i

OKAFOR, MARY ANASTASIA O. (REV. SR.)

PG/MED/07/42813

PG/M. Sc/09/51723

PRIMARY SCHOOL TEACHERS’ MASTERY OF NUMBER BASE

SYSTEM IN UNIVERSAL BASIC EDUCATION

(UBE) MATHEMATICS CURRICULUM

SCIENCE EDUCATION

A THESIS SUBMITTED TO THE DEPARTMENT OF SCIENCE EDUCATION, FACULTY

OF EDUCATION, UNIVERSITY OF NIGERIA, NSUKKA

Webmaster

Digitally Signed by Webmaster‟s Name

DN : CN = Webmaster‟s name O= University of Nigeria, Nsukka

OU = Innovation Centre

JULY, 2010

ii

PRIMARY SCHOOL TEACHERS’ MASTERY OF NUMBER BASE SYSTEM IN UNIVERSAL

BASIC EDUCATION

(UBE) MATHEMATICS CURRICULUM

BY

OKAFOR, MARY ANASTASIA O. (REV. SR.)

PG/MED/07/42813

DEPARTMENT OF SCIENCE EDUCATION

FACULTY OF EDUCATION

UNIVERSITY OF NIGERIA

NSUKKA

JULY, 2010

iii

TITLE PAGE

PRIMARY SCHOOL TEACHERS’ MASTERY OF NUMBER

BASE SYSTEM IN UNIVERSAL BASIC EDUCATION

(UBE) MATHEMATICS CURRICULUM

BY

OKAFOR, MARY ANASTASIA O. (REV. SR.)

PG/MED/07/42813

A PROJECT REPORT SUBMITTED IN PARTIAL

FULFUILLMENT OF THE REQUIREMENTS FOR THE

AWARD OF MASTERS’ DEGREE IN MATHEMATICS

EDUCATION TO THE DEPARTMENT OF SCIENCE

EDUCATION

SUPERVISOR: DR. K.O. USMAN

JULY, 2010

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CERTIFICATION PAGE

Rev. Sr. Okafor, Anastasia, a postgraduate student in the Department of

Science Education, with registration number PG/MED/07/42813 has

satisfactorily completed the requirements for the Master‟s Degree in

Mathematics Education. The work embodied in this Thesis is original and has

not been submitted in part or full for any other Diploma or Degree of this or

any other University.

_________________________ __________________

Rev. Sr. Okafor Mary Anastasia Dr. K. O. Usman

Student Supervisor

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APPROVAL PAGE

This thesis has been approved for the Department of Science Education,

University of Nigeria, Nsukka.

BY

____________________ _____________________

Dr. K. O. Usman Dr. C. R. Nwagbo

Supervisor Head of Department

_____________________ _____________________

Internal Examiner External Examiner

________________________

Prof. S. A. Ezeudu

Dean of Faculty

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DEDICATION

This thesis is dedicated to the Daughters of Divine Love Congregation, to all people of God

and to my beloved mother Mrs. Alice U. Okafor.

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ACKNOWLEDGEMENT

The researcher ascribes all the glory, honour and adoration to the almighty God

who had made this works a good success. Her profound gratitude also goes to Dr. K. O.

Usman, her supervisor, whose sincere guidance, encouragement and supervision made the

work a reality.

The researcher equally acknowledges the unquantifiable contributions of the

following: Prof. A. Ali, Prof U. N. V. Agwagah, and Prof. S.O. Olaitan. Dr. E. N. Nwosu,

Dr. C. R. Nwagbo, Dr. J. D. Ezeugwu and Dr A. O. Ovute for their interest in reading and

making development and improvement of this study. She also appreciates the contribution

of all the lecturers and staff of the Department of Science Education through the period of

the study.

The researcher also wishes to show profound gratitude to her Education Secretary

Hon. H. H. Amodu and Hon. Alhassan, Rev. Mother Ifechukwu Udorah, Late His Lordship

Most Rev. Dr. E. S Obot, His Lordship Most Rev. Dr. A. A. Adaji and Daughters of Divine

Love Sisters, Idah community for their understanding, patience and prayers throughout the

duration of this study. The researcher‟s special thanks go to her mother and her siblings

who stood solidly by her. Also her regards goes to Rev. Sr. Gorgemary Ezenwa, Rev. Sr.

Dr. Basil Nwoke, Rev. Fr Dr. T. Onyioma and her room mates at room 203 Nkrumah hall,

University of Nigeria Nsukka.

Finally, the researcher heartily appreciates Mr. Felix Egara, Miss Uche Maureen

Udenweze and all her friends for their assistance in so many ways.

(Rev.Sr.) Okafor, Mary Anastasia

Nsukka 2010

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TABLE OF CONTENTS

Title Page - - - - - - - - - i

Certification Page - - - - - - - - ii

Approval Page - - - - - - - - iii

Dedication - - - - - - - - -` iv

Acknowledgements - - - - - - - - v

Table of Contents - - - - - - - - vi

List of Tables - - - - - - - - - viii

Abstract - - - - - - - - - x

CHAPTER ONE: INTRODUCTION - - - - - 1

Background of the Study - - - - - - - 1

Statement of Problem - - - - - - - - 10

Purpose of the Study - - - - - - - - 11

Significance of the Study - - - - - - - 12

Scope of the Study - - - - - - - - 13

Research Questions - - - - - - - - 14

Research Hypotheses - - - - - - - - 15

CHAPTER TWO: LITERATURE REVIEW - - - - 16

Conceptual Framework - - - - - - - 17

Concept of Mastery - - - - - - - - 17

Problems of Teaching and Learning of Mathematics - - - - 18

Qualities of Primary School Mathematics Teachers and their Attitude towards

Mathematics Teaching - - - - - - - 22

Challenges of Primary Mathematics for Universal Basic Education (UBE)

Programme - - - - - - - - - 25

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Teachers‟ Competencies for Mathematics Teaching - - - - 28

Achievement in School Mathematics - - - - - - 30

Concept of Number Base System in UBE Mathematics Curriculum - - 32

Theoretical Framework - - - - - - - 36

Jean Piaget‟s Cognitive Learning Theory - - - - - 36

Skinner‟s Theory of Learning - - - - - - - 38

Empirical Studies - - - - - - - - 39

Studies on Mastery and Teachers‟ Competencies for Mathematics Teaching - 39

Studies on Gender as a factor on Achievement in Mathematics - - 42

Summary of Literature Review - - - - - - 44

CHAPTER THREE: RESEARCH METHOD - - - - 46

Design of the Study - - - - - - - - 46

Area of the Study - - - - - - - - 46

Population of the Study - - - - - - - 46

Sample and Sampling Techniques - - - - - - 47

Instrument for Data Collection - - - - - - 47

Validation of the Instrument - - - - - - - 48

Reliability of the Instrument - - - - - - - 48

Method of Data Collection - - - - - - - 49

Method of Data Analysis - - - - - - - 49

CHAPTER FOUR: RESULTS - - - - - - 50

CHAPTER FIVE: DISCUSSION, CONCLUSION, RECOMMENDATION

AND SUMMARY - - - - - - - - 56

Discussion of the Findings - - - - - - - 56

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Conclusion - - - - - - - - - 57

Educational Implications of the Study - - - - - 57

Recommendation - - - - - - - - 58

Limitation - - - - - - - - - 59

Suggestions for Further Studies - - - - - - 59

Summary of the Study - - - - - - - 60

REFERENCES - - - - - - - - 62

APPENDICES - - - - - - - - 70

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LIST OF TABLES

Table 1: the means and standard deviation of primary school teachers that have

mastery of number base system in UBE mathematics curriculum.

Table 2: the means and standard deviation of primary school teachers that have

mastery of the application of binary number to computer.

Table 3: the means and standard deviation of experienced teachers in contribution to

their mastery of number base system in UBE mathematics curriculum.

Table 4: the means and standard deviation of teachers of the influence of gender

(male and female) in the test mastery test on number base system

(TMTNBS).

Table 5: the means and standard deviation of teachers of the influence of location

(urban and rural) in the test mastery test on number base system

(TMTNBS).

Table 6: t-test of difference b/w the mean mastery scores of experts and less

experienced teachers in the TMTNBS.

Table 7: t-test of difference b/w the mean mastery scores of male and female teachers

in the TMTNBS.

Table 8: t-test comparison of the mean mastery scores of teachers in urban schools

and teachers in rural school in the test mastery test on number base system

(TMTNBS).

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ABSTRACT

The study sought to determine the extent of primary school teachers‟ mastery of number

base system in Universal Basic Education (UBE) mathematics curriculum. The study also

sought to find out the percentage of primary school teachers that have mastery on

application of binary number to computer. The mastery of number base system by male

and female experienced and less experienced and urban and rural were also considered.

Five research question and three null hypotheses were formulated to guide the study. A

descriptive survey design was used for the study. The population of the study was made up

of primary five and six teachers in urban and rural schools in Idah Education Zone. The

sample was made up of 40 primary five and six teachers. Multi-stage sampling technique

was used. The simple random sampling technique was used to select 20 schools from 57

schools in Idah Education Zone and purposive sample technique was used to select one

male teacher and one female teacher from each school in 10 urban schools and one male

teacher and one female teacher from each school in 10 rural schools. The instrument used

for this study was Teachers Mastery Test on Number Base System (TMTNBS). This was

developed, validated and used for data collection. Mean and standard deviation were used

to answer the research questions and t-test statistic tool was used to test the hypotheses.

The study revealed that the mean scores of the primary school teachers that have adequate

mastery both of number base system in UBE mathematics curriculum and application of

binary number to computer are greater than those that do not have. It also revealed that

some teachers scored below 80% which is the expected minimum score that indicates

mastery. The result of the study also revealed that there is significant difference between

the mean mastery scores of experienced and less experienced teachers, male and female

teachers and teachers in urban and rural schools. Based on the findings, some

recommendations were made; these include frequent seminars, workshops and conferences

should be organized for primary school teachers to enhance meaningful teaching and

learning of mathematics.

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CHAPTER ONE

INTRODUCTION

Background of the Study

“Mathematics is the science of numbers, quantity and space” (Odili, 2006). He

stated that it is a systemized, organized and exact branch of science. He also viewed

mathematics as the creation of the mind, concerned primarily with ideas, processes and

reasoning. Therefore, mathematics can be seen variously as a body of knowledge,

collection of techniques and methods, and the product of human activity. Nurudeen (2007)

stated that all sciences have their roots in mathematics and described mathematics as the

gate way to human endeavour. Many mathematicians viewed mathematics in various ways

based on its activities and importance. Usman (2002) stated that mathematics arose from

the peoples‟ need in organized society. It is also one of the most powerful and acceptable

tool, which the intelligence of man has made for its own use over the centuries. According

to Obodo (2000), mathematicians viewed mathematics as a universal language that uses

carefully defined terms and concise symbolic representations to add precision to

communication. This shows that mathematics has different dimension and in the context of

this study, one such dimension is number bases system.

Azuka (2009) defines number bases as systems of counting or grouping of numbers

(e.g. 12 = 1ten + 2units = 10 + 2). Mathematics in the context of this study is the study of

number bases, their structures, symbolic representation and operation. Mathematics is an

important subject that is indispensable to the development of any nation. It has been

regarded as the bedrock of scientific and technological development. Okafor (2000) stated

that no nation can develop scientifically or technologically without exposing her citizens to

good foundation in school mathematics. It is very useful in everyday activity. In essence,

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the subject is one of the compulsory subjects in both primary and post primary schools in

the country.

Despite the place of mathematics in a child‟s development, its applications in every

day activity is still very poor. This is because pupils begin very early to complain about

mathematics, right from the primary school. Just as pupils find it very hard to understand

the lessons, teachers equally find difficulties in teaching many topics (e.g. squares of

numbers, profit and loss percent, ratio; population issues and number bases), (Amazigo,

2000). This has created challenges for parents, pupils, teachers and educationists.

According to Kurumeh and Imoko (2008), Common Entrance Examination and primary

school mathematics Olympia reveal so much about the pupils‟ lack of foundation in

mathematics. This mathematics foundation which is very weak in primary level is carried

forward to junior secondary and is culminated in senior secondary school. This situation,

according to Usman, (2003), could be as a result of shortage of human resources in

mathematics education. This has resulted in the co- opting of unprofessional mathematics

teachers to teach mathematics, making it difficult to have effective implementation of

mathematics curriculum (programme of study).

The curricula are the subjects that are included in the course of study in a school.

Bamus (2002) defined curriculum as the set of experiences planned to influence learners

towards the goals of an organization. Organization here refers to school. Azuka (2009)

stated that curriculum of a school consists of all experiences that a learner encounters under

the direction of school. The curriculum of any educational system is planned and developed

according to the needs of the society. The author further said that just as the society is

dynamic, the curriculum is also dynamic. Hence, curriculum is usually changed from time

to time.

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Of all levels of education, primary education is the foundation on which the rest of

education is built upon. The Federal Republic of Nigeria (FRN, 2004) affirmed that

problem at this level would definitely affect the educational system. Hence, the importance

of primary school teachers is tremendous. Joachim (2005) said that teachers are highly

intelligent people with an ability to impart knowledge and understanding to their pupils.

Quintan (2005) viewed a teacher as more than someone who passes on knowledge. The

author said that being a great teacher means knowing when to assist, when to stand back

and insist on independence. Over pampering a learner leads to reliance and lack of

perseverance, which will in turn lead to lack of self-esteem. Reaching that gaol with

encouragement but no physical help will enable the learner experience the feeling of

achievement that inspires further learning. A teacher provides the opportunity which allows

the learner to learn for themselves. Piaget (1970) stated that, in order for a child to

understand something, he/she must reinvent it. Every time a teacher teaches a child

something, the teacher keeps the child from reinventing himself/herself. This does not

mean to say that the teacher must not teach, but he/she should provide opportunities for

pupils to explore and discover new things themselves. This provides an increased level of

understanding than solving the problem for them.

However, a teacher in the context of this study is somebody who exposes the

pupils/learners to many relevant aspects of mathematics such as addition, subtraction,

multiplication, and division of numbers. In general, all these are arranged in number base

system in mathematics. Salman (2005) stressed that the achievement of a solid foundation

for pupils in mathematics learning had strong implication for the quality of primary school

teachers. Primary school teachers especially teachers of mathematics will be masters in the

contents of number base system. A good primary school teacher is the one that has mastery

skill in the teaching of number base contents.

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Hornby (2001) defines mastery as having great knowledge about a particular thing.

Mastery according to Hornby (2006) involves having complete knowledge or

understanding of a particular thing. In other words, it involves thorough awareness of

something. Mastery in the context of this study identifies primary school teachers as having

thorough knowledge and understanding of number bases. This involves understanding its

operations and the strategies to be employed which would lead to a lasting learning on the

part of the pupils. Teachers‟ mastery of number base system also implies having

knowledge about number base, it embraces understanding challenges associated with

experience especially among the rural and urban areas.

The rural areas could be seen as areas that lack basic amenities such as good roads,

electricity supply etc, and while urban areas could be seen as areas that have basic

amenities such as good roads, electricity, tap water supply etc. The rural areas are usually

and generally educationally backward. Most teachers prefer urban areas to rural areas in

their teaching profession. According to Ekwue and Umukoro (2009), rural communities

gave little or no support to schools and that many parents showed little interest in the

education of their children. Results from Ekwue and Umukoro on the awareness of

mathematics teachers in UBE programme show that teachers in rural areas have low level

of Universal Basic Education (UBE). Teachers‟ mastery of number base could be a very

important instrument with such negative attitudes could be disabused. No doubt, mastery

level of number base system among mathematics teachers will affect in no small measure

the personal and professional commitment. Kolawole and Popoola (2009) in their study

investigated Four Ability Process Dimension (4ABP) as a function of improving teaching

and learning of basic mathematics. The study revealed that the academic achievement of

students was not influenced by location. It will be interesting to know if teachers‟ mastery

in number base system could be influenced by location.

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Furthermore, Okafor (2009) views that competency and subject mastery is positive

characteristics that must be possessed by any good mathematics educator. A teacher does

not give out what he/she does not have. The knowledge of number base among

mathematics teachers will not only transform but build in them, capacity to acquire

appropriate information, skill and competence for their professional survival.

Darling-Harmmond (1994) said that to emphasize the importance of subject mastery, more

than 300 schools of education in United States of America have created programmes that

extend beyond the traditional four-year bachelors degree programme. Okafor (2001)

suggested that adequate time will be spent in training and re-training of teachers so as to

ensure teachers‟ mastery and effectiveness. Federal Republic of Nigeria (FRN, 2004)

affirmed that no education system can arise above the quality of their teachers. Adesokan

(2000) referred to the teacher as the spark and key man in the drive to progress in the

education system.

According to the National Policy on Education, Primary education is the education

given in institutions for children aged 6 to 11 years plus (FRN, 2004). It went further to

state that since the rest of the education system is built on it; the primary level is the key to

the success or failure of the whole system.

The duration is six years. The goals of Primary education according to the National Policy

on Education are as follows;

a. Inculcating permanent literacy and ability to communicate effectively.

b. Laying a sound basis for scientific and reflective thinking.

c. Giving citizenship education as a basic for effective participation in and contribution to

the life of society.

d. Moulding the character and developing sound attitude and morals in the child.

e. Developing in the child the ability to adapt to the child‟s changing environment.

xviii

f. Giving the child opportunities for developing manipulative skills that will enable

the child function effectively in the society within the limits of the child‟s capacity.

g. Providing the child with basic tools for further educational advancement,

including preparation for trade and crafts of the locality (FRN, 2004).

Primary education shall be tuition free, universal and compulsory. Teaching shall be by

practical, exploratory and experimental methods (FRN, 2004). The government shall put all

efforts for the realization of these goals at the primary school level.

The new National Mathematics curriculum is for the Universal Basic Education

Programme (UBEP) beginning from Basic 1 to 9. In this new curriculum, the levels of

education (Primary 1 to 6 and Junior secondary 1 to 3) have been infused into basic 1 – 9.

Pupils are expected to continue their education from basic one to basic nine without

interruption. In this new mathematics curriculum, some mathematics topics were dropped

while new ones were added (e.g. binary number system, computer application etc.). Also,

there are shifts in topics from one class to the other (upwards/downwards) where necessary.

The thematic approach was also adopted in electing the content and learning experiences in

the curriculum. The themes in the revised curriculum are: Number and Numeration, Basic

Operations, Algebraic Process, Geometry and Mensuration, and Everyday Statistics.

The revised nine-year National Mathematics Curriculum for Basic Education in

Nigeria is focused on giving children the opportunity to:

- Acquire mathematical literacy necessary to function in an information age.

- Cultivate the understanding and application of mathematics skills and concepts

necessary to thrive in the ever changing technological world.

- Develop the essential element of problem solving, communication, reasoning

and connection within their study of mathematics.

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- Understand the major ideas of mathematics bearing in mind that the world has

changed and is still changing since the firs National Mathematics Curriculum

was developed in 1977(NERDC,2006).

The new UBE curriculum is geared towards improving the well being of man and to bring

about National development. According to Azuka (2009), teachers are facing challenge to

achieve effective teaching of the topics in the new mathematics curriculum in the

classroom. The author further stated that the emphasis should be placed on the application

of the mathematics concepts in the curriculum by the teachers.

Universal Basic Education (UBE) programme is a policy reform measure by the

Federal Government aimed at addressing the issue of inequality in education opportunity at

the basic level and improving the quality of education by reforming the basic education

sector in Nigeria, (Kurumeh and Imoko, 2008). Its major goal is to bring about positive

change in ways we have been implementing basic education. The programme is intended to

provide free, compulsory and qualitative education at primary and junior secondary school

levels as aspects of basic education. It includes adult and non-formal education levels, for

the adult and out- of - school youths. The UBE implementation guidelines derive its

objectives from the requirement of the constitution of the Federal Republic of Nigeria

(FRN, 2004) which states that:

- Government shall direct its policy towards ensuring that there are equal and

adequate educational opportunities at all levels.

- Government shall eradicate illiteracy by providing free, compulsory and

universal primary education.

To back the national goals, the government came out with National Economic

Empowerment and Development Strategy (NEEDS) and seven Millennium Development

Goals (MDGs) which will be attained by 2015 as well as Education for All (EFA).

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Nkolelonye (2007) stated that these goals clearly emphasized the need for the change of

attitude in repositioning of public service for optimum service delivery. Obioma (2007)

summarized the Millennium Development Goals (MDGs) as poverty and hunger

eradication, job creation, gender equality and empower women, improve maternal health,

reduce child mortality, combat HIV/AID and other diseases, wealth generation and using

the education to empower the people. It has become imperative that existing curricula for

primary and junior secondary school (JSS) should be reviewed, restructured and realigned

to fit into a 9- year Basic Education Programme. Number bases are inclusive in the new

mathematics curriculum for the smooth transition of knowledge from primary school to

secondary school. This is done in order to in order to meet the national goals. It is very

important to be equipped for the task. Davis (2001) has decried the ineffectiveness of many

methods and approaches for teaching mathematics and suggested that mathematics should

be taught to fall in line with what are obtained in the society. It is imperative that teacher

education will continue to be given a major emphasis in all our educational planning to

improve the teachers‟ knowledge in number bases contents.

Hornby (2001) defined number simply as an idea or a concept of a quantity. The

author also opines numeral as a sign or symbol that represents a number. Davis in Odili

(2006) states that numbers are indispensable tools of civilization, serving its activities into

sort of order. The complexity of civilization is mirrored in the complexity of its numbers.

Number and numeration are the science, art of computation. The knowledge of Number

Base System in primary school mathematics is very necessary for the smooth transition of

knowledge. The binary number or base two systems are based on the number two. This

base two is second best among the usual base ten and is used in computers for numerical

calculation. Binary numbers are made up of only two digits, 1 and 0. A computer contains a

large number of switches. Each switch is either „on‟ or „off‟. An „on‟ switch represents 1

xxi

and „off‟ represents 0. Binary numbers are used for coding computer programs. In this case,

letter A = 1, B = 2, C = 3 … Z = 26. But these numbers are also converted to binary

numbers for example, 2 = 102, 3 = 112, 4 = 1002, etc. This is used by some examination

bodies as candidates code their names and other relevant information. The use is also

manifested in punch cards. The teaching of this system cannot be done in isolation of other

bases. The understanding of other bases like eight, seven, six, etc will facilitate that of

binary system. Odili (2006) said that it is a common defect in the educational set up that

most of the subject teachers is not adequately competent in the subject (number bases

system) concerned. It is an indisputable fact that an adequate supply of competent and

subject mastery teachers is an essential ingredient for the teaching of number base(s)

system. The changes in Mathematics Curriculum are designed to improve the mathematical

skills on Nigerians in order to meet up with Millennium Development Goals of the nation.

It is hoped that if the changes are well implemented by subject mastery teachers; it would

help to solve the problem of pupils/students poor academic performance in Mathematics

and Nigeria would join the advanced economies of the world. Against this background, this

study is posed to investigate the primary school teachers‟ mastery of number base system

in UBE mathematics curriculum.

Gender issues and teachers‟ experience have been identified as potent factors

influencing students‟ achievement in mathematics. Gender is the condition of being male or

female. There are many contrasted opinions on gender related issue on performance in

mathematics. Various studies have been carried out by researchers. Studies like Ogunkunle

(2007) and Ezeameyi (2002) have reported significantly difference in favour of males by

indicating that males have higher mathematics reseasoning ability or perform better. While

others like Kurumeh (2006) and Alio (1997) reported significantly difference in favour of

females by indicating that females perform better than males. It would be interesting to

xxii

know if this also could be true of primary mathematics teachers in mastery of number base

system.

Moreover, according to Hornby (2006), experience is the knowledge and skill

someone has gained through doing something for a period of time. Various studies have

been carried out and teachers‟ experience has been reported as factors influencing teaching

and learning of mathematics contents. Harbor-Peters and Ogomaka (1991) reported no

significant difference in the mean scores of experienced teachers and less experienced

teachers on mastery of Primary School Mathematics content, while Popoola (2009)

reported that a significant relationship exists between the practice of continuous assessment

and teachers‟ experience. It is the aim of this study to find out whether there is any

difference in mastery between experienced teachers and less experienced teachers.

Statement of Problem

For decades now, teachers, parents, government and the general public have been

perplexed and disturbed immensely by the mass failure of pupils in mathematics. Primary

school teachers are trained in Colleges of Education (C.O.E.) and universities. These

teachers are trained to have good knowledge of mathematics such as Number Bases System

and pedagogical theories learned during the course of training. They are also expected to

teach the pupils effectively in mathematics especially Number Bases System. Having been

trained effectively and efficiently during their training in colleges, they have been prepared

or trained to achieve certain objectives of mathematics such as providing the child with

necessary basic skills in numeracy like Number Base System. All these are to solve the

problem of pupils‟ poor achievement in mathematics. In spite of the efforts made by

training and retraining the primary school mathematics teachers, the problem of pupils‟

xxiii

poor performance in mathematics has persisted. Pupils‟ achievement in mathematics is

poor probably due to lack of knowledge of number base.

Although, some researchers such as Harbor-Peters and Ogomaka (1991) identified

the cause of pupils‟ poor achievement in mathematics as teachers‟ lack of mastery in

mathematics contents. Parents and guardians complain bitterly about their children‟s poor

calculation at home and their poor performance in the school mathematics. Most pupils in

primary schools find it difficult to do simple basic operation such as addition of numbers,

subtraction, multiplication and division and number base system in mathematics. These

have resulted to pupils‟ poor performance in mathematics. In an attempt to solve this

problem, number base system has been implemented in primary school mathematics

curriculum. To the best of the researcher‟s knowledge, no studies have investigated the

extent of primary school teachers‟ mastery of Number Base System in UBE mathematics

curriculum. The problem of this study is to determine the extent to which the primary

school teachers have mastered Number Base System in Universal Basic Education (UBE)

mathematics curriculum. Another issue of academic concern for this study posed as a

question will be; are there any differences as regards to teachers‟ experiences, gender and

school location of teachers on primary school teachers‟ mastery of number base system in

UBE mathematics curriculum?

Purpose of the Study

This study seeks to determine the extent of primary school teachers‟ mastery of

number base system in Universal Basic Education (UBE) mathematics curriculum.

Specifically, the study aims at:

1. Determining the extent to which the primary school teachers have mastered number

base system in Universal Basic Education (UBE) mathematics curriculum.

xxiv

2. Determining the extent to which the primary school teachers have mastered

application of binary number to computer.

3. Determining the extent to which the primary school teachers‟ experiences in their

service contribute to the mastery of number base system in UBE mathematics

curriculum.

4. Determining the influence which teachers‟ gender (male and female) has on the

mean mastery scores of teachers in the Teachers‟ Mastery Test no Number Base

System (TMTNBS).

5. Determining the influence which school location (urban and rural) of teachers has

on the mean mastery scores of teachers in the Teachers‟ Mastery Test on Number

Base System (TMTNBS).

Significance of the Study

The findings of this study will be beneficial to the pupils, teachers, curriculum

planners, the government and Nigeria as a nation. To the pupils, this will result in high

academic achievement of the pupils because the teachers having mastered the number base

system will be able to impart the knowledge on the pupils. If the pupils are well taught by

their teachers, they will learn well and this will result to high academic achievement on the

part of the pupils. The pupils that have learnt number base system will be able to code

items from punch cards using 0 and 1. They can represent the combination of food they eat

in a day by binary number. They can even code names, numbers and other things. A good

desire in Mathematics could increase pupils‟ choice of science subjects in secondary

schools.

The findings of this study will be beneficial to the teachers. A primary school

teacher can deliver a lesson well to the pupils if and only if he/she has the knowledge of the

xxv

subject matter. Those who succeed in understanding the knowledge can transfer it to other

situation in their lives. For instance, the knowledge of number base system learnt in

primary school can be utilized in the secondary and tertiary institutions. The result of this

study will therefore help primary school teachers‟ master number base system and

effectively inculcate the knowledge in their pupils for a better performance in Mathematics.

This study will provide good information to most curriculum planners who consider

needs of the society. A study of this nature will help the curriculum planners to evaluate

their work, to know whether number base system is useful, both to the pupils, teachers and

the society. They will also know when to adopt or review the curriculum.

It is hoped that the finding of this study would help the government to know the

level of primary school teachers‟ mastery of number base system. This would help the

government to organise programmes suited for primary school mathematics teachers to

equip them with strategies for improving teaching and learning of number base system in

Mathematics. This package can be in form of seminars, workshops and conferences for the

training and retraining of teachers to enhance the professional competence of the

mathematics teachers. The government can also help in providing instructional materials

the teachers need in teaching number base system such as textbooks and other materials

like computer to help the pupils in fast learning.

Nigeria as a nation could equally benefit from this study. Mathematics is the pivot

on which science and technology rotates, and it is this science and technology that the

nation seriously needs. If the pupils who are future scientists and technologists are taught

well by teachers, they would likely choose pure and applied science (technology) careers

thereby increasing the nation‟s hope of achieving progress in science and technological

development.

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Scope of the Study

The following are the Number Base System to be covered;

1. Converting from base ten to base two (binary number).

2. Place value of a digit in a 2- digit or more number in base two.

3. Converting from base two to base ten.

4. Addition, subtraction and multiplication of numbers in base two.

5. Application of binary number to computer, (limited to Punch Cards)

The study was limited to primary five and six teachers in Idah Education Zone. The

choice of classes is based on the fact that teachers in these two classes are fully involved in

teaching the topic and the topic also falls within primary five and six mathematics

curriculum. The choice of this zone is based on the fact that the researcher is very familiar

with the school location and this gave the researcher opportunity to effectively monitor and

supervise the study. Idah Education Zone is made up of four zones namely; Zone 1 St.

Boniface Primary School; Zone 2 Pilot Primary School; Zone 3 Ayegba Primary School

and Zone 4 Ugwoda Primary School.

Research Questions

The following research questions guided the study:

1. What are the mean of primary school teachers that have mastery of number base

system and those that do not have?

2. What are the mean of primary school teachers that have mastery of the application of

binary number to computer and those that do not have?

3. To what extent do job experiences of teachers contribute to teachers‟ mastery of

number base system in UBE mathematics curriculum?

xxvii

4. What is the influence of teachers‟ gender on the mean mastery scores of teachers in

the Teachers‟ Mastery Test on Number Base System (TMTNBS)?

5. What is the influence of school location (urban and rural) of teachers on the mean

mastery scores of teachers in the Teachers‟ Mastery Test on Number Base System

(TMTNBS)?

Research Hypotheses

The following research hypotheses have been formulated to guide the study. Each

was tested at 0.05 level of significance.

1. There is no significant difference between the mean mastery scores of experienced

teachers and less experienced teachers in the Teachers‟ Mastery Test on Number

Base System (TMTNBS).

2. There is no significant difference between the mean mastery scores of male and

female teachers in the Teachers‟ Mastery Test on Number Base System

(TMTNBS).

3. There is no significant difference between the mean mastery scores of teachers in

urban schools and teachers in rural schools in the Teachers‟ Mastery Test on

Number Base System (TMTNBS).

xxviii

CHAPTER TWO

LITERATURE REVIEW

This chapter reviews literature related to the present study. The chapter is organised

under the following sub-headings:

- Conceptual Framework

- Theoretical Framework

- Empirical Studies

- Summary of Literature Review

Conceptual Framework

- Concept of Mastery

- Problems of teaching and learning of mathematics.

xxix

- Qualities of primary school mathematics teachers and their attitudes towards

Mathematics teaching.

- Challenges of primary mathematics for Universal Basic Education (UBE)

programme.

- Teachers‟ competencies for mathematics teaching.

- Achievement in school mathematics.

- Concept of Number Base System in UBE mathematics curriculum.

Theoretical Framework

- Jean Piaget cognitive learning theory.

- Skinner‟s Theory of learning.

Empirical Studies

- Studies on mastery and teachers‟ competences for mathematics teaching.

- Studies on Gender as a factor on Achievement in mathematics.

Summary of Literature Review

Conceptual Framework

Concept of Mastery

Hornby (2006) defined mastery as complete knowledge of something. The author

also saw mastery as having control over something. Hawkins (1995) viewed mastery as

having thorough knowledge or skill of something. Hornby (2001) opines that mastery

meant having great knowledge or understanding about a particular thing. In the context of

this study, mastery refers to someone having great knowledge; skill and understanding in

something and ability to expose the pupils to learn them. Aghamie, Ugbechie and

Ughamadu (2009) agree that the mastery of skills in mathematics (number base system)

equipped one with the ability to acquire attitude of problem solving, making relevant

xxx

judgment and then using information correctly. The authors added that it enables one to

think independently and acquire a kind of discipline of mind. Skills in number bases such

as addition, subtraction, multiplication and division are needed in farming, sewing, driving,

computer programming and even in the day to day activities of buying and selling.

Teachers‟ mastery includes all positive characteristics of the teachers. Okafor (2009)

analyzed some positive characteristics of the primary mathematics teachers that can make

them successful and enable them to achieve their objectives in the classroom. These

positive characteristics include having a thorough training and certification, more than

enough subject mastery, a thorough knowledge of methodologies, a show of competency

and capability in the teaching of the subject (number base). The author further said that

primary mathematics must be knowledgeable with facts. Their problem solving skills must

be convincing so that the pupils do not doubt their mastery. State Board for Education

Certification (SBEC), 2002) postulated that the master mathematics teacher understands

number concepts that apply to knowledge of numbers, number systems and their structure,

operations and logarithms, quantitative reasoning and the vertical alignment of number

concepts to teach the state-wide curriculum. The above literature shows standards a

primary mathematics teacher can attain to show his/her mastery level of number base

system in UBE mathematics curriculum.

It has been observed that the teaching of mathematics (number base system) in

primary schools leave much to be desired. Harbor-Peters and Ogomaka (1991) investigated

primary school teachers‟ mastery primary mathematics contents. Frequently, lack of

mastery of content was exhibited by teachers during classroom instruction. During a

teaching practice supervision of the University of Nigeria Associateship Certificate in

Education (ACE) students in 1991, the authors observed a student teacher teaching Highest

Common Factors (HCF) of numbers to an elementary class. The first observation indicated

xxxi

lack of knowledge of concept. The second showed that the teacher neither knew the

concept nor the procedure of solving such problems. The third showed lack of mastery of

concepts involved. The evidence also showed that primary school teachers did not improve

on their mastery of primary school mathematics content with increase on teaching

experience. Are these observations true of primary mathematics teachers today in the

mastery of number base system? The answer may be yes or no, but if yes who are the more

susceptible, the experienced teachers or less experienced teachers? Does teachers‟ location

school influence their mastery of number base system? These need to be determined. It

becomes necessary therefore to determine the extent to which the primary school teachers

have mastered number base system in UBE mathematics curriculum.

Problems of Teaching and Learning of Mathematics

Mathematics has been described as part of human cultural heritage and therefore, a

tool for explaining the world of space and number (Ekwueme & Onah, 2002). Mathematics

apart from being a science of quantity and space is the cornerstone in every field of

education (Alio & Ezeamenyi, 2004). It is self-creating. It is completely man-made

(Kolawole & Oluwatayo, 2005). The role of mathematics in all facets of life put

mathematics in a special place both in primary and secondary education. Mathematics is a

core subject in the curricula for school pupils and students at both primary and secondary

(Federal Republic of Nigeria (FRN), 2004). This implies that every pupil/student must

offer mathematics. This shows the importance attached to mathematics in nation-building

and technological development (Anyor & Tsue, 2006). Amoo (2002) said that the position

mathematics occupies in the National Policy on Education and its role towards

technological and industrial development put mathematics in a special place in primary

education.

xxxii

Despite the role of mathematics in national development in Nigeria, its study has

not been effective in meeting the demands of national development. Pupils‟ performance in

mathematics in both internal and external examinations is regrettably poor. Students‟

performance has not been encouraging. Nwabueze (2008) said that the reason given by the

West African Examination Council‟s Chief Examiner, (WAEC), 2001) in his report is that

teaching method is a contributing factor. The methods usually adopted by teachers seem

not to sustain the development of students‟ interest in mathematics. According to

Nwabueze (2008), the problems facing mathematics in Nigeria are mainly in its teaching

and learning and these cannot be dismissed by a wave of hand. These problems start right

from the primary school. As pupils shying away from mathematics in lower levels, so do

teachers find it hard to teach some topics in mathematics. According to Anih (2000), some

pupils develop their indifference and dislike for mathematics at early stage(s) of their

education. Such indifference, together with several other factors contributes to the very low

performance observable in many pupils.

Negative attitude of pupils to mathematics is another problem leading to the low

performance of pupils in mathematics (number base system). Anih in Obodo (1997) viewed

attitude as the way an individual feels, thinks and is predisposed to act towards some aspect

of his environment. Pupils‟ attitudes constitute problems to their grasping mathematical

knowledge. The author stated that many pupils prefer to be absent from mathematics lesson

or have irregular attendance, among others. Ochepa and Sanni (2002) observed that some

pupils often state that mathematics is difficult, abstract, a magic, like a game, not useful to

them and so on. In the teaching and learning of certain concepts which the pupils regard as

being abstract, past knowledge prevents the pupils/s students from grasping the new ones.

The success and failure of any programme depends greatly on the implementation

and evaluation of the programme. Kolawole and Oluwatayo (2005) opine that behind every

xxxiii

successful mathematics lesson, there is a good teacher. Effective teaching implies

productive result-oriented, purposeful, qualitative, meaningful and realistic teaching. For

this reason, the mathematics teachers are said to be responsible for the general education of

the pupils mathematically. Akinsola and Popoola (2004) agree that many teachers in

schools use strategies that are known to them, even if it is not relevant to the concept under

discussion. Pupils are left at the mercy of the syllabus which cannot teach but only guide

the teacher.

Certain factors have been also identified as being responsible for the problems of

teaching and learning of mathematics. These clusters of problems according to Betiku

(2000) include government–related variables, home-related variables, curriculum-related

variables, examination-related variables and textbook-related variables. Amoo (2002)

concludes that government-related variables among others are inadequate and insensitive to

the supply of facilities in schools, recruitment of unqualified mathematics teachers, delay in

payment of teachers‟ salary, insensitivity to developing teachers through training and

retaining, attendance in workshops and conference where the interaction about classroom

teaching and learning would be discussed. Other set of problems in teaching and learning

of mathematics which are in teacher-related variables; According to Usman (2002),

teachers do not know when and what concept to teach, how to make concept meaningful,

when and why pupils are having difficulty, inadequate preparation by teachers, lack of the

knowledge of the subject matter, attempt by teachers wanting to cover so many topics

within a short time, lack of requisite skills and mathematical techniques by the teachers to

develop the pupils, poor management of the class, teachers do not use instructional

materials, failure to use appropriate method of teaching and issue of population explosion

of pupils enrolment.

xxxiv

Ukeje (2000) stressed that Universal Primary Education (UPE) of 1976 failed

because teachers lacked necessary skills and competencies needed to face new challenges.

In other students-related variables, pupils are irregular in attendance and lack of interest

among others. The disadvantaged home background, poor environment background which

a child encounters as he/she leaves the school for his immediate environment, cultural

background that does not conform to the kind of sophistication that mathematics requires,

for instance exactness in measurement such as ruler, metric system contribute to problems

in teaching and learning of mathematics (Adebayo, 2000). The author viewed that

overloaded and unrealistic nature of the curriculum is also one of the problems facing

teaching and learning of mathematics. In recent past, substantial changes have been taking

place in the mathematics curriculum particularly at primary level. Changes in content have

often been accompanied by recommendations for improving the teaching of mathematics

(Badmus, 2005). Unfortunately, new curricula in Nigeria are not often given appropriate

trial-testing before full-scale adoption. Pupils do not often get the needed aids from their

predecessors because they are not familiar with the new curriculum contents such as

number base system. And sometimes teachers, whose pre-service training is at variance

with the contents and methods of the new curriculum, find it difficult to teach them

effectively to the pupils. As a result most pupils feel frustrated and develop lack of interest

in the learning topics. Given this fact that the problem of mathematics teaching and

learning in primary school depends on its effective teaching and learning, it becomes

axiomatic to determine whether mastery of number base system in UBE mathematics

curriculum by primary school teachers can enhance effective teaching and learning of

mathematics and improve pupils‟ poor academic performance in mathematics.

Qualities of Primary School Mathematics Teachers and their Attitude towards

Mathematics Teaching

xxxv

The primary school mathematics is the foundation upon which the secondary and

tertiary mathematics are built. Any problem at this level would definitely affect the whole

educational system (Ale, 2009). Hence the importance of primary school mathematics

teachers is tremendous. What the primary school teacher knows and can do would make the

future of the pupils but what he/she does not know and cannot do will be an irreparable loss

to the child. The primary school teachers should shoulder the responsibility of producing

pupils who have well-formed basic concepts in mathematics (number base) and who are

able to use these concepts to further their knowledge in mathematics. Azuka (2009) opines

that teachers are the main determinants of the quality of any educational system. This is

because upon their number, quality, devotion to duty, effectiveness and their efficiency,

depend the success and future of any educational system.

In this regard, low achievement of learners of mathematics has been attributed to

ineffective instructional skills and methodologies by primary mathematics teachers.

Teachers‟ skill remains the key figure in changing the ways mathematics is taught and

learnt in schools (Ale, 2009). This has a direct impact on the qualities of the mathematics

teacher to handle the curriculum design for this process. According to the Federal Republic

of Nigeria (FRN, 2004), no educational system can rise above the quality of its teachers.

Ogomaka (1988) and Ali (1989) are of the view that teachers‟ incompetence in the new

curriculum which makes them operate almost at the same level as their pupils is a

contributory factor to the pupils‟ poor performance in mathematics. Odili (2006), in

support of this observed that there is a general decline in the quality of teachers produced in

Nigeria over the last sixteen years. Therefore, it is necessary to note that there are qualities

that anyone called a mathematics teacher will have and with appropriate mathematical

background can develop many requisite skills for mastering the art of teaching

mathematics. To achieve effective teaching;

xxxvi

- teachers must know the stuff,

- they must know the pupils whom they are stuffing

- they must know how to stuff them artistically (Max cited in Ale, 2009; 5).

The author further said that mathematics teachers should be effective and efficient in

understanding the various activities they find themselves doing in the school. They must be

creative; ones full of initiative, readily able to convert impossible situations to

advantageous ones, readily produce improvised teaching materials and can show

knowledge of teaching in the three domains of learning. They must acquire skills and

competencies in mathematics teaching generally. They must have mastery in the subject

they teach such as number base system. Good primary mathematics teacher must work on

the motivation of pupils in the study of mathematics. They must become proficient in the

use of innovative methods and strategies in the presentation of school mathematics topics

such as number base system. Kekere (2009) postulates that primary mathematics teachers

must not be harsh on pupils but show love and concern for pupils. They must be friendly so

that the pupils will develop interest in the subject. Ukeje in Azuka (2009) points out that

teaching is more than transmitting facts and information. The author continues that:

A poor teacher tells.

An average teacher informs.

A good teacher teaches.

An excellent teacher inspires.

The above shows the importance and qualities of primary mathematics teachers.

Despite the importance of primary school mathematics teachers as the key figure in

changing the ways mathematics is taught. The primary school mathematics teachers‟

attitude towards mathematics teaching is inadequate. The most useful characteristics of

successful mathematics teachers are their interaction with pupils and their attitudes towards

xxxvii

the subject they teach. According to Peskin (1994) the best achievement occurs in the

classes of mathematics teachers who demonstrate knowledge of subject-matter, positive

attitude towards their subject, who prepare and present their lessons well and whose

mathematics pupils can transfer the knowledge to another situation.

Kankia (2008) defined attitude as the way an individual feels, thinks and is

predisposed to act towards an aspect of the environment. Obodo (2001) commented that the

way Nigerians feel, think and act towards mathematics influences greatly mathematics

education in Nigeria. The negative attitude of mathematics teachers affects pupils‟ attitude

towards the subject. The author observed that the behaviour of most primary mathematics

teachers deviate from expected normal behaviour of teachers. They tend to exhibit very

queer characteristics which scare many pupils away from studying mathematics. Some

primary mathematics teachers create the impression to the pupils that mathematics is

difficult and not meant for everybody to study except for those with exceptional

endowment like themselves who can teach the subject. Others do not give adequate

corrections to mathematics assignments while still others do not mark exercises or

assignments given to pupils. It is a well known fact that modelling is a way of learning.

Pupils model their mathematics teachers‟ Behaviour for effective learning and where

teachers‟ behaviour or attitude does not promote effective learning in mathematics (number

base) it will result to pupils‟ low performance and poor achievement in mathematics. In

support of this, Tahir (2005) stated that the quality primary mathematics education would

depend on the quality and attitude of primary mathematics teachers because what pupils

learn is directly dependent on what and how the primary mathematics teachers teach, which

in turn depends on their knowledge, skills, competence and commitment. The pupils‟

success or failure in mathematics is completely in the teachers‟ hands (Okafor, 2009).

xxxviii

In view of the above literature, the good qualities of primary school teachers such

as mastery of subject matter (number base system) and positive attitudes are considered as

possible components for improving classroom instruction in mathematics. With these good

qualities such as mastery of subject matter by the teachers, pupils‟ high academic

performance can be best achieved. The researcher finds it necessary to determine the extent

to which primary school teachers have mastered Number Base System in UBE

mathematics curriculum.

Challenges of Primary Mathematics for Universal Basic Education (UBE)

Programme

The Universal Basic Education (UBE) programme covers primary and junior

secondary school up to JSS 111 which now forms the basic education sector. Ene (2007)

stated that one of key elements in achieving the UBE success is the primary school

teachers. One of the challenges facing Universal Basic Education programme is persistent

poor performance in primary mathematics in Nigerian schools. Mathematical Association

of Nigeria (MAN) has stepped into the matter. Ale (1989) entitled its 1989 Silver Jubilee

conference, “War against Poor Achievement in Mathematics (WAPAM)”. In spite of

WAPAM, however, poor achievement mathematics persisted until Ale (2003) in his

capacity as Director of National Mathematics Centre, Abuja, launched Mathematics

Improvement Programme (MIP). Other eminent scholars have expressed great concern

about the disheartening poor performance in mathematics in Nigerian schools and the

frustration it has brought to our youths (Amazigo, 2000 & Animalu, 2000). According to

Ibuot (2000: 5), a leading teacher Okubodejo commenting on the frustrating situation in

Nigerian schools has this to say:

„Government has not been happy with the performance of

students in mathematics in recent times because of students‟

poor performance. Mathematics is the bedrock of the

xxxix

sciences and technology. Without mathematics it would be

difficult for the nation to move forward.‟

Another challenge that is facing the primary mathematics for Universal Basic

Education (UBE) programme is the effective mathematics curriculum implementation in

primary schools. Effective curriculum implementation involves qualitative teaching which

requires qualified teachers to handle mathematics content (number base system) in primary

school. In view of this, Usman (2003) stressed that effectiveness of curriculum process

depends largely on the availability of both human and material resources. According to

Kojigili, Tumba and Zira (2007), many factors militating against the effective

implementation of mathematics curriculum in the primary school as identified by the

teachers are as follows;

- The constant curriculum changes.

- Lack of funding of school by the government.

- Teachers‟ attitude to mathematics and their inability to cope with efficient handle of

mathematics.

Iji (2007: 21) in his paper on “challenges of primary school mathematics for

Universal Basic Education (UBE); the following are considered as the challenges the UBE

pose to the primary mathematics;

Teachers of primary mathematics require cognitive, affective and psychomotor

competencies.

Creative approach must necessarily be adopted in the teaching of primary

mathematics since the target population has different and peculiar environments.

Vocational mathematics must necessarily be included in the on-going curriculum

restructuring of the UBE.

The mathematics curriculum and the activities contained in it must be to the

teacher‟s companion.

xl

There should be a renewed interest by mathematics educators in research in the

teaching and learning of mathematics.

There should be sufficient training for primary mathematics teachers in pursuant for

the special requirements of mathematics teachers.

.The challenge of more pupils with weaker skills in mathematics demands that

mathematics educators must evolve newer methods that will meet with today‟s

problems.

Other challenges of primary mathematics for Universal Basic Education (UBE)

programme largely bother on finance are qualified teachers, size of the UBEP,

infrastructures, adequate supervision and monitoring, instructional materials, walking

distance from home to school and funding (Ajayi, 2007) Several studies have shown that

UBE is under funded (Maduewesi, 2001 & Nwagwu, 2004). The challenges of UBE earlier

above are indicators of inadequate funding of the UBE programme. To allocate and release

funds is one thing and to make judicious use of it is another. All these are anchored on

inadequate funding of the programme. Poor management of fund and lack of accountability

further compound the challenges of primary mathematics for Universal Basic Education

(UBE) programme. These may be the cause of persistent pupils‟ poor performance in

mathematics. From the literature review, it becomes necessary to find out whether these

challenges influence teachers‟ effective teaching with regard to their mastery in number

base system in UBE mathematics curriculum.

Teachers’ Competencies Mathematics Teaching

The complex nature of mathematics teaching in primary school requires that very

competent teachers should guide the learning activities at this level. Hornby (2001) defined

competence as the ability to do something well. Teachers‟ competency is very vital in the

xli

teaching and learning of mathematics. The curriculum at primary school level is both pre-

vocational and academic (FRN, 2004). Therefore, teachers with sufficient exposure and

training in both content and pedagogy are required. It is understandable that the problems

and learning difficulties experienced by pupils in mathematics(number base system) must

have had influencing factors like bad teaching, lack of appropriate instructional materials,

interest, attitude and lack of positive teacher characteristics (Okafor, 2009).

The issue of teacher competency and effectiveness in mathematics has been one of

the orchestrated problems in mathematics education. Begle (1997) discerned that teacher-

variable in mathematics education include knowledge of mathematics, teacher

effectiveness, teacher competencies, teacher effective characteristics and teacher training

programmes. The author emphasized that unless teachers can compatibly guide the learning

process of pupils, their subject matter mastery would be floored by poor achievement

arising from that faulty interaction.

A number of competencies are aimed at during the professional training of teachers.

Once teachers are certified by the appropriate authority, it is assumed that these

competencies have been attained. Muhammad (2002) conducted a study on assessing

competency level of Pakistani primary school teachers in mathematics and pedagogy. The

result of the study showed that primary school teachers had a low level of competency in

mathematics. Gender was found to be a significant indicator in the study that the

competency level of female teachers was lower than their male counterparts. Obioma and

Ohuche (1983) investigated on how primary school teachers perceived their mathematics

competencies. The result of the study indicated that the teachers claimed to be competent

only in number and numeration and basic operations. According to Farrell (1979), no

mathematics educator minimizes the complex problem of preparing teachers, who do teach

mathematics better. Harbor-Peters and Ogomaka (1991) state that a fundamental

xlii

assumption of teacher education is that the teachers should nave learned more of their

subject than the material which they teach. The author further said that if the primary

school teachers have competence only in some aspects of the mathematics content they are

supposed to teach; then this a violation of the fundamental assumption made on primary

school teachers. This is applicable to mathematics teaching and learning in Nigeria.

A competent mathematics teacher will be a teacher with good academic and

pedagogical backgrounds, who is not easily won out by the “system” (Sizer, 1984). Based

on this terse definition, (Farrell in Fajemidagba, 2007) derived the indicators of teachers‟

competency in mathematics teaching and learning. The two types of competencies were

identified by Farrell namely mastery types and developmental types. It was suggested that

the first type of competency is a specific capability that primary school mathematics

teachers should certainly possess. Farrell (1984) cautioned the over-use or abuse of the

mastery-type of teacher competency. Farrell (1979) listed the indicators of mathematics

teachers‟ competencies as follows;

-Teacher gives history, etymology of terms and symbols.

-Teacher explains why (e.g. graphing) techniques are being taught.

-Teacher correctly indicates the “why” of certain conventions in mathematics.

-Teacher uses counting and measuring examples before a formula is developed and

point out the usefulness of the formula.

The developmental type of competency calls for a balance between the subject

matter knowledge of mathematics and the pedagogical component of mathematics teacher

education programme. Ivowi cited in Audu (2006) is of view that the teachers‟

competencies are in the following areas; subject matter, pedagogy, skill process,

resourcefulness, behaviour motivation and evaluation. Since teachers‟ competencies

emphasize proper understanding of concepts among other attributes; unless teachers can

xliii

competently guide the learning process of pupils, the subject mastery would be floored by

poor achievement arising from that faulty interaction.

From the above literature review, it is found that competencies call for teachers‟

ability to solve problems and a balance between the subject matter knowledge of

mathematics and the pedagogical component of mathematics. No mathematics teacher can

be competent in his/her subject matter (number base system) without mastery the subject.

Given the fact that teacher‟s competencies can influence the pupils‟ performance in

mathematics and the result of Obioma and Onuche (1983) work may be a humble claim on

the part of the primary school teachers. It becomes necessary therefore to verify the truth of

their claim through investigating mastery of number base system in UBE mathematics

curriculum by primary school teachers.

Achievement in School Mathematics

Achievements in this content refer to the cognitive achievement of pupils that can

be measured in terms of passes in mathematics tests or examination that would be

administered by the teacher or examination bodies. In line with this, Sofolahan (1986)

states that when a learner accomplishes a task successfully, reaches a set goal for learning

experiences, he/she is said to have achieved something.

For the past decades, mathematics education in this country is in a sorry situation.

There has been so much concern and outcry from many quarters about the poor

performance of pupils/students in mathematics. This poor performance is best observed

from chief examiners of WAEC report from (2002-2004). This shows that students‟

achievement at credit pass has never reached 50% (Kurumeh 2006). Some research reports

show that achievement in mathematics has continued to be low. Kurumeh (2006) also

pointed out to the Nigerian secondary school students‟ poor achievement in ordinary level

mathematics examinations over a decade now cast doubts on the country‟s hope of higher

xliv

attainment in science and technology. A study conducted by Maduabum and Odili (2006)

on students‟ performance in General Mathematics at senior school certificate level in

Nigeria over a period of twelve years (1991-2002) has confirmed students‟ poor

achievement in mathematics. These situations call for some investigation in order to

address the problems of mathematics education in Nigeria.

The students‟ performance in Senior Secondary Certificate Mathematics

Examination has remained very low as many of the candidates scored zero or marks within

zero range. Aburine (2003) observed that the standard of mathematics teaching in Nigeria

is low and identified teaching problems as one of the root causes of poor achievement in

mathematics. Some renowned educators have always pointed accusing fingers to some

other reasons for the pupils/students‟ poor performance in mathematics. Such educators

include Eraikhuemen (2003) who noted that students dislike certain topics in mathematics

because they feel that the topics are difficult and cannot be understood easily. Some

teachers also believe that these topics are difficult and are not easy to teach. Some teachers

experience difficulties in achieving effective teaching in school system. Harbor Peters,

(2002) and Ali, (1989) are of the view that teachers‟ incompetence in the new curriculum

which made them to operate almost at the same level with their pupils/students is another

contributing factor (Harbor-Peters, 2002 & Badmus, 2002) These foster negative

achievement of mathematics at the primary and secondary schools.

Many researchers have made efforts to approach the problem of pupils‟ poor

achievement in mathematics in many ways to improve this poor performance in

mathematics. Bala and Musa (2006) the effect of the use of Number Base Game,

Ogunkunle (2007) the Effect of Gender on the Mathematics Achievement of students and

students still failed massively in mathematics. Achievement in mathematics has been

consistently low and unimpressive. With this consistent poor performance in mathematics;

xlv

however, no research work to the best of the researcher‟s knowledge has been done on this

dimension such as mastery of number base system by primary school teachers to facilitate a

change in pupils‟ low achievement in mathematics. This study focuses its attention on

primary school teachers‟ mastery of number base system in UBE mathematics curriculum.

Concept of Number Base System in UBE Mathematics Curriculum

The restructured National Mathematics curriculum for the primary and junior

secondary school is focused on giving the pupils the opportunity to acquire mathematical

literacy to function in an information age; also to cultivate understanding of the skills

necessary for the changing technology (Ekwueme, Meremukwu & Uka, 2009) The authors

define curriculum as a teaching guide that provides maximum aids both the teachers and

the pupils. Badmus (2002) defined curriculum as the set of experiences planned to

influence learners towards the goals of an organization. Organization here refers to both

schools and many other situations for which courses may be run. The curriculum tries to

make mathematics more of real life than abstract concept and advocates training and re-

training of mathematics teachers to update their technology, competence and acquire more

teaching skills (Ekwueme & Meremukwu, 2008). The new National Mathematics

curriculum is for the Basic Education Programme beginning from Basic 1 to 9,

hierarchically arranged. In this new curriculum, there is neither Primary Mathematics

curriculum nor Junior Secondary curriculum. The two levels of education (primary1-6 and

JS1-3) have been infused into Basic1-9 (Ojo, 2009). Pupils are expected to continue their

education from Basic one to Basic nine without interruption.

In the primary school curriculum, number bases fall under number and numeration.

The meaning of number and numeration is usually confused by many including the

teachers of mathematics. Hornby (2001) defines number simply as an idea or concept of a

quantity. For instance, the number two (2) represents the quantities that are two e.g. two

xlvi

boys, two cows, two Naira etc. But different cultures have different ways of representing

two. Our forefathers used strokes // to represent two. Some even used objects. But the

Arabs represent two with symbol 2 while the Romans represent two with symbol ii. These

symbols used to represent numbers are called numerals. Hence one talks of Arabic and

Roman numeral.

Number bases simply means grouping of numbers. Azuka (2007) has the view that

number bases are simply system of counting or grouping of numbers. Pupils are very

familiar with base 10 where numbers are grouped in ten.

12 = 1ten + 2units = 10 + 2

25 = 2ten + 5units = 20 + 5

127 = 1hundred, 2tens and 7units = 100 + 20 + 7

Recall that place values are simply power of 10, just as one counts or grouping tens

one can also count in other number bases such as 2, 3, 4, 5, 6, 8, 12, etc. Number bases can

be introduced in the classroom using counters.

Azuka (2009) states that numbers are written in base two are called binary numbers.

Just as one counts or groups objects in base 10, one can also count in base 2. The only

digits in binary system are 0 and 1. Counting in base two can be done using concrete

materials. Thus, the place values of digits in base two are simply the powers of 2. The

author further explained the conversion of binary number to base ten giving this example:

10102

2 2 2 2

1 0 1 02

= 1 x 23 + 0 x 2

2 + 1 x 2

1 + 0 x 2

0

= 8 + 0 + 2 + 1

= 1110

xlvii

These help to explain the conversion of numbers in base two to base ten and vice versa.

The tabular representation below will help to explain the conversion of numbers from base

10 to base two by continuous division and bringing out the remainders in a vertical form.

For example, Convert 810 to base two.

(i) 810 = ( )2

2 8 R 0

2 4 R 0

2 2 R 0

2 1 R 0

2 0 R 1

810 = 10002

Just as one operates numbers in base 10, one can also add, subtract and multiply in base

two. But one needs to understand and remember the following identities.

Addition

0 + 0 = 0, 1 + 0 = 1

0 + 1 = 1, 1 + 1 = 10

Multiplication

0 x 0 = 0, 1 x 0 = 0

0 x 1 = 0, 1 x 1 = 1

Example1: 1012 + 1112

(a) 11

10 12

+ 1 1 12

11 0 02

Example11:

10112 x 112

xlviii

1 0 1 12

x 1 12

1 0 1 1

+ 1 0 1 1

1 0 0 0 12

Subtraction

Example111; 101002 - 1012

(a) 1 0 1 0 02

- 1 0 12

1 1 1 12 (Mathematical Association of Nigeria (MAN), 2006)

Punch cards are used to store information about people or things. They use binary system

of a hole punched out (O) or a slot cut out (U). The figure below shows the food taken by

Udoka John.

O U U O

Rice Yam Garri Beans

Name: Udoka John

Class: 5A.

In records of food eaten by pupils in a day, punch card shows that Udoka John eats yam

and garri and not rice and beans.

If 1 represents the food eaten and 0 the food not eaten; each possible combination of food

eaten in a day can be re presented by a binary number (Azuka, 2009).

Binary numbers are also used for coding computer programs. In this case letters A = 1, B =

2, C = 3, D = 4… Z = 26. But the numbers are also converted to binary numbers (Azuka,

2002).

Letter Base Binary Number

xlix

A 1 00,001

B 2 00010

C 3 00011

D 4 00100

E 5 00101

- - -

- - -

Z 26 11010

This is used by some examination bodies as pupils/students‟ code their names and other

relevant information (Azuka, 2007).The binary system is important as it is applied in

computing including punch cards and binary code system. Against the above review and

the usefulness of number bases especially binary number in this computer age in solving

mathematical problem. Maybe teachers‟ mastery number base can improve pupils/students

low performance in mathematics. It becomes necessary to determine the extent of mastery

of number base system by primary school teachers in UBE mathematics curriculum.

Theoretical Framework

Jean Piaget’s Cognitive Learning Theory

The first theory backing up this study is Piaget‟s theory of learning. Piaget spent 30

years in studying the nature of children‟s concept and thus indicated that cognitive

development proceeds through an orderly sequence of stages. The author stated that the

basis of learning is the child‟s own ability as he/she interacts with his/her physical and

social environment. Piaget also observed that certain periods are critical in the child‟s

mental development and they have to be considered during curriculum planning.

l

The developmental stages of cognitive growth in Piaget according to Selah (2008)

consist of:

1. Sensory-motor stage (Birth-2years): During this stage; the infant learns by means of

his/her senses and manipulation of objects. Actions are the only form of

representation of child‟s thought.

2. The pre-operational stage (2-7years): This consists of pre- conceptual thought

period (2-4years) and the period of intuitive thought (4-7years). During pre-

conceptual thought period, the child demonstrates that he/she is capable of

extending his world beyond here and there by imitation and other forms of

behaviour. During the period of intuitive thought, the child uses concepts as stables

generalization of the past and present experiences. His reasoning is not logical. He

depends on imitation rather than systematic logic.

3. The concrete operational stage (7-11years): In this stage, there exist some logical

inconsistencies in the thinking process of the child. He/She prefers concrete objects.

He/She has started formal schooling and deals with the world, things and events.

The child begins to acquire concepts of numbers, length, weight and volume and

deals with concrete facts.

4. The formal operational stage (11years and above): During this stage, the thought

process of the child now becomes systematic and reasonably well-integrated.

He/She is able to transfer understanding from one situation to another and indicates

a particular orientation to problem solving. The hallmark of formal operational

period is the development of the ability to think in systematic terms and understands

content meaningfully without the help of physical objects even visual or other

imagery which are based on past experiences with such objects (Obodo, 1997).

li

Piaget‟s mental theory has a lot of implications on teaching and learning of

mathematics. Since the child‟s mental development advances qualitatively through

different stages, these stages should be considered when planning the mathematical

experiences of a child at any given age. There should be first experiences which he/she is

ready for, in view of the mental stage growth of which the child has attained. This theory

should be of great help to teachers in preparing the pupils to the next stage. A topic should

neither be taught too early or too late. Physical action is a base for active learning. Active

learning implies the strategies where the pupils touch, feel, participate, discover, reason,

deduce and infer facts and ideas in the learning process (Azuka,2009).Learning is not a

spectator sport. For pupils to learn effectively, teachers are to use teaching strategies which

enable pupils to actively participate in the lesson and discover things for themselves. The

most important concern of the mathematics teachers should be in designing of experiences.

The primary mathematics teachers who have mastery in number base bear child‟s mental

development stages in mind in designing the learning experiences which give the pupils

opportunities of performing desirable mental operation at their stages of development. In

teaching of mathematics, the general principle is “things before ideas and ideas before

words” (Ukeje, 1979).

Skinner’s Theory of Learning

The second theory backing this study is the Operant Conditioning Theory of

learning by Skinner. Operant Conditioning learning is the type of learning in which a

voluntary response is strengthened or weakened, depending on favourable or unfavourable

consequences (Skinner in Agboeze, 2009). Skinner becomes interested in specifying how

behaviour varied as a result of alterations in the environment. The author called the process

that leads to some certain behaviours reinforcement. Skinner developed a system of

lii

learning known as Programmed Instruction that has great impact on teaching and learning

process in recent years all over the world, (Chauhan in Obodo, 1997). This theory has two

major concepts and both concepts are very interesting because they are all about repeating

or withdrawing from certain behaviours.

Reinforcement is the process by which a stimulus increases the probability that a

preceding behaviour will be repeated. According to Skinner, reinforcer is an event that

increases the rate of responding. It can be positive or negative reinforcer. The author was of

the view that certain behaviour would reoccur if psychological, physical and emotional

needs are provided. Skinner further explains that punishment decreases the probability of

the previous behaviour reoccurring again. Punishment often presents the quickest route to

changing behaviours but if allowed to continue might be dangerous to children.

The implications of this theory on mathematics teaching and learning are as

follows: Mathematics teachers have to make rewards (reinforcement) upon the knowledge

they want pupils to gain in learning mathematics. They can reinforce desired behaviour in

mathematics class by showing approval (e.g. nodding the head, smile or even telling the

pupils/students to clap for the achiever) to correct attempts in mathematics. Healthy

attitudes can be built up for mathematics learning by setting up incentives to be awarded to

learners who attend mathematics classes regularly and participate actively or to the best

mathematics pupils in the class.

Empirical Studies

Studies on Mastery and Teachers’ Competencies for Mathematics Teaching

Not much study has been done in connection to mastery in science education

particularly in mathematics. Harbor-Peters and Ogomaka (1991) conducted a study on

survey of primary school teachers‟ mastery of primary school mathematics content. The

population consisted of primary school teachers in Imo and Anambra States with a

liii

purposive sampling consisting of 700 primary school teachers from Imo and Anambra

currently attending Sandwich Programme in University of Nigeria, Nsukka. The instrument

used was Primary Mathematics Content Mastery Test (PMCMT). Z-test statistics was

use to analyze the test at 0.05 level of significance. The findings of the study showed that

primary school teachers have no adequate mastery of primary school mathematics content.

It was also found that increase in experience have no significance difference on primary

school teachers‟ mastery of primary school mathematics content.

In another study, Harbor Peters and Ogomaka (1986), using the same instrument

investigated whether teachers trained within given periods has mastery of the current

mathematics content. 420 primary school teachers from Anambra and Imo States were used

for the study. The result findings indicated no mastery by all the defined groups. This still

exposes primary school teachers as a “generalist” - teaching all school subjects in one class,

which does not make for effective mathematics curriculum implementation.

Lassa (1978) conducted a study on the training received in mathematics by grade

two teachers. This study was carried out on prospective teachers in 6 northern states of

Nigeria. The study among others investigated the academic preparation in mathematics of

prospective primary school teachers on the mathematics they would be called upon to

teach. The study indicated that these prospective primary school teachers knew only 53

percent of the mathematics content they were required to teach.

From the reviews above, it is very clear that mathematics educators are much

concerned with a change in mathematics instruction. The studies above made use of

prospective teachers, is it not likely that practicing teachers do improve in their mastery of

the mathematics content such as number base system while on the job? This needs to be

ascertained. It becomes necessary to determine the extent to which primary school teachers

have mastered number base system in UBE mathematics curriculum.

liv

Mastery of mathematics concepts may play major role in determining

competencies. Researchers in mathematics education in Nigeria have their attention on the

content of mathematics with regard to the competencies of teachers in mathematics

teaching. Muhammad (2002) in his study investigated the competency level of primary

school teachers in disciplines of science, mathematics and pedagogy. The sample

comprises 1,800 randomly drawn Primary Teachers Certificate (PTC) teachers working in

different state primary and middle/ elementary schools of 22 districts of the Punjab

province. The competency was determined by developing standardized achievement tests

in each of three subjects. The results show that teachers have a low level of competency in

all these areas. On average, their achievement rate remained 30.8 percent in mathematics,

34.1 percent in science and 39.2 percent in pedagogy, even below the minimum set

criterion of 40 percent against each subject. Gender was found to be a significant indicator

in the study that the competency level of female PTC teachers was lower than their male

counterparts.

Ohuche and Obioma (1983) conducted a study on how primary school teachers

perceived their mathematics competencies. The study made use of 130 practicing primary

school teachers in Imo and Anambra States of Nigeria. The result of the study indicated

that the teachers claimed to be competent only in number and numeration and basic

operation. These researchers confirmed the importance of teachers‟ competencies for

mathematics teaching. It is also necessary to investigate the extent of primary school

teachers‟ mastery of number base system in UBE mathematics curriculum.

Bahru (2005) conducted a survey research on teachers‟ competency in the teaching

of mathematics in English in Malaysian secondary schools. A sample of 575 teachers was

used in the study. The instrument for data collection was questionnaire which comprised of

structured items to elicit information with respect to facts, perception, opinion and attitudes

lv

the teachers towards PPSMI were administered to the teachers. The data were analyzed

using Statistical Package for Social Sciences (SPSS) software. The findings revealed that

the implementation of teaching of mathematics in English in schools was at satisfactory

level (53.4%).The respondents also agreed that they have improved their command of the

English Language and that their level of confidence to teach mathematics in English have

also improved.

From the above studies reviewed, it is noted that none of these researchers have

investigated the influence of teachers‟ competency on primary school teachers‟ mastery of

number base system in UBE mathematics. This study tries to investigate that.

Studies on Gender as a factor on Achievement in Mathematics

Gender is the condition of being male or female. There have been different opinions

on gender as a factor on achievement in mathematics. Many studies have been carried out

to ascertain whether or not the gender influence academic achievement in mathematics.

Differences in opinion abound as regards this gender differentiation. Some eminent

scholars are of notion that the male students are significantly superior to their female

counterparts in academic performance.

Maduabum and Odili (2007) who studied the trends in male and female students‟

performance in senior school certificate further mathematics in Nigeria. The sample

consisted of all students who entered for senior secondary certificate examination (SSCE)

in further mathematics in Nigeria from 1999 to 2005.The design adapted was an ex-post

facto design. The population was a total of 1, 02,502 candidates (males = 82,149; females =

20,353). Data were collected from the statistical records of the West African Examination

Council (WAEC) Headquarters, Lagos. Result indicated that male attained higher

percentage scores at credit level than their female counterparts in each of the seven –year

period survey and performed significantly better.

lvi

Ezeameyi (2002) studied the effect of game on mathematical achievement, interest

and retention of Junior Secondary students in Igbo- Etiti Local Government Area,

purposefully sampled two secondary schools 221 (JS11) students by random sampling. The

data collected were analyzed using mean, standard deviation and ANCOVA. The findings

revealed that the male students benefited more than their female counterparts.

Some other researchers have conflicting views in their findings. Such findings favoured

females more than males. For instance, Alio (1997) studied Polya‟s problem solving

strategies in senior secondary students‟ achievement and interest in Enugu State, sampled

320 students purposively. The data were analyzed using mean, standard deviation and

ANCOVA. The findings revealed that the females enjoyed the strategies more than their

male counterparts.

Kurumeh (2006) investigated the effect of ethno mathematics approach on students‟

achievement in mathematics in geometry and mensuration. The population of the study was

200 junior secondary one (JSS1). The design of the study was experimental. The

instrument used for data analysis was Mathematics Achievement Test on Geometry and

mensuration (MATGM).The result revealed that female students benefited more

significantly than their male counterparts. Kurumeh (2006) agreed with Alio (1997) that

females are superior to males in achievement.

Still some other researchers held neutral opinion of how gender makes no

differentiation as regards to performance of students. Galadima and Yusha‟u (2007)

investigated the mathematics performance of senior secondary school students in Sokoto

State. A sample of 368 was involved in the study, comprising of 187 males and 181

females. The instrument adapted for the study was standardized test constructed and

validated in Malaysia. Percentage, means, standard deviation and One-Way analysis of

variance (ANOVA) were used to analyze the data at 0.05 level of significance. The result

lvii

of the study revealed that there is no significant difference between the group means of

males and females.

Eke (1991) investigated the effects of target task and expository on the performance

and retention of SSI students in learning number and numeration. The author used

purposive sampling technique to sample 120 students. Means, standard deviation and t- test

statistics were used to analyze the data. The findings revealed that male and female

students benefited equally, showing that gender is not a factor in achievement in

mathematics.

From the reviews above, the researcher observed that different stands emanating

from their studies as regards gender differentiation students‟ achievement in mathematics.

This may be applicable to primary school teachers. It is the aim of this study to find out

whether there is any difference in the mastery of male and female teachers in number base

system in UBE mathematics curriculum.

Summary of Literature Review

From the literature review, it can be deducted that the teaching of mathematics

(number base system) leaves much to be desired. Several researchers have observed that

teachers‟ mastery of mathematics contents is a potent positive characteristic for primary

mathematics teachers in teaching of mathematics contents.

The literature review has equally shown that good qualities of primary school

mathematics teachers and positive attitudes are considered as components for improving

classroom instruction in mathematics. The literature review revealed some challenges of

UBE which embodied on lack of fund to sponsor the programme such as training and

retraining of teachers, recruitment of qualified teachers and provision of infrastructure

among others. Therefore, will these challenges influence teachers‟ effective teaching with

regard to their mastery in number base system in UBE mathematics curriculum?

lviii

Jean Piaget‟s cognitive theory and Skinner‟s theory of learning were reviewed as

regards to their relationship with the present study. Piaget‟s theory revealed that the basis

of learning is the child‟s own ability as he/she interacts with his physical and social

environment and from birth progresses through cognitive development stages. This implies

that mathematics teachers should identify the development levels so as to help pupils to

have permanent knowledge of what is taught at each level. Skinner‟s Operant learning

theory revealed that Conditioning Learning is the type of learning in which a voluntary

response can be strengthened or weakened depending on favourable or unfavourable

consequences. Therefore, mathematics teachers knowing this fact should help them to

reinforce the behaviour in the learner which they want to repeat and negatively reinforce

the behaviour they do not want to repeat in the learner. Also, gender has been identified as

an important factor on achievement in mathematics. Studies have shown that contrary to

general belief that males achieve more in mathematics than females. Some studies showed

that males and females achieve equally. Some studies even showed that females achieve

more. Based on this contradiction, this study will check whether there is any difference

between male and female teachers in mastery of number base system in UBE mathematics

curriculum. The study also aims at finding out whether teachers‟ experiences and school

location of teachers have any significant differences in teachers‟ mastery of number base

system.

lix

CHAPTER THREE

RESEARCH METHOD

This chapter is organized under the following sub-headings namely: design of the

study, area of the study, population of the study, sample and sampling techniques,

instruments for data collection, validation of the instruments, reliability of the instruments,

method of data collection and method of data analysis.

Design of the Study

The design for this study was a descriptive survey design. Descriptive survey design

is employed in studies designed to describe the characteristics or attributes of primary

school teachers with respect to mastery of number base in the new curriculum. This design

was adopted because it merely sought to find out and describing events as they were,

without any manipulation of what caused the events or what was being observed.

Area of the Study

The study was carried out in Idah Education Zone in Kogi State. This included all

primary schools approved by the Ministry of Education.

Population of the Study

lx

The population of this study consisted of primary five and six teachers both males

and females teachers in urban and rural primary schools in Idah Education Zone. There

were 57 primary schools and 114 primary five and six teachers within Idah Education Zone

in Kogi State. (Source: LGEA Office Idah of Planning Research and Statistics, (PRS) unit,

2008/2009).

Sample and Sampling Techniques

The sample for the study was made up of 40 primary five and six school teachers.

Multi-stages sampling technique was employed to select the sample. Firstly, simple random

sampling technique by balloting was used to select 20 schools from 57 schools in Idah

Education Zone that was used for the study (See Appendix A).

Secondly, purposive sampling technique was also used in drawing one male and

one female teacher from each of the selected 20 schools in urban and rural schools in Idah

Education Zone. The consideration that guided the purposive selection was that only the

schools that had male and female teachers either in primary five or six were selected in

urban and rural schools which were useful for this study.

Instrument for Data Collection

The instrument for this study is Teachers‟ Mastery Test on Number Base System

(TMTNBS) developed by the researcher. TMTNBS was used as a mastery test to determine

the extent to which primary school teachers have mastered Number Base System in UBE

mathematics curriculum. It consisted of two sections A and B. Section A of the instrument

contained personal information of respondents. The personal information of the

respondents was designed to elicit personal information about each respondent such as sex,

class, years of experience and location of schools.

lxi

Section B of the instrument contained test which was developed following the table

of specification/test blue print on Appendix F. The TMTNBS consisted of 25-essay type

test items covering primary school mathematics content, specifically Binary Number

System which included conversion of numbers in base two to base ten, place value of a

digit in a 2-digit or more numbers in base two, conversion of number in base ten to base

two, addition, subtraction and multiplication in base two and application of binary number

to computer (limited to punch cards) (See Appendix E). Out of the 25 questions, 11 were of

higher cognitive process and 14 were of lower cognitive process.

Validation of the Instrument

The instrument TMTNBS was subjected to content and face validation. The content

validation TMTNBS was ensured through strict adherence to the table of specification

attached. The test blue print and scheme of work for primary five and six were also

validated by experts in Mathematics Education and Measurement and Evaluation in

Department of Science Education from University of Nigeria, Nsukka.

The face validation of the instrument was also done by three experts and one

experienced graduate teacher of Mathematics Education. The experts were from

Department of Science education while the teacher was from University Primary School,

Nsukka. After the validation of TMTNBS, the 25 items were all accepted for the study.

However, the comments and suggestions made independently by the validators were

reflected for the final production of the instrument.

The test items TMTNBS were subjected to item analysis. They were found to have

difficulty index of 0.30 to 0.80 and discrimination index of 0.20 to 0.80. These indices are

considered high, so they are good to use for this study. This is because Aiken (1979) is of

lxii

the view that test item having difficulty index of 0.20 to 0.80 or discrimination index of

0.20 or above is usually considered acceptable or else it will be discarded or revised.

Reliability of the Instrument

The reliability coefficient of the instrument (TMTNBS) was determined after trial

testing. The trial test was carried out at Nsukka Urban Central which is not part of the study

area. Twenty copies of the instrument were distributed to 20 primary five and six teachers

from five primary schools and four- four teachers were selected from each school.

The data collected from the trial test were used to ascertain the reliability coefficient

of TMTNBS using scorer reliability approach. The scorer reliability coefficient of

TMTNBS was 0.897 (See Appendix H for computation).

Method of Data Collection

The researcher visited the twenty (20) primary schools involved and the set of

teachers concerned. The test was administered on the primary5 and 6 teachers in each of

the selected schools with the help of two research assistants. The research assistants

assisted the researcher in the distribution and collection of the instrument from all the

schools selected. They were also instructed on distribution and collection of the instrument.

This was because the schools were far from each other and the researcher could not collect

all the data alone.

Method of Data Analysis

The collected data were analyzed using mean ( X ) and standard deviation (S.D)

in order to provide answers for the research questions. The bench mark for complete

mastery is 80% and above on a mastery test. This is in line with Anastasi in Harbor – Peters

lxiii

and Ogomaka (1991), who postulated that the complete mastery of a given content is

indicated by a score of 80 – 85% and above, on a mastery test. The teachers were grouped

into two groups. Group 1 were mastery teachers. They were teachers that scored 80% and

above in the mastery test. Group 2 were non mastery teachers. They were teachers that

scored below 80%. In testing the hypotheses, t-test statistical tool was used to determine

whether two means ( X 1 and X 2) were significantly difference. All the hypotheses were

tested at 0.05 level of significance.

lxiv

CHAPTER FOUR

RESULTS

In this chapter, data for this study were analyzed and presented based on the

research questions and hypotheses that guided the study.

Research Question 1

What are the mean of primary school teachers that have mastery of number base

system and those that do not have?

Table 1: Mean and standard deviation of primary school teachers that have mastery

of number base system and those that do not have.

Status Number Mean Standard deviation

Mastery 19 89.26 7.37

Non mastery 21 58.48 16.31

Total 40

The result in Table 1 show a mean of 89.26 with standard deviation of 7.37 for primary

school mastery teachers while primary school non mastery teachers have a mean of 58.48

with a standard deviation of 16.31. The complete mastery of a given content according to

Anastasi in Harbor – Peters and Ogomaka (1991) is indicated by a score of 80 – 85% and

above on a mastery test. Specifically in answering research question 1, the mean of primary

school teachers that have mastery of number base system is 89.26 and the mean of those do

not have is 58.48 ( See Appendix K). This implies some primary school teachers have

mastery of number base system.

Research Question 2:

What are the mean of the primary school teachers that have mastery of the

application of binary number to computer and those that do not have?

lxv

Table 2: Mean and standard deviation of the primary school teachers that have

mastery of the application of binary number to computer.

Status N Mean Standard deviation

Mastery application 20 92.60 7.07

Non mastery application 20 48.00 24.62

Total 40

Table 2 shows that the primary school teachers that have mastery of the application

of binary number to computer have a mean of 92.60 with a standard deviation of 7.07 while

those that do not have mastery have a mean of 48.00 with a standard deviation of 24.62.

Therefore in answering research question 2, the mean of primary school teachers that have

mastery of the application of binary number to computer is 92.60 while the mean of those

that do not have is 48.00 ( See Appendix L).

Research Question 3

To what extent do job experiences of teachers contribute to teachers‟ mastery of

number base system in UBE mathematics curriculum?

Table 3: The mean mastery scores and standard deviation of experienced and less

experienced teachers in contribution to teachers’ mastery of number base system in

UBE mathematics curriculum

Group of teachers Number of

teachers (N)

Mean (X)

Standard

Deviation ( SD)

Experienced

teacher

15 74.27 16.99

Less experienced 25 72.40 22.06

Mean Difference 1.87

The result in Table 3 shows that the mean mastery score of the experienced teachers

is 74.27 with a standard deviation of 16.99 while the mean mastery score of less

experienced teachers is 72.40 with a standard deviation of 22.06. The difference is 1.87 in

favour of experienced teachers. It implies that teachers‟ experience may contribute to

teachers‟ mastery, although the difference is little (See Appendix M).

lxvi

Research Question 4

What is the influence of teachers‟ gender on the mean mastery scores of teachers in

the Teachers‟ Mastery Test on Number Base System (TMTNBS)?

Table 4: The means and stand deviation of teachers on the influence of gender in the

TMTNBS

Gender Number of

teachers (N)

Mean (X)

Standard

Deviation ( SD)

Male 20 73.80 23.20

Female 20 72.40 17.03

Mean Difference 1.40

Table 4 shows a mean of 73.80 and standard deviation of 23.20 for males and a

mean of 72.40 and standard deviation of 17.03 for females (See Appendix N). Their mean

difference is 1.40. This gives a little indication of difference between the male teachers and

their female counterpart in the TMTNBS. This implies that teachers‟ gender influences

their mastery in Teachers‟ Mastery Test on Number Base System (TMTBNS).

Research Question 5

What is the influence of school location (urban and rural) of teachers on the mean

mastery scores of teachers in the Teachers‟ Mastery Test on Number Base System

(TMTNBS)?

Table 5: the means and standard deviation of teachers on the influence of school

location in the TMTNBS

School Location Number of

teachers (N)

Mean (X)

Standard

Deviation ( SD)

Urban 20 75.50 18.14

Rural 20 72.70 22.35

Mean Difference 2.80

lxvii

Table 5 shows that teachers‟ school location with regard to urban schools has a

mean of 75.50 and standard deviation of 18.14 and a mean of 72.70 with standard deviation

of 22.35 for rural schools (See Appendix O). The mean mastery scores of teachers in urban

schools are higher by 2.80. This indicates that the school location influences teachers‟

mastery in favour of teachers in the urban schools.

Research Hypotheses

Hypothesis 1

There is no significant difference between the mean mastery scores of experienced

teachers and less experienced teachers in the Teachers‟ Mastery Test on Number Base

System (TMTNBS).

Table 6: t-test of difference between the mean mastery scores of experienced teachers

and less experienced teachers with respect to mastery

Group of

teachers

Number

of

teachers

Mean

(X)

Standard

Deviation

(SD)

Degree

of

Freedom

Calculated

t-value

Sig.

Experienced 15 74.27 16.99 14 0.23 .000

Less

experienced

25 72.40 22.06 24 .000

Significant at p < 0.05 level

From Table 6, the t- test statistic is 0.23, which is calculated t-value. This is

significance at 0.000, which is also significance at 0.05. This is because 0.000 is less than

0.05 ((0.000 < p 0.05).Therefore, the hypothesis is not accepted. Hence, there is significant

difference between the mean mastery scores of experienced teachers and less experienced

teachers in the Teachers‟ Mastery Test on Number Base System (TMTNBS).This implies

that primary school teachers do improve on their mastery of number base system with

increase on teaching experience (See Appendix M).

lxviii

Hypothesis 2

Table 7: t-test of difference between the mean mastery scores of male and female

teachers in the Teachers’ Mastery Test on Number Base System (TMTNBS)

Gender Number

of

teachers

Mean

(X)

Standard

Deviation

(SD)

Degree

of

Freedom

Calculated

t-value

Significance

Male

20 73.80 23.20 19

0.218 0.000

Female 20 72.40 17.03 19 0.000

Significant at p< 0.05 level

Table 7 shows that the calculated t-value is 0.218. This is significance at 0.000,

which is also significance at 0.05. This is because 0.000 is less than 0.05(0.000<p<0.05).

Therefore, the hypothesis is not accepted. Hence, there is significant difference between the

mean mastery scores of male teachers and female teachers in the TMTNBS.This implies

that male teachers and female teachers perform differently in the mastery test in favour of

male teachers. (See Appendix N).

Hypothesis 3

Table 8: t-test comparison of the mean mastery scores of teachers in urban schools

and teachers in rural schools in the TMTNBS

Location Number

of

teachers

Mean

(X)

Standard

Deviation

(SD)

Degree

of

Freedom

Calculated

t-value

Significance

Urban 20 73.50 18.14 19 0.124 0.000

Rural 20 72.70 22.35 19 0.000

Significant at p < 0.05 level

From Table 8, t-calculated value is 0.124. This is significance at 0.000, which is

also significance at 0.05. This is because 0.000 is less than 0.05 (0.000<p<0.05) Therefore,

the hypothesis is not accepted. Hence, there is significant difference between the mean

mastery scores of teachers in urban schools and teachers in rural schools. This implies that

lxix

these two groups of teachers differ in performance. The teachers in urban schools perform

better than teachers in rural schools in the TMTNBS (See Appendix O).

Summary of the Finding

Based on the results of the analysis of data presented in this chapter, the follow

major findings emerged.

1. The research findings revealed that the mean of the primary school teachers that have

adequate mastery of number base system is 89.26 with a standard deviation of 7.37 while

those that do not have mastery of number base system have a mean of 58.48 with a

standard deviation of 16.31.

2. The research question 2 revealed that the mean of the primary school teachers that have

mastery of the application of binary number to computer is 92.60 with a standard deviation

of 7.07 while those that do not have mastery of the application of binary number to

computer is 48.00 with a standard deviation of 24.62.

3. The research findings revealed that there is significant difference between the mean

mastery score (74.27) of experienced teachers and the mean mastery score (72.40) of less

experienced teachers. This implies that primary school teachers do improve on their

mastery of number base system with increase on their job experience.

4. The fact that male teachers achieved higher than the female teachers when their mean

mastery scores are 73.80 for males and72.40 for females in TMTNBS were considered.

Table 7 also showed that there is significant difference between the mean mastery scores of

male female teachers in the mastery of TMTNBS. Hence, gender does significantly

enhance teachers‟ mastery in number base system.

5. It was also revealed that there is significant difference between the mean mastery

lxx

scores of teachers in urban schools and mean mastery scores of teachers in rural schools.

This implies that primary school teachers in urban schools perform better than

primary school teachers in rural schools.

CHAPTER FIVE

DISCUSSION OF FINDINGS, CONCLUSION, RECOMMENDATION AND

SUMMARY

This chapter are presented under the following sub-heading: discussion of the

findings, conclusion, implications recommendations, limitation, suggestions for further

studies and summary of the study.

Discussion of the Findings

From the tables presented, the result revealed that the primary school teachers that

have mastery of number base system have a mean of 89.26 while those that do not have

mastery of number base system have a mean of 58.48. The study also revealed that some

primary school teachers have adequate mastery of the application of binary number to

computer and some do not have. This finding confirms the assertion of Harbor-Peters and

Ogoamka (1991) who concluded from their investigation that primary school teachers have

no adequate mastery of primary school mathematics content.

Table 6 revealed that there is significant difference between experienced and less

experienced teachers in their mean mastery scores. This implies that they are academically

differed. This result agreed with Popoola (2009) who reported that significant difference

exists in the practice of continuous assessment and teachers‟ experience.

The result of this finding had proved that male teachers and female teachers

performed differently in academic. The finding disagreed with Galadina and Yusha‟s

lxxi

(2007) who investigated the mathematics performance of senior secondary school students

in Sokoto State. Their study revealed that there is no significance difference between the

group means of males and females.

The result in table 8 showed that there is significant difference in the mean mastery

scores of teachers in urban schools and teachers in rural school. This disagreed with

Kolawale and Popoola (2009) who concluded from their investigation that the academic

achievement of students was not influenced by location.

Conclusion

Based on the findings of the study, the researcher draws the following conclusion.

1. Empirical evidence has shown that some primary school teachers have

adequate mastery of number base system in UBE mathematics curriculum

and some do not have.

2. Some primary school teachers also have mastery of the application of binary

number to computer and some do not have.

3. There is significant difference between the experienced teachers and less

experienced teachers in their mean mastery scores in the TMTNBS.

4. There is significant difference in the mean mastery scores of male and

female teachers in the TMTNBS.

5. Primary school teachers in urban schools differ significantly from primary

schools teachers in the rural schools in their mean mastery scores.

Educational implications of the study

The result of this study has some obvious implications to teachers, pupils,

curriculum planners, institutions, the government and Nigeria as a nation. The result

lxxii

revealed that some primary school teachers have adequate mastery of number base system

and the application of binary number to computer. But there are some primary school

teachers that do not have. Therefore, it may be necessary for primary school teachers to

attend seminars, workshops and conferences related to learning and teaching of

mathematics content specifically, number base system. Having mastery of number base

system and application of binary number to computer may avail primary school teachers

the opportunity to be participants in the on going technological development worldwide.

The quality of the education the pupils receive bears direct relevance to adequately

subject mastery possessed by the primary school teachers. Primary school teachers having

mastery of number base system would help them positively inculcate the knowledge in

their pupils for a better performance in mathematics. The result of this study also revealed

that the mean of the primary school teachers that do not have mastery of number base

system is very low comparing with the mean of those that have. Therefore, there may be

need for curriculum planners to review the curriculum.

However, the cause of this inadequate mastery of number base system taught by

some primary school teachers may be due to:

1. The teachers not being adequately exposed to the content they teach.

2. The fact that they have forgotten what they learnt in their school days.

Whichever is the case, various institutions responsible for the training of primary

school teachers need to be review. Authorities also need to ensure that mathematics

teachers in the teachers training have adequate mastery and competences essential to teach

prospective teachers in order to ensure meaningful teaching and learning of mathematics.

Recommendation

lxxiii

Based on the findings of this study, the following recommendations have been made by

the researcher.

1. It is recommended that the primary school teachers and teachers in training should

be properly trained to ensure that they have adequate mastery and competencies

essential to teach mathematics.

2. Frequent seminars, workshops and conferences should be organised for primary

school teachers to enhance the meaningful teaching and learning of mathematics.

3. The government/management should sponsor female teachers who want to study

mathematics education in the higher institutions to encourage them.

4. Primary mathematics teachers should put more interest in attending seminars,

workshops and conferences to keep them abreast with innovative strategies of

teaching mathematics.

5. Curriculum planners should review the mathematics curriculum from time to time

and the teachers‟ guide also should be provided for the proper teaching of such

curriculum.

Finally, the government and Nigeria as a nation should sponsor mathematics teachers in

regular and in service training courses, seminars and workshop. Such training courses

should emphasize mastery of primary school mathematics content to keep the teachers

abreast with effective teaching of mathematics.

Limitation

The under listed are the limitations of the study.

1. The use of the primary school teachers only for the study rather than both the

teachers and the pupils.

lxxiv

2. The time given to the teachers to solve the problems on the Teachers‟ Mastery Test

on Number Base System (TMTNBS) might not have been sufficient for the

expected level of mastery.

3. The randomization of the teachers might have affected the result of the study.

Suggestions for Further Studies

Based on the limitation of this study, the following suggestions are for further

studies.

1. This study, teachers‟ mastery of number base system in Universal Basic Education

(UBE) should be replicated in other part of states in Nigeria.

2. Another similar study should be designed to involve the pupils and the teachers.

Summary of the Study

This study sought to determine the extent of primary school teacher‟s mastery of

number base system in Universal Basic Education (UBE) mathematics curriculum. To

guide the study, five research questions and three hypotheses were formulated.

A descriptive survey design was used for the study. A sample of 40 primary five and six

teachers was randomly selected from 20 primary schools in Idah Education zone, Kogi

State with two teachers (one male and one female teacher) from each school. The

instrument for the study was Teachers‟ Mastery Test on Number Base System (TMTNBS).

The instrument was validated and a trial test was carried out to ascertain the reliability of

the instrument. The reliability coefficient of the TMTNBS was established using scorer

reliability approach. The reliability coefficient was 0.897.

The data generated from the study were analyzed using means and standard

deviations. They were used to answer the research questions and t- test statistic tool was

lxxv

used to test the hypotheses. The result of this study has shown that some primary school

teachers have adequate mastery of number base system in UBE mathematics curriculum

while some do not have. The result also revealed that some primary school teachers have

adequate mastery of application of binary number to computer and some do not have. It

indicated that there was significant difference between the experienced teachers and less

experienced teachers in the mastery test. The result has shown that gender is a significant

factor on mastery of number base system. It showed that there was significant difference

between the mean mastery scores of teachers in urban schools and teachers in rural schools.

Based on these findings, some implications, limitation, and recommendations were

made. Among the recommendations were that primary school teachers and teachers in

training should be properly trained to ensure that they have adequate mastery and

competences essential to teach mathematics. Frequent seminars, workshops and

conferences should be organized for primary school teachers to enhance the meaningful

teaching and learning of mathematics and teachers should put more interest in attending

seminars and workshops to widen their knowledge.

lxxvi

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Instruction of Mathematics in Secondary Schools. The Journal of World Council of

Curriculum and Instruction (WCCI) Nigeria Chapter, 4 (2), 176-184.

lxxxiv

APPENDIX A

SAMPLED SCHOOLS FOR THE STUDY SCHOOLS

A. From Urban Schools

S/N Name of Schools No. of male

Teachers

No. of

female

teachers

Total

1 LGEA St Boniface Primary School I, Idah 1 1 2

2 LGEA St. Boniface Primary School II, Idah 1 1 2

3 LGEA Pilot Primary School I, Idah 1 1 2

4 LGEA. St. Michael Primary School, Idah 1 1 2

5 LGEA Arabic Primary School I, Idah. 1 1 2

6 LGEA Qua Iboe Central School I, Idah. 1 1 2

7 LGEA Qua Iboe Centrlal School II, Idah 1 1 2

8 LGEA Inikpi Primary School, Idah 1 1 2

9 LGEA Omepa Primary School, Idah 1 1 2

10 Bishop Crowther Memorial Primary School,

Idah

1 1 2

Total 10 10 20

B. From Rural Schools

S/N Name of school No. of male

teachers

No. of

female

Total

lxxxv

teachers

1 LGEA Primary School, Ogenegwu 1 1 2

2 LGEA primary School, Alla-Ijobe 1 1 2

3 LGEA Primary School, Ugbetulu 1 1 2

4 LGEA primary School, Akpataga 1 1 2

5 LGEA Primary School Angwa 1 1 2

6 LGEA Primary School Adumu 1 1 2

7 LGEA Primary School Ichala Edeke 1 1 2

8 LGEA Primary School Ugwoda 1 1 2

9 LGEA Primary School, Kabawa 1 1 2

10 LGEA Primary School Alla-Okweje 1 1 2

Total 10 10 20

C. Grand total from the Urban and Rural Schools

S/N Location of School Total Number of Teachers

from the location

1 Urban Schools 20

2 Rural Schools 20

Grand Total 40

lxxxvi

APPENDIX B

REQUEST FOR CONTENT VALIDATION OF RESEARCH INSTRUMENT

School of Postgraduate Studies,

Department of Science Education,

Faculty of Education,

University of Nigeria, Nsukka

25th

April, 2010

Dear Sir/Madam,

REQUEST FOR CONTENT VALIDATION OF RESEARCH INSTRUMENTS

I am a postgraduate student of the above named department. I am currently undertaking a

research project titled “Primary School Teachers’ Mastery of Number Base System in

Universal Basic Education (UBE) Mathematics Curriculum.”

Attached is a draft of the instruments proposed for data collection. You are please

requested to read through the items and vet the clarity of the questions asked, the

appropriate answer for each of multiple- choice items as well as the clarity of the language

used.

lxxxvii

Your assistance in this regard is appreciated.

Thanks.

Okafor Mary Anastasia (Rev.Sr.)

PG/ MED/07/42813

lxxxviii

Title of the Study

Primary School Teachers‟ Mastery of Number System Base in Universal Basic

Education (UBE) Mathematics Curriculum.

Purpose of the Study

This study seeks to determine the extent of Primary School Teachers‟ Mastery of

Number Base System in Universal Basic Education (UBE) Mathematics Curriculum.

Specifically, the study aims at;

1. Determining the extent to which the primary school teachers have mastered number

base system in Universal Basic Education (UBE) mathematics curriculum.

2. Determining the extent to which the primary school teachers have mastered

application of binary number to computer.

3. Determining the extent to which the primary school teachers‟ experiences in their

service contribute to the mastery of number base system in UBE mathematics

curriculum.

4. Determining the influence which teachers‟ gender (male and female) has on the

mean mastery scores of teachers in the Teachers‟ Mastery Test on Number Base

System (TMTNBS).

5. Determining the influence which school location (urban and rural) of teachers has

on the mean mastery scores teachers in the Teachers‟ Mastery Test on Number Base

System (TMTNBS).

lxxxix

Research Questions

The following research questions guided the study;

1. What are the mean of the primary school teachers that have mastery of number base

system and those that do not have?

2. What are the mean of the primary school teachers that have mastery of the

application of binary number to computer and those that do not have?

3. To what extent do job experiences teachers contribute to teachers‟ mastery of

number base system in UBE mathematics curriculum?

4. What is the influence of teachers‟ gender on the mean mastery scores of teachers in

the Teachers‟ Mastery Test on Number Base System (TMTNBS)?

5. What is the influence of school location (urban and rural) of teachers on the mean

mastery scores of teachers in the Teachers‟ Mastery Test on Number Base System

(TMTNBS)?

Research Hypotheses

The following research hypotheses have been formulated to guide the study. Each was

tested at 0.05 level of significance.

1. There will be no significant difference between the mean mastery scores of

experienced teachers and less experienced teachers in the Teachers‟ Mastery Test

on Number Base System (TMTNBS).

2. There will be no significant difference between the mean mastery scores of male

and female teachers in the Teachers‟ Mastery Test on Number Base System

(TMTNBS).

xc

3. There will be no significant difference between the mean mastery scores of teachers

in urban schools and teachers in rural schools in the Teachers‟ Mastery Test on

Number Base System (TMTNBS).

xci

APPENDIX C

REQUEST FOR PERMISSION FOR ADMINISTING OF RESEARCH

INSTRUMENTS

School of Postgraduate Studies,

Department of Science Education,

Faculty of Education,

University of Nigeria, Nsukka.

25th

, April, 2010.

The Headmaster/Headmistress

………………………………………………………………………………………………

……………….

Dear Sir/Madam,

REQUEST FOR PERMISSION FOR ADMINISTING OF RESEARCH

INSTRUMENTS

I am a Master in Education degree student of the above University. I am currently

conducting a study on “Primary School Teachers’ Mastery of Number Base System in

Universal Basic Education (UBE) Mathematics Curriculum”.

Please, kindly give me permission to administer my test instrument to your teachers.

Thanks in anticipation.

Yours Truly,

Okafor Mary Anastasia (Rev. Sr.)

PG/MED/07/42813

xcii

APPENDIX D

REQUEST FOR COMPLETION OF RESEARCH INSTRUMENTS

School of Postgraduate Studies,

Department of Science Education,

Faculty of Education,

University of Nigeria, Nsukka.

25th

April. 2010

Dear Teachers,

REQUEST FOR COMPLETION OF RESEARCH INSTRUMENTS

I am a Master in Education degree student of the above university. I am currently

conducting a study on “Primary School Teachers’ Mastery of Number Base System in

Universal Basic Education (UBE) Mathematics Curriculum.”

Please feel free in responding to the questions. You are assured that the information given

will be treated with maximum confidentiality.

Thanks in anticipation.

Yours Truly,

Okafor Mary Anastasia (Rev. Sr).

(Researcher)

PG/MED/07/42813

xciii

APPENDIX E

TEACHERS’ MASTERY TESTS ON NUMBER BASE SYSTEM

(TMTNBS)

TMTNBS can be used to evaluate the extent to which the primary school teachers have

mastered the number base system in Universal Basic Education (UBE) Mathematics

Curriculum.

SECTION A

Personal Information of respondents

Instruction: Please tick good (√) against any of the items that agree to your response.

1. Class you presently teach: Primary five ( ) Primary six ( )

2. Gender: Male ( ) Female ( )

3. School Location; Urban ( ) Rural ( )

4. How long have you been teaching? ( - years)

SECTION B

Extent of Mastery of Number Base System by Teachers

Attempt all questions and show your work clearly: Duration: 1hour.

1a.State the place value of the number underlined in each of the following binary numbers.

i. 1 01two

xciv

ii. 1111 two

iii. 101110two

b. State the place value of “0”in the following.

i.101111two

ii.10111two

2a. Convert the following numbers in base ten to base two.

i. 8ten

ii. 9ten

iii. 16ten

b. Convert the following numbers in base 2 to base 10.

i. 1111two

ii. 11101two

3. Addition, subtraction and multiplication of numbers in base 2. Solve the following.

a. 111two + 101two

b. 1011two + 10001two

c. 1101two + 1100twoS

d. X – 101two = 1111two, find X

e. 1111two – 1001two

f. 110two – 101two

g. 11101two – 1011two

h. 110two x 10two

xcv

i. Multiply 10111two by 101two

j. Find the product of 1011two and 11two

4. Application of binary number to computer

U O U O

French English Hausa Maths KEY:

Name; Ojo Sule O - 0 Subject not offered

Class; 6A U - 1 Subject offered

The punched card above showed that Ojo Sule offered French and Hausa in the school but

he does not offer English Language and Mathematics.

a. Write out the code for the following punched cards using 0 and 1.

i

U O U O

ii.

U U U O O U

b. Draw punched cards to represent information as follows.

i. 1001

ii. 000111

iii. 1100

xcvi

APPENDIX F

ANSWERS FOR THE ITEMS (4 MARKS FOR EACH ITEM)

(1) a (20%)

i. 100 (one hundred)

ii. 1 (one unit)

iii. 1000 (one thousand)

b i. 10000 (ten thousand)

ii. 1000 (one thousand)

(2) a i. 1000two (20%)

ii. 1001two

iii. 10000two

b i. 15ten

ii. 29ten

(3) a. 1100two (40%)

b. 11100two

c. 11001two

d. 10100two

e. 110two

f. 1two

g. 10010two

h. 1100two

xcvii

i. 1110011two

j. 100001two

(4) a i. 1010 (20%)

ii. 111001

b. i

U O O U

ii.

O O O U U U

iii.

U U O O

xcviii

APPENDIX G

Table 1: Table of specification on binary number system for primary 5 and 6.

Content Dimension Ability Process Dimension

Lower Cognitive

Process

Higher

Cognitive

Process

Total

S/N % 52% 48% 100%

1 Conversion of numbers

from base ten to base

two and from base two

to base ten

20 3 2 5

2 Place value of a digit in

a 2-digit or more

numbers in base two.

20 3 2 5

3 Addition, Subtraction

and Multiplication of

numbers in base two

40 5 5 10

4 Application of binary

number to computer

(limited to punched

20 3 2 5

xcix

cards)

Topic

total

100% 14 11 25

APPENDIX H

SCHEME OF WORK

CONTENT AREAS OF PRIMARY 6 SCHEME OF WORK ON NUMBER BASE

SYSTEM

Module 12 Unit Content

Binary Number System Unit 1 and

2

Counting Groups of twos, the Binary Number

System and conversation of numbers in base

two to base ten

Unit 3 Place value of a Digit in a 2-digit or more

Number in Base Two

Unit 4 Conversion of Number in Base Ten to Number

in Base Two (Binary Number)

Unit 4 and

6

Addition and subtraction of Numbers in Base

Two

Unit 7 Multiplication of Number are in Base Two

CONTENT AREAS OF PRIMARY 6 SCHEME OF WORK ON NUMBER BASE

SYSTEM

Module 26 Unit 1 Binary System: Conversion from Base Two to

Base ten Number

Binary Number System Unit 2 Conversion of Number in Base 10 to Base 2

Unit 3 Addition and subtraction Base 2

Unit 4 Multiplication of in Base 2

Unit 5 Application Of Binary Number To Computer:

c

Punch Cards.

APPENDIX I

Computation of Scorer Reliability Coefficient

Descriptive Statistics

N Mean Std. Deviation Minimum Maximum

ScoreA

ScoreB

ScoreC

20

20

20

13.0000

13.8000

13.4000

5.57249

4.94815

5.60451

5.00

7.00

6.00

24.00

24.00

24.00

Kendall’s W Test

Ranks

Mean Rank

ScoreA

ScoreB

ScoreC

1.60

2.38

2.02

Test Statistics

N

Kendall‟s Wa

Chi-Square

20

.897

12.359

ci

df

Asymp. Sig.

2

.002

a. Kendall‟s Coefficient of

Concordance

APPENDIX J

S/N TMTNBS

(%)

Location Location Gender Gender Exp Less Exp CA

1 84 - R - F V - 99

2 20 U - M - - V 0

3 100 - R M - - V 99

4 80 U - - F - V 98

5 56 U - M - - V 60

6 92 U - M - - V 98

7 88 U - M - V - 60

8 96 - R M - V - 60

9 92 U - M - - V 99

10 32 - R M - V - 0

11 96 - R - F V - 99

12 60 U - M - - V 98

13 40 - R M - V - 0

14 68 U - - F - V 90

15 94 U - M - - V 90

16 76 U - M - - V 90

17 72 U - M - - V 90

18 96 - R M - V - 99

19 80 U - - F V - 85

20 72 - R - F - V 99

21 80 - R M - - V 60

22 80 - R M - - V 90

23 96 - R M - V - 99

24 82 - R - F - V 70

25 98 - R - F V - 80

26 54 U - - F V - 20

27 66 - R - F - V 60

28 78 - R M - V - 70

29 72 - R - F V - 60

cii

30 96 U - - F V - 90

31 46 - R - F - V 60

32 86 U - - F - V 80

33 50 - R - F V - 60

34 74 U - - F - V 70

35 54 U - M - - V 60

36 40 - R - F - V 20

37 74 U - - F - V 60

38 74 U - M - - V 60

39 80 U - - F - V 80

40 50 - R - F - V 50

Key M

= Male CA= Computer Application

F = Female

Exp = Experienced teachers

Less Exp = Less Experienced teachers

R = Rural schools

U = Urban schools

APPENDIX K

SCORES OF MASTERY TEACHERS AND NON- MASTERY IN THE TEACHERS’

MASTERY TEST ON NUMBER BASE SYSTEM (TMTNBS)

Mastery Teachers Non Mastery Teachers

1 84 1 20

2 100 2 56

3 80 3 32

4 92 4 60

5 88 5 40

6 96 6 68

7 92 7 76

8 96 8 72

9 94 9 72

10 96 10 54

ciii

Result of Data Analysis

Research Question1

APPENDIX L

SCORES OF MASTERY TEACHERS AND NON MASTERY TEACHERS ON THE

APPLICATION OF BINARY NUMBER TO COMPUTER

11 80 11 66

12 80 12 78

13 80 13 72

14 96 14 46

15 82 15 50

16 98 16 74

17 96 17 54

18 86 18 40

19 80 19 74

20 74

21 50

Status N Mean Std. Deviation

Mastery

Non Mastery

19

21

89.2632

58.4762

7.36992

16.30834

Mastery Application Teachers Non Mastery Application Teachers

1 99 1 0

2 99 2 60

civ

Result of Data Analysis

Research Question 2

APPENDIX M

SCORES OF EXPERIENCED AND LESS EXPERIENCED TEACHERS IN THE

TEACHERS’ MASTERY TEST ON NUMBER BASE SYSTEM (TMTNBS)

Experienced teachers

VAR00001

Less experienced teachers

VAR00002

3 98 3 60

4 98 4 60

5 99 5 0

6 99 6 0

7 98 7 60

8 90 8 70

9 90 9 20

10 90 10 60

11 90 11 70

12 99 12 60

13 85 13 60

14 99 14 60

15 90 15 70

16 99 16 60

17 80 17 20

18 90 18 60

19 80 19 60

20 80 20 50

21 50

Status N Mean Std. Deviation

Mastery Application

Non Mastery Application

20

20

92.6000

48.0000

7.06660

24.62348

cv

1 84.00 20.00

2 96.00 100.00

3 92.00 80.00

4 96.00 56.00

5 60.00 92.00

6 68.00 88.00

7 80.00 32.00

8 72.00 40.00

9 82.00 94.00

10 54.00 76.00

11 66.00 72.00

12 72.00 96.00

13 96.00 80.00

14 46.00 80.00

15 50.00 96.00

16 98.00

17 78.00

18 86.00

19 74.00

20 54.00

21 40.00

22 74.00

23 74.00

24 80.00

25 50.00

APPENDIX N

SCORES OF MALE AND FEMALE TEACHERS IN THE TEACHERS’

MASTERY TEST ON NUMBER BASE SYSTEM (TMTNBS)

MALE VAR00001 FEMALE VAR00001

1 20.00 84.00

2 100.00 80.00

cvi

3 56.00 96.00

4 92.00 68.00

5 88.00 80.00

6 96.00 72.00

7 92.00 82.00

8 32.00 98.00

9 60.00 54.00

10 40.00 66.00

11 94.00 72.00

12 76.00 96.00

13 72.00 46.00

14 96.00 86.00

15 80.00 50.00

16 80.00 74.00

17 96.00 40.00

18 78.00 74.00

19 54.00 80.00

20 74.00 50.00

APPENDIX O

SCORES OF TEACHERS IN URBAN AND RURAL SCHOOLS IN THE

TEACHERS’ MASTERY TEST ON NUMBER BASE SYSTEM (TMTNBS)

cvii

LOCATION OF

SCHOOL

TEACHERS IN URBAN

VAR00001

TEACHERS IN RURAL

VAR00001

1 20.00 84.00

2 80.00 100.00

3 56.00 96.00

4 92.00 32.00

5 88.00 96.00

6 92.00 40.00

7 60.00 96.00

8 68.00 72.00

9 94.00 80.00

10 76.00 80.00

11 72.00 96.00

12 80.00 82.00

13 54.00 98.00

14 96.00 66.00

15 86.00 78.00

16 74.00 72.00

17 54.00 46.00

18 74.00 50.00

19 74.00 40.00

20 80.00 50.00

Ho1: There is no significant difference between the mean mastery scores of experienced

teachers and less experienced teachers in the Teachers‟ Mastery Test on Number Base

System (TMTNBS).

Significant level = 0.05

cviii

Test Statistic, t = X1 – X2 Exp Less exp.

S12 + S2

2 X1

= 74.27, X2 = 72.4

n1

n2

S1 = 16.99, S2 = 22.06

S12 = 288.66, S2

2 = 486.64

= 74.27 – 72.4

16.992

+ 22.062

15 25

= 1.87

19.24 +19.47

= 1.87

38.71

= 1.87

8.22

t = 0.23

Decision rule: Reject Ho1 if t – calculated > t-critical value otherwise accepted

t – Tabulated = t0.05, Degree of freedom = n1+ n2 - 2 = 15 + 25 – 2=38

Significance at 0.000

Since t – cal 0.23 > 0.000, the hypothesis is not accepted.

Conclusion: There is significant difference between the mean mastery scores of

experienced teachers and less experienced teachers in the Teachers‟ Mastery Test on

Number Base System (TMTNBS).

cix

Ho2: There is no significant difference between the mean mastery scores of male and

female teachers in the Teachers‟ Mastery Test on Number Base System (TMTNBS).

Test Statistic: t = X1 – X2 degree of freedom = n1+n2 - 2

S12 + S2

2 = 20 + 20 - 2

n1 n2 =38

X1m = 73.8, X2f = 72.4

S1m =23.20, S2f = 17.03

S12 = 538.24, S2

2 = 290.02

2177.043.6

4.1

41.41

4.1

50.1491.26

4.1

20

02.290

20

24.538

4.728.73 t

t = 0.218

Decision rule: Reject Ho2 if t- cal > tab otherwise accept.

t 0.05, Df = 38

Since t- calculated = 0.218 > t-tabulated = 0.000, we reject the null hypothesis.

Conclusion: There is significant difference between the mean mastery scores of male

teachers and female teachers in the TMTNBS.

Ho3: There is no significant difference between the mean mastery scores of teachers in

urban schools and teachers in rural schools in the Teachers‟Mastery Test on Number

Base System (TMTNBS).

Significant level = 0.05 Df = 38 X1u= 73.5, X2r = 72.7

cx

S1u = 18.14, S2r = 22.35

S1u2 = 329.06, S2r

2 = 499.08

1242.0

44.6

8.0

41.41

8.0

95.2445.16

8.0

20

08.499

20

06.329

7.725.73

2

22

1

21

21 t statistic,Test

n

S

n

S

XX

Decision Rule: Reject Ho if t- calculated > t-tabulated otherwise accept Ho.

t- tabulated = t 0.05 , n1+ n2 - 2 = 20 +20 – 2 = 38

Conclusion: Since t- calculated = 0.124 > 0.000, we do not accept Ho meaning that there is

significant difference between the mean mastery scores of teachers in urban schools and

teachers in rural schools.