agriculture depends largely upon the availability and access to accurate and reliable information. Positive Agricultural management rests on farmer’s ability to make good decisions. While good decision making depends on correct information dissemination. Community’s farms are becoming larger and Jigawa State farms are improving as well as people becoming new farmers, and affected by changes in many Agricultural factors especially with introduced good farming information.

Decision making has become more and more complex requiring more types of information. With that, it is viewed that a farmer should set goals for his farming and accepts responsibility for decision made in reaching these goals.

The world is leaving the industrial age and entering the information age. According to Dillman (1988), with society‟s entrance into the information age, farmers must be able to adopt management practices to take advantage of the information technology becoming available to them.

Geographic Information Systems (GIS) are being used for developing ranking systems that evaluate land and provide a site assessment to aid, what is now known as precision agriculture. These hi-tech, interactive systems provide information based on a variety of factors such as soil conditions, drainage and slope conditions, soil pH and nutrient status.

Prior to the use of these systems, farmers were often in the dark about soil output, and unpredictable weather conditions affecting crop quality and profitability (precision agriculture). Agriculture provides farmers with control by predicting vital information including fertilizer application and problems with drainage, insects, and weeds (precision agriculture).

This kind of technology equips farmers with enough information to increase crop yield in a manner that is consistent with the best environmental practices for sustainable Agriculture (Preeti, 2011). The research attempts to contribute to the better understanding of how Geographic Information System (GIS) and 3D visualization tools can be used to disseminate farms agricultural information to farmers in Jigawa state.

It will determine how farm information can be represented through the use of visualization tools to allow farmers make good farm use decisions. The visualization tools used include the Google Earth digital globe product. Google Earth is one of a family of 3-D geo browsers (that includes Microsoft Virtual Earth and ArcGIS Explorer) that offer easy to use service for visualizing a 3D digital model of the earth via the Internet.

It is readily extended to act as an output medium for a wide range of products that contain spatial data and facilitates data access on information dissemination. One of the main functionality of the geographical information systems is to visualize geo related objects based on their geometry stored and determined by coordinates in a reference system.

The study of geo-related features and the relationships between them can be applied to many areas of the Agriculture industry. Regardless of scale –whether at the farm field level analyzing crop yield information or across an entire country– GIS is becoming fully integrated and widely accepted for assisting government agencies to manage programs that support farmers and protect the environment.

These are the Agriculture GIS application in the field (Kumar, 2011).

The thesis includes Google Earth for the research in visualizing the farm information. Where Google Earth is geo browser software for viewing satellite imagery, spatial data layers and allows adding place marks, lines, polygons and 3D models.

The software also creates virtual environments of user selected areas, such as a farm. Using Google Earth people may choose to simply view a location as a virtual 3D environment or to view the effects of an environmental process on that area.

Also the thesis uses geographic information system (GIS) for mapping the areas of the research. According to United States Geological Survey (USGS) GIS is a computer hardware and software system designed to collect, manage, analyze and display geographically (spatially) referenced data.

It is concluded that, GIS is a computer system that is capable of storing, managing, and presenting geographically referenced information. GIS systems are used in many fields, such as environmental control, tourism, scientific researches, resource management, and the definition is suitable for Agricultural applications of GIS.

Agricultural production are supported by use of GIS systems, because if you look at origin of Agricultural data for example, it is frequently geo referenced and may consist of elements of Agricultural activities such as climatic features like air pressure and soil quality.

Farmers can make experiment on soil samples or product taken from different places at the farms. Later, the samples are taken to a laboratory for processing. This is part of the GIS system work on Agriculture.

 

1.1. Statement of the Research Problem

A lot of researches have been done based on 2D to improve Agricultural productivity through information dissemination. Kakade(2013); views that Radio is one of the most powerful mass media for the dissemination of Agricultural information, and its effectiveness has been well established by many researchers.

According to Shahidet al, (2003) the most used form of print media for Agricultural information was pamphlets followed by posters, newspapers, book/booklets, magazines and journals. But our research focuses on Agricultural information dissemination in 3D visualization technology with help of GIS and digital globes.

Disseminating of Agricultural information is one of the most important factors that affect production. This means that getting better agricultural production depends on the enough and latest technological Agricultural information. Considering this, therefore 3D technology with support of GIS and Google Earth can bring better Agricultural information for good production.

According to ESRI (2010), Producers use GIS to better manage their farms by creating information-dense reports and maps that give them a unique perspective of their operations. The powerful analytical capabilities of GIS offer an array of options for visualizing farming conditions, as well as measuring and monitoring the effects of farm management practices, ESRI (2010).

With that, it is concluded that for a qualitative, attractive and better visualize access to Agricultural information to provide greater yield of farm product in farming system, the use of three dimension is the solution to problem of other forms of accessing Agricultural information.

1.2. Motivation

Jigawa State is naturally blessed with large expanse of land, rivers and flood plain resources for production of wide range of crops. The diversity of climate, soils and vegetation across the state provides a conducive environment for sustainable Agriculture. This, indeed explains why nearly 90% of the adult population depends solely on agriculture as a means of livelihood.

This therefore motivates the researcher to place the state in the line of computer simulation. Internet has become a media which can allow displaying Geographical Information in better position and compromise interfaces familiar to user.

The attractive feature of Geographic Information System (GIS) in the present history called three dimensions (3D), especially with help of Google sketch up and Keyhole Markup Language (KML). This also motivates me to enhance the technologies in 3D.

Another motivation is possibility that farmers could try different scenarios on models to disseminate information on Agricultural activities of their farms. For this reason, the study is interested in providing interactive and well developed information dissemination to farmers for better agricultural productivity to people living in rural areas.

The emergence of the World-Wide Web (www) has produced a new computing technology in farming system. This has motivated me in this discipline to develop the web based farming system toward a better crop production.

1.3. Aim and Objectives of the Thesis

The aim is to: Accesses farm information to farmers over a network through the application of 3D visualization technology, with the help of geographic information system (GIS) and digital globes (Google earth) technology. The objectives are to:

a. Develop web based farm information system using 3D visualization technology.

b. Import created 3D models on Google earth.

c. Associate Google earth with Geographic Information System (GIS).

d. Assess information dissemination results of the 3D system side-by-side those of the 2D system

1.4. Methodology

Comparing real world in which people are living and the imaginary worlds designed by computer designers or game designers is usually considered as three-dimensional. As such, the need for 3D in disseminating information is rapidly increasing.

a) The area of study (Jigawa State) will be drawn using GIS. The State map consist of four zones drawn with GIS were local governments of the each zone will be viewed on the Google map through satellite imagery. The portion of the information displayed shows the major plant of that area in 3D format, and the information associated with the plant. With that the farmers will be inform and to decide on the suitability of farm management.

b) Spatial referencing to extract points for the area captured in the satellite imagery that is Jigawa State will also be used as mentioned in (a) to display the farm information of the area in 3D form to allow farmers making plant use decisions.

ArcGIS software was used for this thesis in digitization and modification of Jigawa State map. Google Earth is Earth browser software, which can be used to view satellite imagery of the area. Keyhole Markup Language (KML) file format that can be used to store and display geographic data.

Number of plants models and farm can be created in Sketch up with help of Ruby. Hyper Text Markup Language (HTML) and File Geo-database can be used in developing a web site as well as database of the map system.

1.5. Organization of the Thesis

This thesis has five chapters that concentrate on a web based 3D farm information system for enhanced information dissemination. The general outline is as follows: Chapter One, Introduction, begins with a general discussion of the background of the thesis, statement of the problem, motivation of the study, objectives of the thesis, and methodology of the thesis.

Chapter Two outlines literature review, where in the introduction the concept of 3D was discussed together with GIS and Google earth. In this chapter the study area was described and a review of farm management was discussed. The review of related literature touched the work of some organizations and other project related to this work is carried out.

Chapter Three outlines the design of web-based farm information system, system requirement, system architecture, data flow diagram of the system, design of GIS map, design of 3D farm and 3D farm on Google Earth. Chapter Four is about implementation and discussion which consist of implementation tools and platform, code implementation, testing, results and discussion.

Chapter Five provides summary, conclusion and recommendation for future work

Impact of Christianity on the Cultural Values of Esan People

ABSTRACT

The role of religion particularly the Christian religion in the development process of a society has continued to be a subject of study. Some people think that religion contribute positively to the well-being of the society, while others think it has negative effects. In Esanland, some people that are knowledgeable in the culture of Esan see religion as “Opium of the people”, this simply means that the Christian religion has negative influence on the development and cultural values of Esan people.

This study aim at the impact of Christianity and western culture on the cultural values of Esan people. Particular attention was given to Eguare and Emaudo-Ekpoma, both in Esan West Local Government Area. It also shows that the traditional Esan society was a well ordered society, with a viable social structure, social institutions and cultural values before the advent of Christian religion and western culture.

Historical-analytic method was adopted for the study. Two Hundred respondents were randomly selected within the Local Government Area for the study. Data for the study were collated through the use of self-developed questionnaires.

The study also adopted the theoretical framework of Prudential Personalist Ethics theory of Benedict Ashley who was a 20th Century American theologian and philosopher. The result of the study showed that the impact of Christianity and western culture on the Esan people were both positive and negative.

It is recommended that the Christian witnesses and missionaries should establish relationships of respect and love with those men (to whom they witness), they should acknowledge themselves as members of the group in which they live, and through the various undertakings and affairs of human life, they should share in their social and cultural life.

The study concluded, that long before the advent of Christianity into Esan land, the traditional society has already been structured to reflect socio-cultural status. There were such socio institutions that serve the purposes of Integration and sustenance. Such institutions also promoted the well-being of the society.

TABLE OF CONTENTS

Title Page……………

Certification. ii

Dedication. iii

Acknowledgements. v

Contents. vi

Abstract ix

CHAPTER ONE.. 1

INTRODUCTION.. 1

1.1. Background to the Study. 1

1.2. Statement of the Problem. 8

1.3. Objectives of the Study. 9

1.4. Research Methods. 9

1.5. Location of Study. 12

1.6. Scope of Limitation of Study. 12

1.7. Clarification of Terms. 13

1.7.1. Christianity. 13

1.7.2. Culture. 14

1.7.3. Values. 15

1.7.4. Esan. 16

1.8. Organization of the work. 17

CHAPTER TWO.. 19

LITERATURE REVIEW… 19

2.0. THE ESAN PEOPLE.. 19

2.1. History. 19

2.2. Geographical Location. 34

2.3. Occupation. 36

2.4. Traditional Religion. 37

2.5. Social Structure. 43

2.5.1. The Village Council 44

2.5.2. The Lineage (Idumu) 47

2.5.3. Uelen (Family) 47

2.6. Major Institutions. 50

2.6.1. Marriage. 51

2.6.2. Iruen (A rite of Initiation) 63

CHAPTER THREE.. 66

3.0. CULTURAL VALUES OF ESAN PEOPLE.. 66

3.1. Culture: A Definition. 66

3.2. Cultural Values of Esan. 70

3.2.1. Communalism.. 71

3.2.2. Respect for Elders. 73

3.2.3. Chastity. 75

3.2.4. Sacred Days. 76

3.2.5. Festivals. 77

3.2.6. Music. 80

3.2.7. Life After Death. 81

3.2.8. Sanctity of Life. 84

3.2.9. Unity. 85

3.2.10. Name. 88

3.2.11. Faith Healing. 90

3.2.12. Language. 93

3.2.13. Mode of Dressing. 94

3.2.14. Hair Styles. 94

3.3. Cultural Evolution in Esan. 97

3.4. Economy Evolution in Esan. 98

3.5. Culture and Religion. 101

CHAPTER FOUR.. 106

4.0. CHRISTIAN RELIGION IN ESAN.. 106

4.1. The Advent of Christianity in Africa. 106

4.2. Advent of Christianity in Esanland. 111

4.3. The Spread of Christianity in Esan. 114

4.4. Conflicts between Christianity and Esan Cultural Values. 119

4.4.1. Reasons for the Conflicts. 120

4.4.2. Inculturation: A Solution to the Conflicts. 121

4.5. Impact of Christian Religion on Esan Cultural Values. 130

4.5.1. Christianity as it Affects Cultural Values. 131

4.5.1.1. Social Values. 131

4.5.2. Religious Values. 145

4.5.3. Educational Values. 153

4.5.4. Economic Value. 156

4.5.5. Christianity and Development in Esan. 158

4.5.6. Religious Development 159

4.5.7. Social Development 160

4.5.8. Educational Development 161

4.5.9. Economic Development 161

CHAPTER FIVE.. 164

5.1. EVALUATION.. 164

5.2. Summary. 173

5.3. Findings. 175

5.4. Contributions to Knowledge. 176

5.5. Conclusion. 176

5.6. Recommendations. 177

Works Cited. 180

APPENDICES. 188

CHAPTER ONE

INTRODUCTION

1.1 Background to the Study

Before the advent of Christianity into Esanland in the first decade of the twentieth century, the Esan society was a well organised society with a viable social structure, social institutions and cultural values. The Esan people occupy the Edo Central Senatorial District of Edo State Nigeria.

It is made up of five (5) Local Government Areas viz:- Esan West, Esan Central, Esan North-East, Esan North-West and Igueben, with Ekpoma, Irrua, Uromi, Ubiaja and Igueben as Headquarters respectively. It is made up of thirty (30) clans; Ekpoma, Egoro, Opoji, Irua, Ewu, Uromi, Ugoha, Ubiaja, Ukhuesan, Emu, Ohodua, Ewatto, Ewosa, Ewohimi, Ekpon, Ebelle, Okalo, Amahor, Iria, Ugun, Ujiagba, Ogwa, Igueben, Ugbegun, Idoa, Uzen, Orowa, Udo, Onogholo and Ukhun (Okogie 29).

The people had a religion with certain basic beliefs similar to those of the Christian religion. They believed in an Almighty or -Overall God (Osenobua) to whom worship was given through the minor communal household gods known as ebo (Donatus Akhilomen 12).

Ebo, divinities or gods who were worshipped by the traditional Esan society were only approached as intermediaries between Osenobulua, Supreme Being and them (the people). ‘They act for Him in the theocratic government of the world’ (Alli 45). As they,s the ebo were brought forth by Osenobulua, Supreme Being Himself, they have no absolute existence or authority.

They were appointed and are commissioned by him to serve a purpose. Hence, their authority and power is derived from Him and delegated by Him. This is why in Esan, every act of worship or ritual has an ultimate reference to Osenobulua the Supreme Being who in turn sanctions it.

Apart from this, the traditional Esan society cherished their cultural values such as family unit or communalism, respect for elders and constituted authority, ancestral worship, to mention but a few. All of these were strictly adhered to as their guiding principles. This was the position in Esan when Christianity and western culture began to make inroads.

The coming of Christianity with its civilizing influence has greatly affected the cultural life of Esan people. This impact has been greatly felt in the economic, political, educational, medical and in the overall cultural life of the people. In essence, it could be said that the presence of the Christian Church stimulated the socio-cultural development of the Esan people.

These are, in spite of the deficiencies of the early Christian missionaries (who could not distinguish between the culture of Europe and the principles of Christianity). Those aspects of the Esan cultural values that were not in the best interest of the people (according to the missionaries) had to give way or abolished.

One could say here, that, it might be one of the reasons why in the mid-nineteen seventies, there was a constant call for the revival of culture in Nigeria. Every ethnic group in Nigeria was encouraged and motivated to revive the apparently dormant cultural values of its peoples.

General Yakubu Gowon, a former Head of State, said at the fourth National Festival of Arts in 1975, that some people had wondered whether the aim of cultural revival was to abandon all modern amenities and conveniences and return to pre-historic times, or whether it was to raise a new religion which would replace the existing ones.

He maintained that such views were wrong since Cultural Revolution is not synonymous with cultural bigotry (Kato 4). Nwafor Nduka, argues that Cultural Revolution or emancipation does not mean a call to return to the past. What he is saying is that there are much of our past that are no longer relevant to the society today and therefore, should be discarded (vi), but those that are relevant should be revived and reserved.

This is because much of our past is no longer relevant to the society today. Matthew Omo-Ojugo, agrees with Nduka when he said that, Edo State and Nigeria have excellent cultural values which should be revived for the survival of our society and for our people to compete meaningfully wzith other societies in the world in the 21st century and beyond.

He added that there are, however, some traditional and cultural traits which must be discarded because they are no longer relevant in civilized societies (2).

According to Nduka, “we are culturally under-developed; therefore our appreciation of beauty is mundane and almost naive. We instinctively like or dislike what we see. The profound and the intriguing put us off” (7-10). This implies that our cultural values still exhibits the disabilities of adolescents, for, as yet, it has not assumed is final distinctive statures. Therefore, there is need of re-assessment, re-evaluation and development.

If Cultural Revolution is neither a return to the past, nor an introduction of another new religion, then what is it? According to Adrian Hastings, it means “rediscovering the wisdom of the ancestors, revaluing their ceremonies, reawakening their names, renewing their own language” (43).

Nduka, opines that, it is; “a more discriminating, in culturing of foreign cultural elements with the indigenous cultural heritage, instead of just selling our cultural birthright for a mess of Western Cultural Pottage” (vi). In a nut shell, culture is an aggregate concept fundamentally characterized by the distinctive spirit, way of life, device for living and attainments of the people.

Olive Ponting opines that culture determines how social institutions cultivate and impose behaviour that is communally transmitted from one generation to another. Culture is versatile and includes both material and non-material objects and concepts.

It entails the totality of a people’s norms, values, beliefs, codes of socially acceptable conducts, mode of life, religion, philosophy and ideology. It also includes communal informal education and technology (430).

If the above statements are correct, then cultural revival are noble intentions that should be pursued vigorously. Africans generally and Esan in particular, has every reason to seek the revival of their cultural values since their philosophy, value, systems, identity, languages and indeed, all of their cultural values had apparently been threatened with extinction.

They had been humiliated, exploited, oppressed, and denied self-determination (Kato 5), and this also applied to Esan people. They had become strangers even in their own land as a result of colonialism by the Europeans.

The white men had conquered them with their culture, and so anything that gave Africans a sign of relief was welcome, while anything that subjected them to the imperialists was resisted. That was why, what seems to be good was marred by those who conducted the crusade against Christianity, “the White man’s religion”,and directed their energies to the persecution of Christians.

The Christian religion was rightly or wrongly identified with imperial Europe, therefore, all appeared culturally alienating. Those who felt that Christianity was detrimental to the cultural values of the people wanted a cultural revival without prejudice to the schools, medical facilities, architectural designs, and indeed the benefits of science and technology from Europe.

Culture has been defined as the total life style of people. According to Edward Tylor, culture is; ‘that complex whole which includes knowledge, belief, art, moral, law, custom, and any other capabilities and habits acquired by man as a member of society’(21).

Also, culture comprises ideology, including ideas, beliefs and values, technology including skills, crafts, arts and material items; and social organization- including rules, regulations and roles (Hobbs and Blank 84).

In this study, we shall present the cultural setting of the Esan society before the coming of the Christian religion, of particular interest on the fact that the society was a religious one and given these ideas about cultural values, we observed a situation of cultural clash between the Africans and the Europeans at the coming of the Christian religion.

A change in any aspect of a cultural value affects other aspects. This is more evident in connection with religion which has been regarded as the heart of culture. The Esan people, however, already had values that they would not give up. They liked some of the things Christianity taught and did, but it was not possible to throw away everything they had so cherished before the coming of Christianity.

The result was a conflict of values. Conflict between the traditional Esan values and the Western Christian values. The westerners insisted on the superiority of their culture and religion and demanded a complete abandonment of the traditional Esan values such as their mode of worship, polygamy, communalism et cetera. This was not acceptable to the Esan people.

Christians were persecuted, and on many occasions taken to court at Ubiaja (interview with Chief Samuel Omofumaat Ukpoke-Uhiele on June 5, 2016). The Esan people who accepted the Christian religion, did so mainly because of the benefits they would get from the civilizing influence of Europe. Their conversion was superficial; there was no deep commitment to the Christian religion.

However their life-style was bound to change. Those cultural practices that were not in agreement with the new religion had to be completely dropped or modified (Ayandele 243). For instance, people were made to change their traditional names which expresses their philosophy and religion to Western names at conversion even without knowing the meanings.

Those who answered traditional names on conversion to Christianity, changed them to Christian names particularly at baptism. Some who even answered meaningful traditional names considered a change necessary to march with the demands of the new religion.

This trend almost destroyed the value in names as people abandoned meaningful names that expressed their cultural philosophy, religion amongst others. (interview with Omofuma at Ukpoke, June 5, 2016).

Some Esan people however resisted changing their names and have ever since not been any less Christians. A good example is the researcher whose father did not change her tradition name at baptism. Till today, she bears her traditional name. Apart from these, the Esan people’s cherished culture such as respect for elders, communal life, ancestral worship amongst others were distorted in the name of western civilization which was encouraged by the Christian faith.

Service Elman, affirms that, “the human race is proceeding toward greater and greater homogeneity-racially, culturally, and linguistically” (xiii). Regrettably, Elman noted that, through this process of homogeneity, many of the world’s ancient cultural values had disappeared.

Elman continued that, while some cultural values are simply dying out or being exterminated, some are undergoing radical changes as they become involved in various kinds of functional relationships with expanding industrial civilization, and others are being ethnically assimilated (xiii).

This is sad observation and it is not in the best interest of Africans who are endowed with their God-given cultural values. Some anthropologists have also expressed fear over such findings, such that the disappearance of cultural values has brought a great loss to human knowledge, art, history and science (xiii).

Is it in any wonder therefore, that, a people whose culture is threatened with extermination would seek means of protecting their cultures? They need to be sympathised with. Their predicament is caused in most cases by “the ignorance and sometimes the cruelty with which ‘civilized’ peoples had treated them” (xiii). This situation could be the sad story of the Esan people.

They have complained about the apparent extinction of their cultural values including their language. Omo-Ojugo, “Time News” states; “A language is endangered when it is on a path toward extinction. A language is in danger when its speakers cease to use it in an increasingly reduced number of communicative domains and cease to pass it on from one generation to the next.

That is, there are no new speakers, adult or children. In Esan today, there are many literate parents, who deliberately use the English language as the only means of communication between themselves and their children at home.

Even among illiterate and semi-literate parents, it is becoming something of ‘fashion’ to use adulterated English, Nigerian Pidgin English or a mixture of both Esan and English or Esan and Nigerian Pidgin English, reflecting an apparent diglossie situation in a society that otherwise was homogenous linguistically” (81).

There is need for Esan people to revive their language so that Esan language will not go into extinction. In the face of such apparent extinction, what could be the justification of the Esan society playing host to Christianity for these number of years?

Could it be that the Christian religion has not done what it was supposed to do in the land? Is it also true that the total cultural values of the Esan people have been threatened with extinction? These and other related issues shall be examined in the course of our discussion.

In this work, we shall present some cultural values of Esan people as it has been affected both negatively and positively by Christianity and western culture. This thesis, therefore examines the impact of Christianity and Western culture on cultural values of Esan, the conflicts between Christianity and culture in Esanland and then proffer possible solutions to the conflict so that future Christian evangelists do not make the same mistake of the early missionaries.

1.1. Statement of the Problem

The common opinion by some knowledgeable and highly placed men and women in Esan is that the Christian religion is a mere “opium of the people”. Karl Marx used this expression to argue that religion functions as an instrument of maintaining stratification systems in society and of keeping the masses under subjection to a few privileged rich. By this position they contend that the Christian religion is detrimental to the development process of the Esan society.

The introduction of Christianity to Esanland was viewed as a threat to the old order and was therefore strongly resisted by the Chief Priests of the various traditional religions who were supported by village elders. It is not surprising that, most of the pioneer Christians in Esanland were persecuted in their attempt to win converts (Kio-Apori 63).

The implication of this position is that, the Christian religion has no positive effect that it can offer to the cultural values of the Esan people. Such a negative view of the Christian religion in Esanland fails to recognize the contribution that Christianity has made in the areas of education, commerce, health, housing, politics, economy, social services, among others.

These improvement have been a direct result of the coming of the Christian religion with Western civilization and culture. Instead of recognising this, these antagonists contend that in spite of the number of years that Christianity came to the land, its impact has been very minimal on the cultural life of the Esan people.

If these submissions are proved to be correct, they will have devastating effects on the Christian religion in Esan society. It is the burden of this essay therefore, to assess the impact of Christianity and Western culture on the Cultural values of Esan people.

This task is carried out with the consciousness that whereas there is a difference between the Christian Religion and Western culture and civilization, on one hand, it is impossible to separate one from the other in the context of our present discussion. The reason is that Christian religion came into Esan on the wings of Western civilization and colonialism.

1.2. Objectives of the Study

The overall aim of this study is to critically examine the impact of Christianity on the cultural Values of Esan people. The specific objectives of the study, therefore, are to:

(a) examine the negative and positive impact of Christian religion on the cultural values of the Esan people;

(b). establish that the traditional Esan society was a well ordered, with a viable social structure, social institutions and cultural values before the advent of Christian religion and Western Culture;

(c). prove that Esan people are not atheists: they were not irreligious, that religion guided their total life before the coming of Christian religion; and

(d). make useful recommendations in addressing the conflict between Christian teachings and Esan cultural values.

1.3. Research Methods

This study relies on primary and secondary sources of information. It made use of historical and evaluative methods of research.

For the primary sources, copies of questionnaire were administered to respondents and key informant interview (K.I.I) was conducted among Esan people in order to get up to date data. The instrument used was the random sampling method.

For the secondary sources, relevant materials such as journals, articles, books and other resources were consulted. The lack of ample literature in the subject area has made key informant interview and the use of questionnaire compelling and inevitable.

It is expected that an objective historical and evaluative study of this kind would give fresh perspectives on the impact of Christianity and western culture on the cultural values of Esan people.

Theoretically, this study adopts the Prudential Personalist Ethics theory propounded by Benedict Ashley, which is basically teleological in nature, but different from emotivism and voluntarism or deontologism. “Prudential Personalist Ethics stresses that the “ends’’ of human action are always persons and the community of interrelated persons responding to each other” (173).

This ethical model is qualified Prudential because this indicates the practical goal-seeking character and even the situational or contextual character of this ethics. Personalism advocates that morality is not solely a matter of obeying abstract rules, but to intelligently seek appropriate, concrete behavior by which an individual achieves personal goals.

According to Anthony Flannery, “the value of the law or rule is not denied, but the emphasis is on the fact that what makes such law obligatory is their helpfulness in guiding prudential decisions to successful goal-achievement’’ (955). The goals that are morally right for a human being are such that are determined by the nature of the human person and human action.

Thus, this Prudential Personalist model of ethics is not based on intuitionism or idealism of any sort since its principles are derived from human historical experience, especially the experience of perfect human actualization (John Onimawhawo “Youths and Moral”16).

Ashley claims that this ethics is called ‘’personalism’’ because it evaluates human goals and the means to these goals in terms of the self actualisation or fulfillment of the human person in the community (173). In Prudential Personalism, therefore, the consequences of any human act must be assessed not in terms of immediate pains and pleasures or even in terms of other immediate qualitative values but must have bearing on the actualization of the human person in relation to other persons (17).

In the debate on ethical issues, that ethical decisions are always taken within the context of some value system is an obvious fact. In considering any ethical debate within a historical-theological context, we need a paradigm which will help us make our conclusions not only consistent with historical-theological norms, but also that which takes into account the value systems of others.

This is why this work adopts Prudential Personalism ethical model in evaluating the impact of Christianity and western culture on the cultural values of Esan people. It is an ethical model whose logic goes beyond those who take their stand on absolute principles or authoritative laws and those who argue only for pragmatic solutions.

Therefore it is when Prudential Personalism logic is employed that we shall be able to achieve a synthesis of extreme positions on Christian religion and western culture on cultural values of Esan people.

In this study, a historical-analytic approach based on Prudential Personalism ethical model was adopted. With the historical approached, we were able to discourse, explain and analyze critically the negative and positive impact of Christianity and western culture on the cultural values of Esan people.

The evaluative method of research was employed to achieve the overall aim and specific objectives of this study. The study, therefore, examined the impact of Christianity and western culture on cultural values of Esan people, using the Prudential Personalist Ethics theoretical framework to ascertain the significance of the solution proffered to harmonise the two cultural differences.

This theory was considered basically because of the moral and cultural values highlighted in the work. It is an ethical model whose logic goes beyond abstract rules; it is to intelligently seek appropriate, concrete behaviours by which human personal goals are achieved.

1.4. Location of Study

Esan is made up of 30 clans and it is located in the northern part of the forest regions. It occupies longitude 5o 301 7o 301 and latitude 5o 301 north and 7o 301East of Benin (Olayinka 12-33). The area is bounded in the north and northeast by Akoko-Edo Local Government Area; on the south by Ika Local Government Area; on the west by Owan Local Government Area.

It occupies an area of about 2,987.52 kms (Okogie 2).Before the colonial period, there were rigidly fixed geographical boundaries. The areas expanded and contributed under various political and social-economic circumstances which reflected possible strength and weaknesses of the period.

The boundaries were often along roads and demarcated by geographical and environmental features such as hills, rivers and streams. Iyala or moat demarcated an in-group from out-group of Esan settlers (Okoduwa 1).

1.5. Scope of Limitation of Study

This study is poised to explore the impact of the Christian religion and western culture on the cultural values of the Esan people. The area of concentration is basically in these five (5) Local Government Areas viz:-Esan West, Esan Central, Esan North-East, Esan North-West and Igueben Local Government Areas, all in Edo State.

These areas have been selected by the writer because the writer is well abreast with these areas and quite conversant with the custom and cultural values of these areas.

In the course of the study, the researcher had financial and transportation constraints due to the deplorable situation of the roads in Esanland and such could not move round all the Local Government Areas; therefore, could not access those to be interviewed in such areas personally except through the questionnaires distributed with the assistance of some members of my church. Also managing my family as a widow with my job and the state of my health was quite demanding during the course of this study.

1.6. Clarification of Terms

Some key terms will be defined and explained for purpose of clarity. They include: Christianity, Culture, Value and Esan.

1.6.1. Christianity

Christianity is an Abrahamic monotheist religion based on the life and teachings of Jesus Christ who served as the focal point of the Christian faith. It is the world’s largest religion with over 2.4 billion followers or 33% of the global population, known as Christians.

It is one of the most popular religions through the western world. Members of the religion are called Christians. It is a monotheistic religion, meaning it has only one God (Encyclopedia; Monotheistic Religion.

Web 5th Febuary 2016). It is also the act of voluntarily accepting Jesus Christ as personal Lord and saviour and as such become his disciple who learns and behaves like him. In respect of this study, Christianity shall be referred to as religious activities carried out by religious people with the aim of proclaiming the gospel of Jesus Christ.

As an adjunct to the above considered definition; I have put forward my own definition of Christianity. Christianity is a term that refers to the beliefs espoused by various group of churches that derive their doctrines from the teaching of Jesus Christ and His apostles.

The most important thing for Christians is love and charity towards all manners of men. Christians group sometimes differ in traditions that come to surround their practices of faith. The expression of the basic tenets as indicated above is a unifying factor that shapes the outlook of Christians.

1.7.2. Culture

From the beginning of a person’s life to when he goes to the grave he is regulated by certain creations of man called culture. In spite of the fact that all anthropologists’ agree on the importance of the concept culture, yet no particular definition has a universal acceptable definition.

Different definitions are given depending on the persuasion and perspective of the proponent. It must be noted here that men of letters have usually adopted a descriptive and practical approach in their effort to define culture. According to Paul Mussen, culture is; “a body of stored knowledge, characteristic ways of thinking and feeling, attitudes, goals and ideas” (Mussen 62).

Edward Taylor defined it as “that complex whole which includes knowledge, belief, art, morals, law, custom, and any other capabilities and habits acquired by man as a member of society” (21). John Fichter a sociologist has also concisely defined culture as: “the total configuration of institutions that the people in society share in common” (270). Onyerisara Ukeje summarized all the above mentioned definitions as an all-embrasive sort of descriptive definition when he said:

In general therefore, culture may be defined as the fabric of ideas, beliefs, skill, tools aesthetic objects, methods of thinking, of eating and of talking as well as customs and institutions into which each member of the society is born. In short it includes the way each individual makes a living the music he plays, celebrations and festivals, modes of communication and transportation, the house we live in and the food we eat. (3)

From the definitions we have attempted from above, it is very clear that culture is descriptive and complex concept with wide-ranging and comprehensive connotations and significance. It is also clear that culture refers to the way of life of a people-away of life that reflects their distinctive genius and spirit,

their fundamental character or ethos, their values orientations, world-view, institutions and achievements in the various fields of human endeavors-Legal and literary, artistic and scientific, religious, philosophical and technological (Leonard Broom and Philip Selznick 50-51). Therefore, culture is an aggregate concept fundamentally characterized by the distinctive spirit, way of life, device for living and attainment of people.

1.7.3. Values

Values are important and lasting beliefs or ideas shared by the members of the society about what is good. Levi Ezeaku defines value as norms which refers to a set of ideas and of opinion commonly held against which member’s actions and achievements are measured and evaluated.

It is these that determine what is socially accepted (89). Every human society has a set of moral issues, what is good or bad, right or wrong. These notions, which have a great deal of influence on the conduct of the members of that particular society are usually based upon some recognized authority whose sanctions are accepted and obeyed.

To some, moral values, sanctions or ethics are derived from human society (Idowu 144). To others, common sense is the source of supernatural source. Whatever the source, moral sanctions have power to compel obedience (146, 152). African society are no exception although, their moral values are not uniform throughout the land.

The moral values or codes of behavior are designed to promote good, right and healthy societal living (Dzurgba 60). They are to regulate the behavioral lives of people individually and collectively for peace, concord and social harmony.

The African traditionalist believes that the society belongs to the deity and the various divinities have been given certain duties to perform among their people. They are the final authority over all laws and moral codes regulating such society. He punishes evil not only here on earth but in hereafter as well.

To avoid this punishment, the African traditionalists are required to live an ideal life here on earth to secure a sure good home hereafter. Ideal life includes honesty, kindness, truthfulness, chastity, loyalty, kindness, humility, obedience, devotion, respect, generosity, hospitality, justice and such other virtues.

One of the agents of cultural values are parents and elders. They are strictly charged with the up keep of the society, to govern their homes and society at large. It is their obligatory responsibility to keep orders and sanity in the society. They are the guardians of the laws, rules, and order regulating the society; hence they are greatly reverenced (Parinder 179). Others are ancestors, divinities and personal names.

However, due to new African modernism generating from western Christianity, civilization and political emancipation a lot of the valuable cultural values are either reinterpreted or set aside with total ignominy. Prominent conversational acts, taboos and rules of the past are no longer regarded today. However, from historical experiences, and for ideal ethical societies, the African (Esan) people have to rediscover their wealth or values to improve upon the present decadent society.

1.7.4. Esan

The word ‘Esan’ is the shortened form of the original Edo phrase “Esanfua” (which means they jumped off’ or they fled or escaped) (Omokhodion 1). It is generally believed that due to the oppressive measures put in place by the Oba of Benin in the 14th century AD, the people, who later came to settle in this part of the State ‘escaped’ or literally put, ‘jumped out’ from Benin kingdom and fled into the jungle. Today, those who descended from them are called the Esan people.

Geographically, Esan is located on a plateau of about 134 miles above the sea level. This Esan plateau rises from river Orhiomo in Esan East Local Government Area and it is drained by river Utor, Orie, Obhu and Oha, including Iyagun stream, Utobo stream and a few other minor streams. The group of people referred to today as Esans can be found to the North-East of Benin.

These people form the bulk of the people in the former Esan division of the Benin province. On the North-West and North of Ishan land, there is the Ivbiosakan land (owan) and Etsako Divisons while on the South and South-East you have the Western Ibo, the Agbor and Asaba people.

On the East, it is boarded by the River Niger and Igala people (Omokhodion 1). Today Esan division is divided into five Local Government Areas, namely; Esan West, Esan Central, Esan North East, Esan East and Igueben Local Government Areas.

The Esans possess a well-defined social political structure in which the family plays vital roles as its unit generates dual social and moral systems (Akhilomen 12).Akhilomen contributed that, Esans as a people had a democratic and egalitarian system of government before the advent of the Europeans. The families form the bases for social unity and thereby exerts great influence on its members.

Members consult one another before major decisions was taken. The Onogie directs the political wheel of the community, while the Odionwele functions at the level of Idumu or quarter to ensure that administration is run smoothly (12).

1.7. Organization of the work

This study is divided into five Chapters. The first chapter is the introductory chapter. It deals with the statement of the problem of the research, the aim and objectives of the study, Research methodology, location of the study, scope and limitations of study, clarification of terms, and organization of works.

Chapter two gives the review of related literature of some Scholars on Esan people history of origin, occupations, traditional religion, social structure and major institutions of the Esans. With these, one was able to appreciate the organisation of the traditional Esan society. In Chapter three, we examine the cultural values in Esanland.

In this regard, a brief definition of the concept of culture was given. We also examine how the economy and religion of the Esan evolved. This was to show that, the Esan society was richly endowed with values that enhanced its integrating and survival before the advent of Christianity into the land.

A brief history of the advent of Christianity into Africa, and Esan is given in Chapter four. The Chapter also focuses on the spread of Christianity in the land of Esan, such advent and spread were not without conflicts.as is the case when there is clash of two forces, there was a conflict between the Christian church and the cultural values of the Esan people.

This is carefully evaluated in this chapter. The impact of the Christian religion on the cultural values of the Esan people was also discussed. Each cultural value is carefully examined to see how Christianity has affected it.

A further look is also taken at what role the Christian religion has played in the religious, social, educational, and economic development of the Esan people. Chapter five focuses on the evaluation, summary, findings, contributions to knowledge, conclusion and recommendations.

ABSTRACT

The study was conducted for images of mathematics stakeholders in teaching and learning mathematics at secondary schools. For the purpose of the study, the research employs various data collection techniques that includes questionnaire conducted on nineteen (19) mathematics teachers, nineteen (19) parents and two hundred and seventeen (217) students of secondary schools.

Teachers, students and parents in the sample schools were administered with questionnaire. Result of the study indicated that mathematics teachers should try to motivate and build up the self confidence of pupils/students and convince them that everybody is bale to be good at mathematics.

One of the respondents suggested that we should admit that mathematics is difficult but then prepares students to take it on as a challenge. In addition, several of the respondents stressed the importance of relating mathematics to daily life experiences or activities and teaching it as a practical tool.

They also suggested that as an effective strategy, students should be allowed to explore and sole problems themselves. A mathematics teacher should not be somebody who just stands there and lectures, but he should teach from the very beginning, how it can be applied to the real world and to see that it excites the students and teacher as well.

TABLE OF CONTENTS

Title Page —————————————————————————————————i
Approval Page ——————————————————————————————- ii
Dedication ———————————————————————————————– iii
Acknowledgement ————————————————————————————– iv
Table of content —————————————————————————————— v
List of Tables —————————————————————————————— viii
Abstract ————————————————————————————————– ix
CHAPTER ONE
1.1 Background of the Study ———————————————————————- 1
1.2 Statement of The Problems ——————————————————————– 2
1.3 Objectives of the Study ———————————————————————— 4
1.4 Research Questions —————————————————————————– 4
1.5 Research Hypothesis ————————————————————————— 4
1.6 Significance for the Study ——————————————————————— 5
1.7 Scope and Delimitation of the Study ——————————————————— 5
1.8 Operational Definition of Terms ————————————————————– 6
CHAPTER TWO
2.1 Introduction ————————————————————————————–7
2.2 History of Mathematic Teaching in Nigerian Schools ————————————-8
2.3 Research Findings on Images Of Mathematics Among Students And Teachers ——9
2.3.1 Research Finding on Attitudes Towards Mathematics ————————————10
2.3.2 Research Finding on Belief About Mathematics ——————————————11
2.3.3. Research Finding on Mathematics Myths ————————————————–12
2.3.4 Research Finding on Conception or View About Mathematics ————————-13
2.3.5 Other Image Related Research —————————————————————14
2.3.5.1 Women’s View of Mathematics————————————————————–15
2.3.5.2 Pupil’s View of Mathematics—————————————————————–16
2.4 Research Finding on Factors Influencing Image of Mathematics ———————-17
2.4.1 Leaner’s Related Factors ———————————————————————-18
2.4.1.1 Belief About the Self ————————————————————————–19
2
2.4.1.2.1 Leaner’s Helplessness and Mastery Orientation—————————————–20
2.4.1.3 Expectancy X Value Theory —————————————————————-21
2.4.1.4 Attribution Theory of Achievement motivation and emotion —————————22
2.4.1.5 Self-attribution Theory and Gender Difference ——————————————–23
2.4.2.1 Environment Related Factors Parental Influence ——————————————25
2.4.2.2 School Experience —————————————————————————–26
2.4.2.3 Teacher Influence ——————————————————————————27
CHAPTER THREE
3.1 Introduction ————————————————————————————28
3.2 Research Design——————————————————————————-29
3.3 Population of the Study ———————————————————————-30
3.4 Sample and Sampling Techniques ———————————————————31
3.5 Instrumentation——————————————————————————–31
3.5.1 Validity of the Instrument——————————————————————-31
3.5.2 Pilot Study ————————————————————————————31
3.5.3 Reliability of the Instrument —————————————————————32
3.6 Administration of the Instrument ———————————————————-33
3.7 Procedure for Data Collection ————————————————————-34
3.8 Procedure for Data Analysis —————————————————————35
CHAPTER FOUR
4.1 Introduction———————————————————————————–36
4.2 Data Presentation and Analysis ————————————————————37
CHAPTER FIVE
5.1 Introduction ———————————————————————————–38
5.2 Summary ————————————————————————————–39
5.3 Conclusion ————————————————————————————40
5.4 Recommendation —————————————————————————–41
5.5 Contribution to Knowledge —————————————————————–41
5.6 Suggestion for Further Studies ————————————————————-42
References I———————————————————————————–43
Appendix I————————————————————————————–44
3
Appendix II————————————————————————————-45
Appendix III————————————————————————————46

CHAPTER ONE

1.1 Background to the Study

INTRODCTION

The word “Mathematics comes from the Greek word (Matherna) meaning science, knowledge or learning and it also derived from other word (mathematiko’s) meaning found of learning” (Simonson & Gouvea 2007).

Agwagah (2008) noted that mathematics is often defined as the study of topics such as quantity, structure, space and change. These topics provide the major subdivision of mathematics into: Arithmetic, Algebra, Geometry and Analysis.

These major disciplines within mathematics arose out of the need to do calculations in commerce among others. The study of mathematics will form in the students the habit of clarity brevity, accuracy, precision and certainty in expression.

According to Osofechinti in Odili (2006),the importance of mathematics to individuals in their daily undertaking is so enormous that the knowledge of mathematics is an indispensable tools for a successful and balanced human existence on earth.

Mathematics helps man to sharpen his understanding and definition of religious concepts. Such concepts are eternity, heaven, spirit, life, power, salvation, wisdom, strength, light, hope, faith, righteousness, glory, blessing, truth, grace, peace, neighbor, sun and death can each be defined with mathematical rigors and precisions (Osah-Ogulu & Odili, 2000).

One of the greatest problems faced by mathematics teachers, school principals, administrators and even parents over the years is the teaching and learning of mathematics at the secondary schools.

However, for some years back, mathematicians had shown a lot of interest in trying to diagnoses the causes of the continues poor images of mathematics stakeholders and not only that suggest and administer. “Treatment” in order to air the illness.

In view of this fact, it is widely claimed in the liberator that, negative images and myths of mathematics are widespread among the public. The majority of the people today are scared of mathematics and feel powerless in the presence of mathematics ideas. Many people’s image towards mathematics represent mathematics negatively, such that mathematics is perceived to be “difficult, abstract, and in many cultures, largely masculine”.

Others describe mathematics as a “set, constant, bounded, enclosed and uncreative or a timed-test”.

There are propositions and speculations about the causes leading to the claimed negative and unpopular image of mathematics.

Swell (1981) propose that “teachers attitudes, the family of much mathematics teaching, the seeming lack of relevance of mathematics top every days contexts, fear of the subject literacy problems gaps in schooling and parental expectations”.

Inspectorates are the few possible causes, this research attempts to find out the images of mathematics stakeholders in teaching and learning mathematics in Sokoto state.

The Nigerian economy requires mathematics that can effectively put science and technology in the for-front of nation building . Mathematics is the precursor and the queen, of science and technology, and the indispensable single element in the modern societal development “mathematics education is therefore indispensable in nation building”. Since the introduction of formal education in Nigeria, mathematics education has gone through several developments.

From the era of formal arithmetic, algebra, geometric and the likes through the period of traditional mathematics controversy to the present everyday general mathematics. These changes have always been necessitated by realization of the role mathematics should play in the nation’s scientific and technological development as well as responses to societal needs and demands (Aguele, 2004).

The world today applies regarded as a global village characterized by computer and information technology. This age has brought with it lots of sophistication in mathematics and be able to sustained these developments.

Today, it is a reality that it is the creation, mastery and utilization of modern science and technology that basically distinguishes the so-called developing from the developed nation of the world. That is to say that the standard of living of a nation is dependent on the level of science and technology of that nation.

While science is the bedrock that provides the spring-board for the growth of technology, mathematics is the fate and key to the sciences. In other words, it is the level of mathematics that determines the level of the science and technological component of nations is mathematics.

Therefore, mathematics plays a vital role in nation building, mathematics as observed by Abiodun (1997) is the major tool available for formulating theories in the sciences as in other fields. It is used in explaining observation and experiments in other fields of inquiry.

Adeyebge (1987) observed earlier that there is concept to explain its own concepts, theories or models. Mathematics is a science of the methods by which quantities sought are deducible from others known or supposed.

Thus, anyone who neglects mathematics may not be able to go far in sciences and infact other things of the world. Practical work and observations of nature are the main source of scientific discoveries. Mathematical methods play a very important role in this. Mathematical methods lie in the foundation of physics, mechanics, engineering, economics, chemistry and soon.

According to Bermant in Harbor-Peters (2000), an important features of the application of mathematics to the science is that, it enables its to make scientific prediction that are to draw on the basis of logic and with the aid of mathematical methods, correct conclusions whose agreements with reality is then confirmed by experience, experiment and practice, thus, mathematics is bed rock of sciences and technology, which is the springboard of national development.

Mathematics today is having an enormous impact on science and society. The influence may be silent and appear hidden but has shaped our world in many ways. Mathematical ideas have helped make possible the revolution in electronics which has transformed the way we think and live today. The information technology (IT) of today has transformed the world into a global village.

The important of mathematics in everyday life activities is not doubted, at home for instance, we have to check the water rate bills, measure quality of food that will satisfy the number in the family to avoid wastage. Also in division of labour among members of the family that is going of lands to sweep.

In hospital, ages of patient’s body weight and temperature are often measure in used by doctors to prescribe quality of medicine to be taken. In the market are used the knowledge of mathematics to calculation to calculate how much is to be paid for goods purchased and how much change if any one collects.

Even in digging a grave the corpse has to be measured to determine the size of the grave. A builder knowledge of shapes and solids of measurement to design and build the house.

Once we start working for other people, meeting other people, or traveling, we have to be able to tell the time. If we are traveling by car we might like to estimate our time of arrival, so we must know what speed means. There are almost limitless applications of mathematics in daily life activities.

Mathematics is an abstract subject, a different language is used to convey elders and we use symbols to explain concepts often the students are not sufficiently conversant with the language and concept we are trying to explain many topics in mathematics rely on the understanding of previous topics (It is a logical subject) a gap in the knowledge of a particular student can make it impossible for him to learn future topics and this leads to failure and frustration and often hatred for the subject.

How can student be convinced that the mathematics they are learning is useful as many people dismiss the problem of mathematics teachers by using what they don’t have today very much just teach the students how to add, subtract, multiply and divided.

This however, is far from the truth, if a student does not reach a satisfactory understanding of the basic mathematical concepts there is little chance area of the subj. Mathematics can be function Therefore, must be taught in a logical order so that student can achieve understanding and enjoy mathematics.

Against this background, this research aims to make a systematic enquiry into the images of mathematics stakeholders in teaching and learning and the possible causal factor of affluence on the formation of those images.

The term image is define as some kind of mental representation (not necessarily visual) of something originated from part experiences as well as associated beliefs attitudes and conception. Since an image original from part experience, it comprise both cognitive and affective dimensions. Cognitively it relates to a person’s knowledge, belief and other cognitive representation.

Affectively, it is associated with a persons attitudes, feeling, and emotions,. Thus the term image of mathematics is conceptualized as a mental representation or view of mathematics presumably constructed as a result of social experiences, medaled through school, parents, peer or mass media.

This terms is also understood broadly to include al visual, verbal representation, metaphorical image and associations beliefs attitudes and feeling related to mathematics and mathematic learning experience. Therefore, the main aim of this study is to study is to explore and identify the range of images beliefs and attitudes toward mathematics as it is perceived by the public (mainly adults).

1.2 Statement of the Problem

The study aims to make a systematic enquiry into the images of mathematic stakeholder and the possible causal influence on the formation of these images among stakeholders in secondary schools in Sokoto state.

Mathematics as a compulsory subject in Nigeria with vigorous problems ranging from teaching learning application on the area of mathematics teaching teachers undergo difficulty especially on the area students fail the relevance and of both

teachers and teaching material this tender the effective teaching of mathematics on the problems of teaching of mathematics in secondary schools if it is confirmed that stakeholders experience difficulties in the area of concepts, understanding availability of relevant materials and applicability to Nigeria situation.

1.3 Objectives of the Study

In considering the needs to promote a better understanding of the image of mathematics the objective of the study are;

1- To explore and identify the range of images, beliefs and attitude toward mathematics among stakeholders of secondary schools in Sokoto state.

2- To explore stakeholder’s view about the possible cause and sources of images of mathematics and their attitudes toward mathematics in secondary school in Sokoto state.

3- To find out whether the instructional materials for the subject of mathematics are available in the secondary school or not.

4- To find out areas of coverage in mathematics.

1.4 Research Questions

The main research question for this study are:

1- What is the range of images, attitudes and beliefs towards mathematics held by sample of stakeholders in some secondary schools in Sokoto state?

2- What are the possible reasons of liking and disliking mathematics?

3- Are there enough essential instructional materials of mathematics teaching in secondary schools?

4- What is the level of coverage of mathematic syllables in secondary schools?

1.5 Research Hypotheses

The research will be base on the following hypothesis:-

1. There are no differences of images, beliefs and attitudes toward mathematics among stakeholders of secondary schools in Sokoto state.

2. There are no possible view about the cause and sources of image of mathematics.

3. There are no enough essential instructional materials in mathematic in secondary school.

4. There is no proper syllables coverage in mathematics.

1.6 Significance of the Study

There are widespread claims about the negative images of mathematics stakeholders in teaching and learning. Therefore, the result of this study will provide systematic and empirical data on image and myths of mathematics among stakeholders in teaching and learning.

Secondly, by examining the different image, attitudes, beliefs and myths of mathematics among stakeholders, there is a potential for such images attitudes beliefs to be challenged, promoted or discouraged. The information obtained will enhance better strategies and measure for promoting stakeholders understanding of mathematics.

Thirdly, the result of this study might inform us what is the extent of the influence of stakeholders in shaping the images of mathematics. This information can be used to promote positive influence while attempting to avoid the negative influence of those sources, it will help to understand better the roles of stakeholders in the shaping of children’s images of mathematics.

Fourthly, the findings will reflect possible implication for mathematics education and mathematics teacher education. Knowing how student perceive mathematics learning experience in school and how this could have influenced their images of mathematics will help us to understand better how mathematics should be presented in the classroom. This knowledge may help to enhance better curriculum planning and teacher development programs.

Lastly, the impact of gender and age difference on images of mathematics resealed in the compression might serve to support or challenge the notion that mathematics is universal value-free, gender-free or age –free. The findings might help to illuminate our understanding on whether the difference in gender, age and value system could have lead to the difference in images of mathematics and consequently the difference in mathematics achievement.

Having described the current scenario of the secondary school stakeholders understanding of mathematics and the importance and significance of the stakeholder images of mathematics I argued that there is an urgent need to carryout this study.

1.7 Scope and Delimitation of the Study

This study is to investigate images of mathematics stakeholder in Sokoto state.

It is also concerned with identifying the possible causal factors of influence on the formation of these images of mathematics stakeholders in sokoto state.

However, for authenticity of this work, the extent is based on the order school in the area. These school are;

1. G.G.D.A.S.S YAR’AKIJA

2. A.A RAJI

3. G.D.S.S K/MARKE

4. S.A.A.S.S

5. G.D.S.S ARKILLA

1.8 Operational Definition of Terms

Mathematical image:- according to Rogers (1992) quoting from the oxford English dictionary define images as a mental construct, he argues that;

Throughout history, philosophers and mathematicians have been involved in the ontological question about the status reality and existence of mental image. Whichever philosophical standpoint we take, we have to admit two fundamental aspect of the debate.

First we are aware of the power of the human mind to construct mental images and

Secondly, our abilities to manipulate these images and use them to inspire creative and thoughts and different forms of communication.

Stakeholders

Stakeholder is anybody who can affect or is affected by an organization strategy or project. They can be internal or external and they can beat senior or junior levels. Some definitions suggest that stakeholders are those who have the power to impact an organization or project in some way. For example, people or small group with the power to respond to, negotiate with change the strategic future of the organization (Eden and Ackermann 1988: 117).

Mathematical Stakeholders: is anybody who can affect or is affected by schools, ministries and teachers services board (T.S.B) in teaching and learning mathematics. They can be internal or external and they be at junior or senior levels.

Examples of stakeholder in teaching and learning mathematics are student, Teacher, Inspectors in the ministry of education, parent etc.

Mathematical Modelling of Optimal Strategies for Improving Industrial Productive Population in the Presence of Perverse Diseases Pandemic

 

ABSTRACT

In this theses, we investigate certain key aspects of mathematical modelling to explain the epidemiology of HIV/AIDS, Tuberculosis, Hepatitis B, Tumour, diabetes and stroke at the workplace and assess the potential benefits of proposed control strategies.

The compartmental epidemiological modelling approach was used in the formulation of the models on HIV/AIDS, tuberculosis (TB), Hepatitis B (HBv), Tumour and Diabetes pandemic. In each of the cases, the dynamics of the disease was studied according to the various compartments based on the transmission dynamics of the disease. The resulting model in each of the diseases was a system of nonlinear ordinary differential equations.

The solutions of the various models were obtained using ODE45 module in MATLAB software built based on Runge-Kutta 4th Order method and the results plotted on graphs. The model on stroke was formulated using fluid dynamics approach where the geometry of the arteries of the employee(s) was used in determining the flow patterns of blood most especially in an occluded internal carotid artery.

The resulting model here is a partial differential equation which was solved using the Galerkindiscretisation scheme implemented by the finite element method in MATLAB and the results plotted on graphs. In the case of HIV/AIDS, a combination of intervention strategies including prevention,

Education / Enlightenment, and HAART treatment was studied showing a great potential to control HIV transmission in the workplace and indirectly improving the productivity of labour force population and also the availability of good labour force.

In the TB model, the two strategies employed, optimal education strategy and chemoprophylaxis clearly showed that both controls reduced/minimized the infected workforce population. In HBV, after introducing therapy, the viral load decreased after 10 days.

In addition, the number of free virons at the final time tf= 100 (days) in the case with control is less than that without control thereby increasing the efficiency of drug therapy in inhibiting viral production.

In tumour disease, the models described how DCs and NK cells of workers, as the innate immune system, and CD8 + T cells, as the specific immune system, affect the growth of the tumor cell population in the body of workers. In the diabetes model, without control, the work force population is lower than that with control.

The work force population increased progressively as the control increases. As the stenotic height increased, the diameter of the arteries reduced leading to occlusion thereby lowering the blood flow velocity with high blood pressure leading to stroke.

The equilibrium analysis showed that, the models were globally and asymptotically stable at both the disease-free and endemic states. The optimal control measure was established alongside with the various strategies for the controls which showed prodigious improvement in the workforce population on the application of the controls.

TABLE OF CONTENTS

Cover Page
Title Page i
Declaration ii
Certification iii
Dedication iv
Acknowledgement v
Abstract x
List of Figures xvi
List of Symbols (Parameters and Variables) xvii
List of Tables xxvii
Table of Contents xxiii
Chapter One : Introduction
1.1 Background of the Study 1
1.2Statement of the Problem 4
1.3Aims and Objective of the Study 9
1.4 Justification of the Study 9
1.5 Scope of the Study 10
Chapter Two : Literature Review
2.1 HIV/AIDS Pandemic 11
2.2 Tuberculosis (TB) Pandemic 14
2.3 Hepatitis B Virus 21
2.4 The Human and Economic Burden of Stroke 25
2.5 Mathematical Models of Tumour 27
2.6 Mathematical Models and Data Used in Diabetology 38
2.7 Ill-Health and its Economic Consequences 40
2.8 Human Capital, Health and Productivity 43
2.9 Sensitivity Analysis 49
2.10 Guidelines for Improving the Labour Productivity 50
Chapter Three : Methodology
3.0 Introduction 52
3.1 Physiognomies of Workers 52
3.2 Tuberculosis 64
3.2.1 Patterns of TB Infection 65
3.3 Hepatitis B 68
3.3.1 Geographical Distribution of Hepatitis B 68
3.3.2 Transmission of Hepatitis B 69
3.3.3 Symptoms of Hepatitis B 69
3.3.4 People at Risk for Chronic Hepatitis Disease 69
3.3.5 Diagnosis of Hepatitis B 70
3.3.6 Treatment of Hepatitis B 70
3.3.7 Prevention of Hepatitis B 71
3. 4 Diabetes Mellitus 72
3.4.1 Types of Diabetes Mellitus 73
3.4.2 Symptoms of Diabetes 76
3.4.3 Complications Caused by Diabetes 77
3.5 Stroke (Cerebrovascular Accident) 79
3.5.2 Diagnosis of Stroke 85
3.5.3 Treatments of Stroke 85
3.5.4 Prevention of Stroke 88
3.6 Tumour Growth 89
3.6.1 Benign tumours 89
3.6.2 Precancerous conditions 89
3.6.3 Malignant tumours 90
3.6.4 How tumours and cancers are named 90
3.6.5 How cancer spreads 91
3.6.6 Prognosis and Survival from Cancer 91
3.7 Theorems Governing the Dissertation 92
3.7.1 Theorem 93
3.7.2 Gronwall’s Inequality 93
3.7.3 Well-Posed Problem 95
3.6.1 Definition 95
3.7.4 Hartman-Grobman Theorem 96
Chapter Four: Model Construction
4.0 Introduction 99
4.1 Formulation of the Various Models 99
4.1 Formulation of HIV/AIDS Model 99
4.1.1 Assumptions of the Model on HIV/AIDS 99
4.1.2 Model Variables and Parameters 99
4.1.3 Model Flow Diagram/Compartmental Analysis 100
4.1.4 Mathematical Model for HIV/AIDS 100
4.1.5 Formulation of the Optimal Control Problems 102
4.1.6 Disease-Free Equilibrium (DFE) and Endemic Equilibrium 104
4.1.7 Formulation of Optimal Control Problem 105
4.2 Formulation of Tuberculosis (TB) Model 107
4.2.1 Assumptions of the Model on Tuberculosis 107
4.2.2 Variables for Tuberculosis (TB) Model 107
4.2.3 Parameters of Tuberculosis (TB) Model 108
4.2.4 Model Flow Diagram for the TB Model 108
4.2.5 Tuberculosis Model 109
4.2.6 Modelling the Optimal Control Problem for TB 110
4.2.7 Existence of an Optimal Control Solution 112
4.2.8 Characterization of Optimal Controls 112
4.3 Formulation of the Model for Optimal Control of Hepatitis B 115
4.3.1 Assumptions of the Model for Optimal Control of Hepatitis B 115
4.3.2 Variables for Hepatitis B Virus Model 116
4.3.3 Parameters of Hepatitis B Model 116
4.3.4 Mathematical Model for Hepatitis B 116
4.3.5 The Optimal Control Problems 117
4.4 Formulation of the Model on Tumour/Cancer 119
4.4.1 Assumptions of the Model on Tumour/Cancer 120
4.4.2 Model Variables for Tumour Growth 120
4.4.3 Parameters of Tumour Growth Model 120
4.4.4 Mathematical Model for Tumour/Cancer 121
4.4.5 Non –Dimensionalisation 121
4.4.6 Steady State and Stability Analysis 122
4.5 Formulation of the Diabetes Model 124
4.5.1 Assumptions of the Diabetes Model 124
4.5.2 Variables of the Diabetes Model 124
4.5.3 Parameters of Diabetes Model 124
4.5.4 Model Flow Diagram for Diabetes 125
4.5.5 Mathematical Model for Diabetes 125
4.5.6 The Optimal Control: Existence and Characterization 126
4.5.6.1 Existence and Positivity of Solutions 126
4.5.6.2 Characterization of the Optimal Control 128
4.6 Formulation of Model on Cardiovascular Accident/High Blood Pressure 129
4.6.1 Assumptions of the Model on Cardiovascular Accident/High Blood Pressure 129
4.6.2 Variables and Parameters of the Model on Cardiovascular Accident 131
4.6.3 Mathematical Model for Cardiovascular Accident/High Blood Pressure 131
4.6.5 Governing Equations 137
4.5.7 Estimating wave generation in the base of the brain 140
4.7 Solution of the Various Models 145
Chapter Five: Results, Discussions, Summary/Conclusion and
Recommendations
5.0 Introduction 148
5.1 Results/Discussion 148
5.1.1 Results/Discussion onWorkforce Productivity in the presence of
HIV/AIDS 148
5.1.2 Results/Discussion on Workforce Productivity in the presence of Tuberculosis 161
5.1.3 Results/Discussion on Workforce Productivity in the presence of Hepatitis 182
5.1.4 Results/Discussion on Workforce Productivity in the presence of Tumour 186
5.1.5 Results/Discussion on Workforce Productivity in the presence of Diabetes 195
5.1.6 Results/Discussion on Workforce Productivity in the presence of Stroke 202
5.2 Summary 207
5.3 Conclusion 207
5.4 Contribution to Knowledge 210
References 211

CHAPTER ONE

INTRODUCTION

1.1 Background of Study

It is obvious that the welfare of individuals, the growth of enterprises and the development of the national economies are largely dependent on their comparative productivity. There exist differences among the various countries of the world based on political ideologies, economic systems or some such reasons but all unanimously recognize the importance of the improvement in the productivity levels.

Productivity is a ratio between the output of the wealth produced and the input of resources used in the process of any economic activity (Rao, 2009). The input creativity can yield greater amount of output through conversion efficiency and here lies the importance of improvement in productivity levels.

The concept of productivity of course, with some degree of confusion has remained a continuous and challenging area of study.

The changes in the productivity levels greatly influence a wide range of human, economic and social considerations, such as higher standard of living, rapid economic growth, improvement in balance of payments, control of inflation culture of the nation etc. The productivity in a most simple way may be defined as ratio of output to input. It is expressed as under:
I
P = O where P = Productivity, O = Output, I = Input

According to Oxford Illustrated Dictionary 2nd Edition (2003), productivity is defined as efficiency in industrial production to be measured by some relationship of outputs to inputs. The Encyclopedia Britannica (2009) defined productivity according to economics as the ratio of what is produced to what is required to produce it.

Usually, this ratio is in the form of an average expressing the total output of some category of goods divided by the total input of say, labour and raw materials. In principle, any input can be used in the denominator of the productivity ratio. Thus one can speak of productivity of land, labour, capital or sub-categories of any of these factors of production.

It should be noted that, the concept of productivity is so closely attached to the labour input that the term productivity is almost used as the synonym of productivity of labour. International Labour Organization (ILO) (2007) defined productivity as, the ratio between the volume of output as measured by production indices and corresponding volume of labour input as measured by employment indices.

The most important reasons why labour is used as the commonest factor in measuring productivity are: It is easy and precise to measure the units of labour inputs as compared to other inputs like materials, capital etc. Productivity can be very easily measured in terms of output per man, output per man hour or output per unit of labour time,

Labour input is universally applied to all types of plants processes, productions and it has become a common practice to link wages, with the productivity.

Productivity is a technique of extracting greater output from the inherent input creativity of various resources through the conversion efficiency. The conversion efficiency which changes the level of productivity is largely affected by numerous factors.

All these factors affect the level of productivity either individually or jointly. Some important factors are classified as: Technological; Managerial; Financial; Natural; Sociological, and Government.

The technological advancement always strives to achieve the increase of production with minimum costs and efforts, which always result into increased productivity for example, application of mechanized power, automation etc. Progressive and imaginative managerial skills always tap greater output of the human and nonhuman resources.

Delegation of authority, true recognition of human factor, imaginative judgment results into increased productivity and contented labour force. The availability of financial resources enables the organization to spend moneys for the research and development, employment of professional executives, adaptation of latest technology, provision of amenities, effective stock piling and material control. All these factors directly affect the level of productivity.

The low level of productivity and poor industrial growth of the underdeveloped countries is due to poor capital
formation constraints on the financial resources and good quality manpower management.
The natural resources like geographical, physical and climatic conditions directly affect the level of productivity.

The effect of these factors is confined to certain type of industries and the possibility of bringing them within control as in humidification in textile industry, quality thickness and depth of the mineral resources; climate effect on the labour efficiency etc.

The generic characteristics and racial quality has a great impact on the productivity of the labour. Productivity is also affected by the attitude of the workers towards the work and the approach of the management towards the workforce and the provision of working conditions.

The Government policy regarding financial incentives, taxation policy, tariff policy, industrial licensing labour laws etc also affect the productivity.Provision of concessional loans for modernization, tax incentives for the expenditures on research and development etc help increase
the level of productivity.

There are still many other ways of improving productivity. In construction, productivity is usually taken to mean labour productivity, that is, units of work placed or produced per man hour. The inverse of labour productivity, man-hours per unit (unit rate), is also commonly used.

Productivity is the ratio of output to all or some of the resources used to produce that output. Output can be homogenous or heterogeneous. Resources comprise: labour, capital, energy, raw materials, etc.

Horner and Talhouni (2008) stated “A popular concept in the USA, and increasingly in the UK, is the concept of earned hours. It relies on the establishment of a set of standard outputs or “norms” for each unit operation. Thus, a number of earned hours are associated with each unit of work completed.”

“Productivity may then be seen also as the ratio of earned to actual hours. The problem with this concept is in establishing reliable “norms”, for setting standards. It also depends on the method used to measure productivity, and on the extent to which account is taken of all the factors which affect it.

Few discussions of the potential economic impact of the global AIDS epidemic fail to observe that HIV/AIDS, unlike most other infectious diseases, strikes working-age adults during what should be their most productive working years. The mortality component of this loss is clear: lives lost to AIDS cannot contribute to economic growth. The morbidity component, however, has rarely been addressed. Although it is generally accepted that the morbidity associated with

HIV/AIDS will lead workers to be less productive, and some estimates of AIDS-related increases in absenteeism have been made (Rosen et al. 2003), the pace and trajectory of the labour productivity decline is not well described. As a result, both firms and governments are hampered in their efforts to develop effective strategies for coping with the disease. One reason for the dearth of empirical studies is that in most settings, neither the health nor the productivity of an individual worker can be directly observed (Strauss& Thomas 1998).

1.2 Statement of the Study

The identification and evaluation of factors affecting labour productivity have become a critical issue facing project managers for a long time in order to increase industrial productivity.

Understanding critical factors affecting productivity are both positive and negative and can be used to prepare a strategy to reduce inefficiencies and to improve the effectiveness of industrial performance.

Knowledge and understanding of the various factors affecting labour productivity is needed to determine the focus of the necessary steps in an effort to reduce project cost overrun and project completion delay, thereby increasing productivity and overall project performance.

Based on the study and survey, factors affecting industrial productivity have been identified and are grouped into 15 categories according to their characteristics, namely: design factors, execution plan factors, material factors, equipment factors, labor factors, health and safety factors, supervision factors, working time factors, project factors, quality factors, financial factors, leadership and coordination factors, organization factors, owner/consultant factors, and external factors.

There are also factors that specifically affect the small and medium companies/establishments. The researcher has presented among many others to include: Lack of material, Labor strikes, delay in arrival of materials, financial difficulties of the owner, unclear instruction to laborer and high absenteeism of labors, bad weather

(e.g. rain, heat, etc.), non-discipline labor and use of alcohol and drugs, no supervision method, design changes, repairs and repetition of work and bad resources management, bad supervisors, absenteeism and far away from location of material
storage, and bad leadership.

On the other hand there are some top factors that affect large companies which the researcher has presented among many others to include: unclear instruction to labourer, delay in arrival of materials, lack of material and financial difficulties of the owner,

no definite schedule, low supervisor’s capability, supervision method, lack of equipment, and high absenteeism of labours, supervisors absenteeism, frequent damage of equipments, and labour strikes, design changes, incomplete drawing and inspection delay, poor communication in site and inaccurate design.

We have summarised the factors that affect industrial productivity to include: lack of material, delay in arrival of materials , unclear instruction to labourer, labour strikes, financial difficulties of the owner, high absenteeism of labours, no supervision method, supervisors absenteeism, lack of equipment and design changes, no definite schedule, poor management, unproductive time

(internal delay, extra break, waiting & relaxation ), lack of skill, supervision delay/ lack of supervision, lack of tools and equipment, poor instructions, poor quality of labour, material factor, execution plan factor, health & safety factors, labour shortages, working time factor, accidents, organization factors, improper training, bad weather, use of alcohol and drug.

Considering all these factors, we have also seen that it is still very evident that these factors affect industrial productivity both negatively and positively. Those factors affecting productivity positively would have to be adhered to and still given a new lease of life while those affecting productivity negatively would have to be optimized for an improved industrial productivity.

In the course of looking into the factors, the barriers to productivity were detected and presented thus: The countries’ economy has become increasingly more dynamic and complex. As a result, economic measurement and analysis, particularly relating to productivity, have become more difficult and complicated.

The main problem involves properly defining units of measurement, evaluating qualitative changes and obtaining reliable data for both inputs and outputs. This process is further complicated by the need to price – deflate this data in order to evaluate changes in productivity in real terms.

Measurement of inputs is problematic. Variations in the rate of input utilization are at best partially picked up in data series. In particular, the rate of capital equipment utilization, i.e. the measurement of machine hours, is rarely accomplished.

Labour input, if measured by hours actually worked, is better suited to reflect the changing rate of manpower utilization, but remains an imperfect measure. The increasing prominence of the service sector within the national economy has generated increased mis-measurement of labour hours.

Information technology may aggravate this measurement error by allowing increased work flexibility and longer effective workdays that are not properly captured by the official statistics.

It is therefore evident that to optimize productivity, the aforementioned factors have to be critically looked into and optimized. It is not out of place that the human factor has a very important role to play in the areas of apportioning work, monitoring/supervising and also in the provision of skilled labour. The health of the individuals cannot be undermined in this course.

Going on the present report from World Health Organization (2010), Global Summary of the AIDS Epidemic – 2010 has shown that; Number of People Living with HIVTotal: 34.0 million [31.6million–35.2million], Adults: 30.1 million [28.4million–31.5million], Women: 16.8 million [15.8million–17.6million], Children: 3.4million [3.0million–3.8million], Number of People Newly Infected, Total: 2.7 million [2.4million–2.9million], Adults: 2.3 million [2.1million–2.5million], Children: 390 000 [340 000–450 000]. AIDS Deaths Total: 1.8 million [1.6million– 1.9million], Adults: 1.5million [1.4million–1.6million], and Children: 250000 [220 000–290 000].

In a similar scenario, the Sub-Saharan Africa HIV and AIDS Statistics – 2010 has shown the Number of People Living with HIV Total – 22.9 million [21.6 million – 24.1 million], Children – 3.1 million [2.8 million – 3.5 million]. Number of people newly infected, total – 1.9 million [1.7 million – 2.1 million], Children – 350 000 [300 000 – 410 000], adult prevalence (15-49 years) [4.7% – 5.2%] and death due to AIDS has a Total of 1.2 million [1.1 million – 1.4 million], children – 230 000 [200 000 – 260 000].

Over 7 000 new HIV infections a day about 97% are in
low and middle income countries, about 6 000 are in adults aged 15 years and older, of whom: almost 48% are women, about 42% are young people (15-24).

In 2002, it was estimated that globally, 40 million people were infected with HIV/AIDS and more than 70% of this disease burden was borne in sub-Saharan Africa where HIV/AIDS is now the number one overall cause of death (Guinness et al. 2003).

Besides the human cost, HIV/AIDS is having profound effects on productive employment and economic development in Africa, and hence its inability to cope with the pandemic (Bloom et al. 2006). The spread of HIV/AIDS is being aided by stigma and discrimination which keep the disease underground and discourage persons from being tested and seeking treatment.

The total number of people tested for HIV globally remains unacceptably low with an estimated 90% of people who are HIV infected worldwide unaware of their status (Waxman et al. 2007).

Despite the magnitude of the problem, little rigorous empirical research on the micro level effects of HIV/AIDS at the firm and industry levels has been published in the literature on African development. Unpublished case studies from Kenya and Botswana in 1994 found widely varying impacts, with costs ranging from less than 1% of profits to nearly 9% (Rosen et al. 2004).

Methodological Models for Optimal Control of Marine Oil Spill

ABSTRACT

The frequency of accidental discharge of oil into aquatic environment has presented a significant threat to marine biota with related adverse effects on the supply of products and services of importance to human cultures. This threat of economic and environmental devastation led to the development of a number of monitoring and clean-up alternatives such as remote sensing and chemical dispersants, respective.

This study proposed a new possible research direction in marine oil spill modeling where the monitoring and clean-up alternatives would be optimized to enhance locations selection for the deployment of containment and combating technique evaluation before actual usage.

A novel optimal control theory has been developed through operational research formalism as a critical first step in mitigating the problem of oil spill look-alike phenomenon associated with remote sensing, and the conflicting priorities in the application of chemical dispersants, which may be toxic to marine biota, during marine oil spill clean-up.

Markovian decision processes with sequential optimization techniques were utilized in formulating the control-theoretic methodological models that would aid environmental managers in minimizing the uncertainty in the remote sensing data to reduce the high number of false alarms

(oil slick look-a-likes) phenomena, minimizing the apparent toxicological effect of clean-up technique like chemical dispersants, determining the control measure that would cause a process to satisfy the physical constraints of chemical dispersants applications, and at the same time optimizing some performance criteria for all future earnings from marine biota.

A dynamic model for a new strategy based on a diffusion process, which makes the distinction between two types of optimization objectives: increasing awareness and changing predisposition to adopt coherent pluralistic technique has been developed and the optimality condition for minimization of false alarm in marine oil spill detection was obtained as:

̇ ( ( )) ( ( )) , where   1 n t denote the regions within which the spill originated in the system,   2 n t denote other regions beyond with probable spill threat due to the spill diffusion process and is captured via remote sensing application,

3 n is the potential regions within 2 n after verification for disparity classification, is the decay variable and is time. Furthermore, a penalty cost for taking, at each time period, any decision following each possible signal was obtained as a decision rule:

TABLE OF CONTENTS

Title page – – – – – – – – – – i
Certification – – – – – – – – – – ii
Dedication – – – – – – – – – – iii
Acknowledgement – – – – – – – – – iv
Abstract – – – – – – – – – – v
Table of contents – – – – – – – – – vii
Chapter One: Introduction – – – – – – – – 1
1.0 Preamble – – – – – – – – – 1
1.1 Background of the Study – – – – – – – 1
1.2 Statement of the Problem – – – – – – – 3
1.3 Aim and Objectives of the Study – – – – – – 3
1.4 Significance of the Study – – – – – – – 4
1.5 Scope of the Study – – – – – – – – 4
1.6 Organization of the Thesis – – – – – – – 4
1.7 Research Methodology – – – – – – – 5
Chapter Two: Review of Related Literature – – – – – 7
2.0 Oil Spill Control Modelling – – – – – – – 7
2.1 Remote Sensing in Oil Spill Control – – – – – – 9
2.2 Conceptual Framework of Operational Research (OR) Techniques in Marine
Oil Spill Control – – – – – – – – 10
2.2.1 The Coherent Pluralism Technique – – – – – – 10
2.2.2 Statistical Methods as Complimentary Tool – – – – – 11
Chapter Three: The Methodological Models – – – – – 15
3.0 Methodological Model for Combination Methodology – – – 15
3.1 The Conceptual Model – – – – – – – 15
3.1.1 The Computational Procedure – – – – – – 17
3.1.2 Formulation of Analytical Scheme – – – – – – 21
3.1.3 Formulation of Analytical Scheme for Penalty Cost and Decision Rule – 33
3.2 Methodological Model for Sequential Optimization Technique in Marine oil Spill
Control – – – – – – – – – 35
3.2.1 Mathematical Preliminaries and Definition of Terms – – – 35
3.2.2 The Conceptual Model Oil Spill Transport – – – – – 38
3.2.3 Formulation of the Optimal Control Problem – – – – 40
3.2.4 The Necessary Conditions for Optimality – – – – – 42
3.2.5 Development of Sequential Optimization Processes for Optimal Response –
Strategy – – – – – – – – – 45
3.2.6 A Decision Rule for Sequential Optimization Processes – – – 47
3.2.7 Formulation of Optimal Costs Model for Marine Oil Spill Response – 49
Chapter Four: Optimal Control Theory for Marine Oil Spill Problem – – 54
4.0 Problem Statement – – – – – – – – 54
4.1 Formulation of the Optimal Control Model – – – – – 55
4.2 The Solution Module – – – – – – – – 57
4.3 Statistical Analogy – – – – – – – – 60
Chapter Five: Concluding Remarks – – – – – – 64
5.0 Conclusions – – – – – – – – – 64
5.1 Contribution to Knowledge – – – – – – – 64
References – – – – – – – – – – 65
Appendix – – – – – – – – – – 70
List of Publications from the Work – – – – – – 70

CHAPTER ONE

INTRODUCTION

1.0 PREAMBLE

Control theory is an interdisciplinary branch of operations research that deals with the behaviour of dynamical systems. while the term „operations research‟, quite often, is associated almost exclusively with the use of mathematical techniques to model and analyze decision problems, optimal control theory, as a distinct discipline in operations research, concerns the choice of disposition of a set of control instruments ( )to achieve a given objective function ( ),

taking into account the dynamic properties of the system under consideration. it can be stated in general terms as the optimization of an objective function of system behaviour that uses a given set of control instruments over a specified period of time (see also, wiegerinck et al., 2006).

This area of research has witnessed remarkable progress over the past decades towards the development of methods for the stabilization and control of a host of linear and nonlinear systems problems (shastriet al., 2008). it is finding increased application in both biological and economic disciplines

(williams and nichols, 1984; behncke, 2000; sethi and thompson, 2000;joshi, 2003), as well as theoretical and applied ecology (houston et al., 1988). according to runge and johnson (2002), it is also central in applied sciences and natural resources management.

1.1 background of the study

Degradation of aquatic ecosystem is generally agreed to be undesirable. historically, most evaluations of ecological effects of petroleum contamination have related impacts to effects on the supply of products and services of importance to human cultures. according to xu and pang (1992),

most pollution control and environmental laws were enacted in order to protect public health and ecological objectives. in these laws, a substance is considered a pollutant if it has been perceived to have an adverse effects on human health and wildlife. in recent years, a Number of substances appear to pose such threats. among them is crude oil spillage which first came to public attention with the torrey canyon disaster in 1967 (pierce et al., 1997).

According to redondo and platonov (2009), the risk of crude oil spillage to the sea presents a major threat to the marine ecology compared with other sources of pollution in the oceans. before now, it was earlier reported that oil spills affect wildlife and their habitats in many ways, which include, the modification of the environmental conditions of marine ecology,

which can be translated into the transformations of the chemical composition of the environment; alterations in its physical properties; destruction of the marine biomass nutritional capita; changes in the environmental biological equilibrium; and danger to human health (usfws, 2004).

the same can also be said about Nigeria, where oil spillage is a major environmental problem and its coastal zone rated one of the most polluted spots on the earth planet in the year 2006 (brown, 2006). according to nwilo and olusegun (2007),

from 1976 to 2007, over 1,896,960 barrels of oil were sunk into the Nigerian coastal waters resulting in a serious pollution of drinkable water, destruction of resort centres, properties and lives along the coastal zone. this was seen to be a major contributor to the regional crisis in the Nigeria Niger-Delta region (alao, 2008).

As a case in point, after a spill in the ocean, oil in water body, regardless of whether it originated as surface or subsurface spill, spreads to form a thin film called oil slick. according to yapa (1996), the movement of this slick is governed by the advection and turbulent diffusion due to current and wind action.

the slick always spreads over the water surface due to a balance between gravitational, inertia, viscous and interfacial tension forces, while the composition of the oil changes from the initial time of the spill. it follows that light (low molecular weight) fractions will evaporate, water soluble components dissolve in the water column, and immiscible components become emulsified and disperse in the water column as small droplets.

In essence, the frequency of accidental oil spills in aquatic environments has presented a growing global concern and awareness of the risks of oil spills and the damage they do to the environment. however, it is widely known that oil exploration is a necessity in our industrial society, and a major sustainer of our lifestyle as most of the energy used in

Canada and the united states, for instance, is for transportation that runs on oil and petroleum products. thus, following the trends in energy usage, this is not likely to decrease much in the future because industry uses oil and petroleum derivatives to manufacture such vital products as plastics,

fertilizers, and chemical feedstock, which will still be required in the future. in what follows, it is a global belief that the production and consumption of oil and petroleum products might continue to increase worldwide while the threat of oil pollution is also likely to increase accordingly (esa, 1998).

Consequently, a fundamental problem in environmental research in recent time has been identified in the literature to be how properly to assess and control the spatial structure of pollution fields at various scales, and several studies showed that mathematical models were the only available tools for rapid computations and determinations of spilled oil fate, and for the simulation of the various clean-up operations. this study was carried out to sustain this objective.

1.2 statement of the problem

Specifically, the problem of oil slick look-a-likes phenomena associated with optical detectors (remote sensing), and the environmental impacts of some cleanup techniques (conflicting priorities) that makes chemical dispersant a limiting factor in the decision-making process has been a major snag in marine oil spill management since early 21st century

(congalton, 1991; marghany et al., 1996; woodcock, 2002; tkalich et al., 2003; keramitsoglou et al., 2006; topouzelis, 2008; mansor et al., 2010). radar satellites was proposed by mansor et al. (2010) to replace the commonly used remote sensors while tkalich et al. (2003)posited that combating techniques should be carefully evaluated before actual usage in order to enhance

oil transport and fates models. nevertheless, studies on the optimization of the remote sensor and chemical dispersants being the most widely and commonly used oil spills monitoring and clean-up alternatives, to the best of our knowledge, was conspicuously missing in the modern marine oil spill literature. this study was therefore motivated by the need to bridge this gap as an innovation in the marine literature.

1.3 aim and objectives of the study

The aim of this study is to formulate mathematical abstractions of the control processes where decisions would be taken at several stages through an optimal control path to achieve the following specific objectives:

1. minimizing the uncertainty in the remote sensing data to reduce the high number of false alarms (oil slick look-a-likes) phenomena,

2. minimizing the apparent toxicological effect of clean-up technique like chemical dispersants,

3. determining the control measure that would cause a process to satisfy the physical constraints of chemical dispersants applications, and at the same time

4. optimizing some performance criteria for all future earnings from marine biota.

1.4 significance of the study

Important attributes of marine oil spill, such as the nature of the spill, scale, type, time, etc., which are usually uncertain and more complex (Grigaluras and Opaluch, 1988), have been studied and applied in formulating decision rules in order to aid contingency planning in case of

oil spill disaster, especially with regard to the possibility of using chemical dispersant and other techniques, in minimizing or preventing shoreline oiling which reduces oil spill clean-up costs. the mathematical expressions have also been developed to assist in optimal computation in order to enhance the sustainability of ecological values of aquatic biota for future earnings.

1.5 Scope of the Study

Generally, the problem of marine oil spillage has a wider dimension and varies in terms of environmental contents. this study focuses specifically on formulation of optimization processes for remote sensing data processing and

chemical dispersants application procedure using or formalism, theoretical illustration of optimal control theory in a specific marine oil spill problem and statistical relevance of the optimal control theory in marine oil spill management.

1.6 Organization of the thesis

The subsequent section of this thesis is organized as follows:

In section 1.7, the research methodology used in this study is presented. chapter 2 focused on the review of related literature with specific attention to oil spill control modelling, the relevance of remote sensing, operational research techniques, and statistical methods.

Chapter 3 is devoted to the development of methodological models used in the course of this research work with section 3.1 and 3.2 centring on the mathematical formulations of the combination methodology and the sequential optimization processes. in

section 3.1.2, the computational procedure of the combination methodology is presented, while the analysis scheme is given in section 3.1.3. the optimal control theory is presented in section 3.2.1, and in section 3.2.3 the oil spill dynamical model is given, while the necessary conditions for optimality are established in

section 3.2.5. the oil spill response cost problem is also treated in section3.2.8. chapter 4 considered the formulation of optimal control theory for a typical oil spill problem. the optimal model is presented in section 4.2 with the statistical analogy given in section 4.3. the thesis is concluded in chapter 5 with useful recommendation, contribution to knowledge in section 5.1.

1.7 Research Methodology

Several studies showed that mathematical models are tools for rapid computations and determination of spilled oil, and for the simulation of the various clean-up operations (chigbu and bassey, 2010).in this work, the basic problem of marine oil spill was specified and formulated mathematically using operational research formalism.

the methodological model for the optimization of the monitoring strategy in order to minimize false alarm phenomena was derived using coherent pluralism (jackson, 1999 and mingers, 2001), while sequential optimization processes were formulated to objectify the evaluation of combating technique application before actual usage, as proposed by tkalich et al. (2003).

The pluralistic method involved the use of statistical technique for disparity classification of information from remote signals based on prior information on the characteristics of the oil density, water content, viscosity, etcetera, while the sequential processes involved a closed-loop optimization based on finding an optimal rule for selecting at each period t, a control for each possible state value in a dynamic system.

In other word, a combination methodology that suggested a move past an analysis of standalone data to one incorporating and synthesizing information from many associated sources was used to tackle the problem of false alarm. in developing the optimization technique for remote sensing data,

the outcomes of remote sensing application were consolidated through reanalyzing possible disparate results within the context of their common endpoints, increasing the sensitivity of the analysis to detect the presence of environmental or human effects, and providing a quantitative scheme for the phenomenon of interest based on the combined information.

Furthermore, a fundamental principle upon which oil spill fate and transport models are based was considered in the development of a sequential optimization technique. we considered the law of conservation of mass, derived from navier-stockes equations (tkalich et al., 2003):
(1)
Where ,
H = oil slick thickness;
C= oil concentration;
V = oil slick drifting velocity;
D= oil fluid velocity;
E = dispersion-diffusion coefficient;
 = computational slick spreading function;
H r and r = physical chemical kinetic terms;
U = grid size;
 = cartesian coordinate; and
T = time,

And introduced a control system into equation (1), which described a change in the Concentration of the spilled oil in the marine environment, resulting from the random motion Of oil slick in the transporting medium, to obtain a new dynamical model for optimal control.

In what followed, we set out the necessary conditions for optimality using the fundamental Theorem of variational calculus and partial differential equation (pde). thus, a dynamical Model that could cause the control system to follow a path such that the objective functional Of the marine environment could be optimized was formulated, and a sequential optimization Technique that followed a bellman‟s optimality principle (ji and zhou, 2006; crespo and sun,
2003) was employed to minimize clean-up operational constraint and enhanced contingency Planning.

This philosophy was illustrated theoretical by formulating methodological models for optimal Control of a typical oil spill situation with specific objective function a specific situation Where the region was assumed to be exposed to a serious oil spill effect that resulted in series of conflicts between the host community in the exploration region and the operating oil firms.

A statistical analogy of the methodological models has also been presented to envisage their Statistical relevance.