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, 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.
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.
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.
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.
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.
– 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). 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 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 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’ 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.
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 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.
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?
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).
This material content is developed to serve as a GUIDE for students to conduct academic research
PRIMARY SCHOOL TEACHERS’ MASTERY OF NUMBER BASE SYSTEM IN UNIVERSAL BASIC EDUCATION (UBE) MATHEMATICS CURRICULUM
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