**CHAPTER ONE**

**INTRODUCTION**

**Background to the Study**

Mathematics is one of the compulsory subjects in the school curriculum. It is a compulsory subject at every stage of the school system, right from primary up to the end of senior secondary school. It is also compulsory subject for entry to higher institutions in Nigeria. This compulsory nature of mathematics carries with it the assumption that the knowledge of the subject is essential for all members of the society. It is generally accepted that mathematics is the bedrock of other sciences. Ayelele and Usman (2007) opined that mathematics is the gate and key to other sciences. Mathematics has been a tool for national development. Illori (1994), states that societies and government around the world recognizes the importance of mathematics for national development. The fabric of society has become more and more underpinned by mathematical ideas. As a result, a major development in mathematics education in this millennium has been the increased amount of mathematics that all citizens are expected to know. Technological leaders and political leaders need mathematics education that takes into account both the new uses of mathematics and technology and new ways in which mathematics can be done with information technology. Mathematics, it is widely understood, plays a key role in shaping how individuals deal with the various spheres of private, social and civil life.

Kolawole and Oluwatayo (2001) defined mathematics as human invention borne out of human resolve to solve human problems. Mathematics has been identified as the ingredient for effective articulation of the abstract element that gives impetus to the development of technologies. The potential of a nation to develop in science and technology is a direct function of its adaptation in the area of mathematics. The gap that existed between developed and developing nations, according to Alex (1989) had their root in mathematical accomplishment.

Mathematics is the central intellectual discipline of any technological society. No society is static, as each develops, its quantitative aspect assumed ever greater and increasing influence and dominance over its qualitative features, and a good account of the quantitative development can only be kept by means of mathematical understanding of the situation.

Mathematics is an essential nutrient for thoughts, logic, reasoning and therefore progress. It liberates mind and not only gives individuals an assessment of their intellectual abilities, but points to the direction for improvement. Mathematics is the sum of human knowledge that has to do with quantification. It uses symbols, quantities and quantitative methods to facilitate reasoning and to summarize and present the process of reasoning and its end results.

In the numerous usefulness and needs of the mathematics by individuals and the nation, the subject, mathematics has experienced mass failure in the Senior Secondary School Certificate Examinations over the years. Eraikhemen (2004) opined that despite its importance in the society, there has been poor performance of students in the subject. According to Micaiah (2013), “the results of candidates in the May/June and November/December Senior Secondary School (SSCE) examinations conducted by the West African Examination Council (WAEC) has been that of mass failure in recent years. The student under-achievement in mathematics is not just a concern for particular countries, but has become a global concern over the years.

Many factors have been attributed to the unpleasant performance of secondary schools students in the Senior School Certificate Examinations. These factors include school related factors, student’s related factors; teacher’s related factors. Among these factors, the one of interest in this study is the teachers related factors. Teachers, as major factor in the teaching-learning process, are expected to be effective in the teaching and learning of mathematics.

Acknowledging that every system has multiple functions and that it exists within an environment that provides unpredictable inputs, a system’s effectiveness can be defined as its capacity to survive, adapt, maintain itself and grow, regardless of the particular function it fulfill. Organizational effectiveness according to Edgar (1987) is achieved when management succeeds in being both productive and people centred. It has been observed that effective mathematics teachers are those who are humane in the fullest sense of the word. They are humorous, fair, firm, empathetic, more democratic than autocratic and apparently more able to relate easily and naturally to their students, either on a one-to-one or group basis. Their classroom reflects miniature enterprise operation in the sense that they are more open, spontaneous and adaptable to change. For this lofty goal of mathematics to human education and societal advancement and development to be achieved, the 9nstitutions, teachers and the mode of transmitting the knowledge – the teaching process must be well executed.

Teaching, according to Clark and Starr (1970) is an attempt to help people acquire some skills, attitude, knowledge, ideas or appreciation. In other words, the teacher’s task is to create or influence desirable changes in behavior in his or her students. Van-Dahen and Brittes (1959) defined teaching as the guidance of pupils through planned activities so that they (students) may acquire the richest learning possible from the experiences.

Teaching is all about imparting on learner the expected behavioural objective set before the lesson; and to achieve this the teaching has to be effective. Awolua (2002) define effectiveness as about doing the right things. He buttresses further that effectiveness concerns the bringing of an effect that is in line with the goal and it is the possibility to correlate a student’s successful achievement with a teacher’s ability to teach. He urges that in school, some teachers can be considered good and effective while others may be considered “terrible” and ineffective. A teacher needs to be effective so as to remain in the teaching training profession, be considered a successful professional, be recognized by his/her peers, be promoted, etc. To be considered effective, a teacher needs to know as much as possible the subject matter he/she teaches. This implies updating himself by reading current books, journals and magazines in the subject and related areas. Apart from this, a teacher must be well grounded in educational psychology (students’ behavior, attitudes, characteristics, etc), the national policy of education and the school curriculum, teaching subject matter and teaching methods and when to apply them.

Awolua (2002) avers that an effective teaching is one that results in the students’ learning maximally what is taught them. To be able to do this, the teacher must identify the needs to his/her students and then prepare the materials or learning experiences that best match their needs. Thus the medium through which the learning experiences are communicated must also be compatible with the needs of the students. It is in this regard that one can say that the teaching is effective. We can know whether teaching is effective after proper preparation and delivering of the lesson have been through the process of assessment and evaluation. Every effective teaching process must result in assessment. Awolua (2002) opined that this is the method of knowing whether or not the students have learnt what they were expected to learn from the particular lesson. He said, if only 30% of the class is shown to have mastered the objectives of the lesson taught the lesson cannot be said to be effective. But, if for instance, about 70% or more of the class mastered the objectives, no body will dispute the fact that the lesson was effective. Therefore, all things being equal, an effective lesson preparation leads to an effective lesson delivery and an effective mastery of lesson objectives.

Laura, Courtheg and Olivia (2008), suggested that the most widely used measure of teacher effectiveness are classroom observation, principal evaluations, analysis of classroom artifacts i.e. rating of teacher’s assignments and students’ work, teaching portfolios, teacher self-reports of performance and value added strategies.

According to Awolua (2002), effective teaching in the classroom consists of three major components, namely; preparation, execution or implementation and evaluation of teaching events. At the preparation stage, the teacher plans the lesson he/she intends to teach. It includes all the activities of the teacher that lead to putting the lesson together i.e. objectives, appropriate subject matter, and logical sequence of the subject matter in a manner that the student can follow, teaching aids, etc. The end result of this stage is the lesson notes. The execution stage is where the teacher communicates the lesson to the students. He/she follows the plans as put down in the lesson notes in implementing the teaching methods/strategies. The classroom management, which is a part of execution and evaluation, entails classroom controls and hygiene. Arrangement of seats, grouping of students, classroom discipline, cleanliness, etc are all under this category. Motivation and engaging students in learning by deriving ways of making each student successful through instilling high expectations in them and nudging them up to meet those expectations. An effective teacher would personalize the learning, accommodate the different needs of students and use techniques that have each student working on tasks that engage and challenge them to achieve their personal best and seek to infuse their culture, background and abilities, as student learn best when teachers incorporate this.

Moreso, effective mathematics teachers can use appropriate technique that best serve their learning needs by exposing the students’ learning opportunities that involve learning themselves and learning through interactions. The effective mathematics teacher teaches in such a way that encourages the student to take great responsibility for their own learning. They have knowledge of their subject content skills and knows how to explain that content in a manner that their students understand. They inspire in their students a love for learning and use their knowledge processes to determine the most effective strategies to use in assisting individual students. Evaluation deals with ascertaining that the lesson is effective, that is, that the students have learned the lesson, and that the teaching methods/strategies were effective for the particular class.

For this study the researcher will use the areas of major component of effective teaching, that is, preparation, execution or implementation and evaluation of teaching events on an observational study of classroom processes used by secondary school mathematics teachers. If the observational study of classroom processes used by secondary school mathematics teachers have bearing on students’ achievement.

**Statement of the Problem**

The comments about fallen standard of education in the mass failure of mathematics students in the May/June and November/December senior secondary school (SSCE) examinations conducted by the West African Examination Council (WAEC) in Nigeria today is a recurring issue and all fingers seem to be pointing at teachers at the major cause of this downward trend. Analyzing the performances of the students in WASSCE mathematics for the years (1991-2012), Charles-Ogan (2014) reported dismal performances of the students in the over twenty-two years’ period, with failure rate of over 80% for 11 out of 22 years results considered. The analysis revealed further that in 20 out of the 22 years results had below 50% of students who had credit pass in the subject. These results show that the failure rate of students in mathematics is very high. So, many researchers have worked on various school related factors, students related factors, teacher’s related factor, parents’ related factor, guardians’ related factor, public related factor and so on. The researches found out that they perceived mathematics as a difficult, abstract and complex subject to study (Harbour-Peters, 2001) and (Obodo. 2004). These perceptions must have led to the general hatred for mathematics as a subject which in turn has led to the general poor performances of students in mathematics in schools. The difficulty, abstraction and complexity in a subject ought to be removed if the teacher is effective. Thus, this study seeks for answers to the following questions: How knowledgeable, effective and motivational is the mathematics teacher during lessons through lessons preparation, use of teaching methods to improve students’ performance in mathematics.

**Research Questions**

- Are mathematics teachers able to prepare and plan lessons?
- Do mathematics teachers possess adequate communication skill while teaching?
- Do mathematics teachers use appropriate teaching methods while teaching?
- Do mathematics teachers have adequate knowledge of subject matter?
- Are mathematics teachers able to create good learning environment?
- Are mathematics teachers able to effectively assess students’ learning?

**Hypotheses**

- The mean rating of mathematics teachers’ ability to prepare and plan lesson is not significantly different from 50%.
- The mean rating of mathematics teachers’ level of communication skill while teaching mathematics is not significantly different from 50%.
- The mean rating of mathematics teachers’ teaching methods is not significantly different from 50%.
- The mean rating of mathematics teachers’ level of knowledge of subject matter is not significantly different from 50%.
- The mean rating of mathematics teachers’ ability to create good learning environment is not significantly different from 50%.
- The mean rating of mathematics teachers’ ability to effectively assess students’ learning is not significantly different from 50%.

**Purpose of Study**

The purpose of this study is for the researcher to assess the effectiveness of mathematics teachers under the following objectives:

- Assess mathematics teachers preparation and planning of lessons.
- Assess mathematics teachers’ use of appropriate teaching methods while teaching.
- Assess mathematics teachers’ communication skills while teaching
- Assess mathematics teachers’ knowledge of subject matter.
- Assess if mathematics teachers create good learning environments while teaching.
- Assess mathematics teachers if they are able to assess their students during teaching-learning.

**Significance of the Study**

Thus, for Nigeria to attain a high level of mathematics competency that will lead to the desired technological advancement, effective teaching of mathematics at all levels of education should not be compromised. It is therefore imperative for the study to be carried out as the results will have implications for students’ teachers, school administrators and government.

This study is expected to promote students’ understanding of mathematics, thereby enhancing their performance in senior secondary examinations.

The result of this study will be of great importance to mathematics teachers in that it will enable them to have an effective training programme for teachers. The findings of the study will help mathematics teachers to improve on their efficiency when such problems are identified and taken care of. It will enable mathematics teachers to perform their instructional roles given the necessary facilities such as instructional materials, good infrastructure, etc.

Government and society will realize the need to find education in general and mathematics education in senior secondary school for the nation to attain global technological advancement on the part of students, the study will be of great significant because they are the direct beneficiary of the services of teachers.

**Scope and Delimitation of Study**

The scope of this study is restricted to the following measures of teacher’s effectiveness – lesson plan and preparation, teaching methods, communication skills, knowledge of subject matter, good learning environment, and assessment. This study will be delimited to teachers in the public schools in Ovia North-East and Egor Local Government Areas of Edo State in order to ascertain the observational study of classroom processes used by secondary school mathematics teachers.

**Operational Definition of Terms**

**Perfect Teacher:** A perfect teacher is one that near 100% effective.

**Effective teacher: **Someone interested in the teaching profession.

**Implementation:** To carry out something that has been officially decided.

**Teacher’s Effectiveness: **Is a matter of degree to which a teacher achieves desired effects upon students.

**Teacher’s Performance: **Is the way in which a teacher behaves in the process of teaching.

**Teacher’s Competence: **Is the extent to which the teacher possesses the knowledge and skill.

**Who is a Mathematics Teacher: **Teacher that teaches mathematics as a teaching subject.

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