**Abstract**

The research investigates teachers and students’ views of difficult areas of Further Mathematics Curriculum which is a special requirement for engineering education in Nigeria using Osogbo Secondary Schools in Osun State as case study. The population of the study consisted of all the further mathematics teachers and all the senior secondary III students in all the 39 Secondary schools in the Local Government Area. A simple random sampling technique was used to select 45 further mathematics teachers and 2019 Senior Secondary school III Students.

Two self designed questionnaires were developed to elicit information for the research questions. Appropriate hypotheses were raised based on the research questions. These questionnaires were validated and their reliability ensured. The data gathered were analyzed using frequency count, percentage, t-test and Chi-square. The results of the analyses revealed that both teachers and students, qualified and unqualified, experienced and less experienced teachers have the same views of difficult areas in teaching and learning of Further mathematics in the secondary schools. Based on the findings, it was therefore recommended that for engineering education to advance, teachers should endeavour to improve themselves academically, be more committed, proactive in their dealings, and see their job as service to humanity; school authorities should have more time schedule for Further mathematics on the time table, qualified Further mathematics teachers should be posted to all schools, appointment of Further mathematics teachers should be purely on merit and should not be politicized. Curriculum planners should be up and doing in planning for teaching of Further mathematics with appropriate instructional materials.

**Keywords: **Teachers, students, perceptions, Further mathematics, curriculum, hypotheses, T-test, Chi-square, Evaluations.

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**CHAPTER ONE**

**INTRODUCTION**

**BACKGROUND OF THE STUDY**

The National Policy on Education states that mathematics is one of the core subjects to be offered by all students at the pre – tertiary level (FRN, 2004). This compulsory nature of mathematics carries with it the assumption that the knowledge of the subject is essential for all members of the society. According to Awoshiyan (2006), in a nutshell, the national policy on education, edition of 1981 from where the 2004 edition took its roots, because of some policy innovation and changes in education, the general objectives of mathematics education as stated there in, remain relevant.

These include;

(I) To generate interest in mathematics and to provide a solid foundation for everyday living;

(ii) To foster the desire and ability to be accurate to a degree relevant to the problem at hand;

(iii) To develop precise, logical and abstract thinking;

(iv) To stimulated and encourage creativity; and

(v) To provide necessary mathematical background for further education.

Also, Betiku (2004), adds that mathematics competence is a critical determinant of the post – secondary educational and career options available to young people. In fact, it is observed that a credit level pass in mathematics is required for admission into Nigerian Universities as a general requirement. The general mathematics curriculum of the senior secondary school is expected to take care of this.

However, not every body in the society requires the same depth of mathematics for career choice. For instance, for those who would want to train as mathematicians, engineers, medical doctors, scientists and the science and technology related courses, may need more mathematics than the general mathematics. As a result, to accomplish the objectives of mathematics education for these categories of persons, a parallel curriculum was produced and institutionalized in Nigerian senior secondary school general mathematics for these categories of persons.

Further Mathematics came into existence when Nigeria’s educational system changed from 6-5-2-4 (six years at primary, five years at secondary, two years at A-level and 4 years at undergraduate level) to 6-3-3-4 (six years at primary, three years at junior secondary, three years at senior secondary and four years at undergraduate level). The subject was referred to as Additional Mathematics during the former system of education. The observed annual poor performance of undergraduates at first year Mathematics courses at the tertiary institutions culminated in the Mathematicians and Mathematics educators clamouring for a Mathematics curriculum that would be a bridge between senior secondary school Mathematics and the first year undergraduate Mathematics (FME, 1976). This led to the introduction of Further Mathematics curriculum at the secondary school level in 1985 and the subject was classified as an elective (optional) at the senior secondary school in the National Policy on Education (FRN, 2004).

The Wikipedia (2010) describes Further Mathematics as the title given to a number of advanced secondary mathematics courses. In Nigeria, Further Mathematics happens to be one of the subjects designed to be studied at secondary school level. As stated in the National Curriculum for secondary schools volume 5 of the Federal Ministry of Education (1988), the aims and objectives of Further Mathematics are to: help develop further conceptual and manipulative skills and their applications; provide an additional intermediate course of study which bridges the gap between elementary mathematics and higher mathematics and meet the needs of potential mathematicians, Engineers, Scientists and other professionals, such as Businessmen and Administrators and Architects.

National Council for Curriculum Assessment (2005) noted that many students view mathematics as a difficult subject and perceive higher mathematics as an elite subject for only the best students. Though the subject was made non compulsory for students, which explains their fewness, the performance of these students is not encouraging after all. One may be right to think that students’ performance in Further Mathematics should be high since it is the students that make a choice to offer the course. But unfortunately the results of previous studies on students’ performance in Further Mathematics have been full of apathy showing the sorry state of affairs surrounding Further Mathematics in the country (Balogun, 1986).

According to Ibrahim (2004), the Further Mathematics Curriculum contains all the topics in the senior secondary general mathematics curriculum plus topics in Further Mathematics, which include pure mathematics, Mechanics and Statistics. This policy is not new. Before the two parallel curriculums there was the general mathematics and the additional mathematics. They were though not parallel. The additional mathematics as the name implies, contains additional topics which are not in the general mathematics. It was there for the students who are mathematically able and need more mathematics. Most times these are students who intend to train in the science related careers. In additional mathematics the students attend the general mathematics classes and attend another class for a shorter period on the timetable for additional mathematics. At the end, the students enter for two separate papers; the general mathematics and another in additional mathematics.

The difference in the two arrangements according to Ibrahim (2004), is that in Further Mathematics, apart from it being parallel, the policy guide regarding the implementation of Further Mathematics, stipulates that, a separate class be run for students who opt for the course. They will not attend regular general mathematics classes, although they cover everything in the general mathematics in the Further Mathematics class. At the end of the course, the student will sit for full set of papers i.e. the senior secondary school general mathematics plus papers set for Further Mathematics. For this, some universities in Nigeria specifically require a credit level pass in Further Mathematics or an attempt in the Further Mathematics in addition to the credit level pass in the general mathematics for some courses.

Further mathematics enjoys a unique status in the A level curriculum. It is not free-standing as it cannot be certificated before the equivalent qualification in AS or A level mathematics has been achieved. Further mathematics, usually perceived as a minority subject, was lost for some schools and colleges in the changes that resulted from the introduction of Curriculum 2000 with its emphasis on breadth. Students who previously had been studying three subjects at A level were now expected to study four or even five in their first year. Finding time to take on further mathematics in addition to this became problematic for both institutions and their learners. The uptake of mathematics – already seen as one of the hardest AS subjects – declined, as did the study of further mathematics.

In 2004 the Qualifications and Curriculum Authority (QCA) issued a questionnaire to schools and colleges to collect data on the provision of A level mathematics and further mathematics (including AS qualifications in these two subjects). Approximately 200 questionnaires were returned by centers and telephone interviews were conducted with 45 of these to obtain more information about the provision of further mathematics in the organizations within which they worked. Four further mathematics centre managers were also interviewed by telephone (although they were not included in the initial survey). In addition, brief face-to-face interviews were conducted with 22 further mathematics students from three classes.

This report is intended to help schools and colleges that do not at present offer further mathematics as part of their AS/A level provision but are considering offering it in the future. It is also intended to help centers already offering further mathematics that would like to know the strategies used by other centres when dealing with issues such as small class sizes and the professional development of staff. It may also help those centres considering widening participation in further mathematics. Examples of practice from individual centre’s are used to illustrate the suggestions.

^{ }The further mathematics centres are part of the Further Mathematics Network funded by the Department for Education and Skills (now the Department for Children, Schools and Families) with a remit to widen participation in further mathematics.

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