**Aristotelian Concept of Good Government**

**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

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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

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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 indispensible single element in the modern societal development “mathematics education is therefore indispensible 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 stakes\holders, 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 programmes.

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.

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