COLLEGE OF EDUCATION,
BENUE STATE – NIGERIA.
The paper tries to expose some existing myths and practices that have negative influence on the quality of mathematics teaching at the post-primary school level. Some consequences of having active mathematics educators in these schools are discussed, which include a healthy collaboration between mathematics educators and mathematicians, and maintaining an active group of mathematics educators in these schools. Recommendation towards a new pedagogy and paradigm of mathematics teaching at this level are proffered.
Post-primary education is the bedrock of tertiary education in Nigeria. Research into philosophy and practices of mathematics is considered a task mandate for the development of mathematics at this level. Even among actors who have divergent views on various issues, consensus on the need for research to develop and make mathematics very relevant at this level is compelling. Infact, research at this level is the most valuable tool that can be used to develop mathematics teaching and learning. In Nigeria, post-primary education has developed very rapidly within decades of the existence of the Nation. Mathematics is one of the many subjects in the schools where academic activities are carried out. Mathematics at the post-primary level is not as complex a field to implore as at the tertiary level. Mathematics at this level prepares students for qualitative, problem solving and symbolic reasoning through general education, service and undergraduate programmes. In recent times, the attention of the stakeholders has been drawn to the perceived policy setbacks in prosecuting a sustainable mathematics education in Nigeria, especially as it relates to synegerising mathematical education at the post-primary level with science and technology researches and development (Obioma, 2002).
Some contributing factors to the above scenario include:-
- Acute low students enrolments in mathematics at the undergraduate level which has made it difficult to find subscribers as mathematics educators;
- Depreciating capacities of mathematics educators, the old generation of mathematics experts are fast disappearing and the paucity of potential post-primary mathematics teachers;
- Obsolete curricular offerings that are out of phase with socio-economic and techno-cultural realities,
- Research endeavours that are not sufficiently linked to the demands of the society.
This is worrisome, especially as mathematics is considered as the bedrock of all scientific and technological breakthroughs and advancement of all activities of human development. It is the only language and culture common to all studies (Barbor-Peters, 2002, Uzo, 2002).
Mathematics is an expanding and evolving discipline as well as a way of perceiving, formulating and solving problems in many other disciplines. It is a constant interplay between the walls of thought and applications. Mathematics departments in Nigerian universities are now admitting a more diverse ability group of students than has been the case two decades ago. This calls for a new pedagogy and paradigm of teaching mathematics at both post-primary and post-secondary school levels.
Although post-primary school enrolment has increased significantly over the years, there has not been a corresponding increase in the number of mathematics majors in the universities. Hence, mathematics educators at the post-primary school level should be more aware of their students’ needs in order to attract them to read mathematics at the university level. Besides, conscious efforts on the part of the government should be made to address the acute shortage of mathematics teachers at the post-primary school level.
Generally, mathematics is categorized into mathematics educators and professional mathematicians. The mathematics educator is concerned with curriculum development, instructional development and the pedagogy of mathematics. He is a mathematician of a type and does research in the areas of curriculum instruction, learning and teaching of mathematics. At his disposal are several pedagogical theories which are readily applied to the teaching and learning of mathematics.
Contrastingly by and comparatively, the professional mathematician is concerned purely with research in mathematics either in pure or applied. Research mathematicians are found in universities, departments of mathematics or mathematics research centres (e.g. National Mathematics Centre). Those at the university, departments of mathematics, lecture mathematics to students. However, some at a certain time of their career develop interest in the pedagogy of mathematics. This is why there is no clear cut demarcation between a mathematics educator and a professional mathematician. Nevertheless, the distinction between the two types of mathematicians is the specificity of functions and roles in the realm of mathematics (Fajemidagba, 1991).
Paradigm of Teaching Mathematics in Nigerian Universities.
Our universities turn out graduates of mathematics who in turn are employed in the post-primary schools as mathematics teachers. Therefore, it is pertinent to take a look at the pedagogy and paradigm of mathematics teaching at the level.
Lecturers in mathematics departments of our universities are usually separated into various groups, specializing in such areas as algebra, analysis, topology, applied mathematics, etc. There is no lecturer in the mathematics department in the university who specializes in mathematics education. This is not peculiar to the mathematics department, rather it is common to all departments of Nigerian universities outside the education faculty. In the light of this scenario, it has been continually argued over the past two decades that every university lecturer must have a teaching qualification to remain effective on the job. In particular, the Federal Ministry of Education has on several occasions expressed concern on when every university lecturer must acquire teaching qualification.
One domain noticeably missing in the mathematics departments of universities is “pedagogical knowledge”. Shulman (1986) defined this component of professional knowledge as;
“The most regular taught topics in one’s subject area, the most useful forms of representations and demonstrations-in a word, ways of representing and formulating the subject that make it comprehensive to others. Pedagogical content knowledge also includes an understanding of what makes the learning of specific topics easy or difficult”…(pp.9-10).
If one takes a cursory look at the instructional practices of mathematics lecturers in our universities, one will notice that there is much to be done to improve their pedagogical content to be able to impart effectively the knowledge of mathematics to the students. According to Borko and Whitecomb (2008), instructional practices in classroom discourse include;
- Asking questions or posing problems to begin a discussion
- Monitoring student participation during discussion
- Keeping the discussion on track.
One may ask, are these observed in a mathematics lecture room at all? As far as teaching of mathematics by lecturers in mathematics departments of our universities is concerned, the teachings of very renowned, committed and dedicated lecturers who make their mark in academics can be void based on the above instructional practices.
The belief that the researcher is always a good teacher has a negative effect on the quality of teaching in the universities. Here, it is claimed that researchers are “ipso facto” good teachers. University mathematicians tend to teach as they were themselves taught. Unless they have a particular interest in teaching, they are unlikely to make changes in their teaching or to exchange views, experiences or knowledge with their colleagues in other institutions.
Emerging Paradigm of Teaching Mathematics in Nigerian Universities
The quality of mathematics graduates from the universities, who are subsequently the teachers of mathematics at the post-primary education level is of utmost importance here. Because their quality is the aggregate of all their experiences in the university as students, it is imperative to take a look at the emerging pedagogy and paradigm which are aimed at improving their performances at the post-primary education level.
The existing situation calls for a National agenda for mathematics teaching and learning in Nigerian universities. There is an increasing effort in developed nations to maintain an active group of mathematics education among the departments of mathematics. The attention of the stakeholders is drawn to some consequences of having an active mathematics educators group within the mathematics departments. The group should include anyone in a department of mathematics whose primary responsibility is carrying out research in mathematics education, developing and teaching mathematics courses for teachers, teaching history of mathematics or providing service to the department, such as overseeing learning resource centres and supervising teaching assistants. This group is distinguished from those in a faculty of education, who develop mathematics teaching methods courses and supervise student teachers. Note here that we are only concerned with staff in a mathematics department whose primary function is in mathematics education as opposed to research mathematicians who have limited involvement with such activities.
Research in mathematics education is fundamentally different from that in pure mathematics in that it tends to deal with teaching and learning problems and not with abstract mathematical problems. One ugly development in mathematics education research is the attempt to create a dichotomy between two definitions of teaching that bear little or no relation to the reality of mathematics classroom. This development is reminiscent of the sort of modern/traditional mathematics dichotomy–a series of unproductive and heated arguments between advocates of different teaching approaches (Becker and Jacobs, 2000; Boaler, 2008; Schoanfeld, 2004; Wilson, 2003). These arguments have raged in mathematics between advocates of constructivist and those of more didactic teaching in the United States (Roser, 2000).
Fortunately, mathematics education has moved beyond such thinking of dichotomy to a broader appreciation of the varied and complex roles in which effective teachers of mathematics need to engage (Boaler, 2008; Kilpatrich, Swafford and Findell, 2001; Lobato, Clarke and Ellis, 2005; Sherin, 2002). Boaler (2008) sums it this way;
Research in mathematics education has shown conclusively that, effective teaching of mathematics does not only involve the precise presentation of knowledge, it also involves changing the ways children think, building on their current understandings and addressing any prior misconceptions.
Boaler (2008) therefore, concludes that one of the main contributions of the field of mathematics education research has been the development of an extensive knowledge base documenting learner’s common conceptions in different mathematics domains.
A healthy development now is that specialists in mathematics education agree on playing down on teacher-centred instruction, which is generally understood to mean a teacher presenting methods to students who watch, listen and then practice the methods (Boaler, 1998). By contrast, they advocate student-centred instruction, which is approach in which learners are given opportunities to offer their own ideas and to become actively involved in their learning. (Boaler, 2008; Cobb, 1994; Confery, 1990).
Active Mathematics Educators Within a Department of Mathematics: Implications
The implications of having active mathematics educators within a department of mathematics are discussed under the following sub-headings:-
- Collaborative effort.
- Courses for teachers.
- Undergraduate lower level courses.
- Mathematics resource centres.
Hitherto, the contact between mathematics educators and practicing university teachers had been very poor. There is need to bridge the gap that exists between mathematics educators and university mathematicians. It is now incumbent on researchers in mathematics education to correct the serious errors that have been made. The presence of mathematics educators in the department of mathematics will initiate a collaboration of research in education that will improve the teaching of mathematics at the undergraduate level. Investigating, acquisition and development of mathematical concepts in students, effective teaching practices and improvement of problem solving abilities are examples of ongoing research efforts in mathematics education. Such research efforts can be valuable to mathematics departments for their application on programme development. In addition, research findings aid mathematics education specialists in developing texts and course materials (Bulger and Schulz, 1984).
“Courses for Teachers”
Students of the Faculty of Education usually take courses from the academic departments. These departments often provide content courses such as mathematics for elementary teachers, etc while education faculties usually provide methodology courses like psychology, philosophy and other foundation courses and arrange for students teaching practice. The need for relevant, high quality content courses for teachers taught by mathematics department staff that are professionally committed to their development and maintenance has persuaded many mathematics departments to include mathematics educators in their staff lists.
The usual misconception that anyone can teach mathematics may lead some to argue that the mathematics content of courses is not sophisticated enough to devote precious regular staff position to them. This misconception is likely to lead to disastrous consequences because the graduates at this level of education are the potential teachers at the post-primary level of education that will handle mathematics. So, these courses are never arithmetic-level courses and are focused on mathematical concepts and structure, underlying the mathematics taught in primary and post-primary schools. Unfortunately, very often, these courses are relegated to in-experienced teaching assistants, resulting in a set of courses that dampen whatever enthusiasm prospective primary school teachers may have had for mathematics. Further, the evolution of school curricula is appropriately brought into discussion in courses for primary school teachers. Mathematics educators who have taught these courses in a College of Education will agree that it is desirable to demonstrate their relevance to prospective teachers. Similar arguments can be made for courses designed for prospective post-primary school teachers.
The challenges expressed above will require special mathematics for teachers courses that will expose pre-service and in-service teachers to a wide variety of current curricular issues, such as uses of calculators and microcomputers in mathematics teaching, applications of secondary mathematics, mathematical problem solving techniques and new approaches to teaching various contents from research findings. Developing and coordinating such courses, which can be part of regular or sandwich programmes, are natural responsibilities of those in mathematics education.
“Undergraduate Lower Level Courses”
An issue of continuing concern is that of low performance of undergraduate students in their first two years in the university as mathematics students. In recent years, a tendency for students to dislike mathematics has been noted with a resulting continuous decline in the performance of students in ordinary level examinations. Before the 1980s, most students who presented themselves for admission into mathematics department had at least credit pass in Additional mathematics. With poor implementation and low student enrolments in Further mathematics, the paucity of potential tertiary mathematics students continue to dip (Obioma, 2002; Odili, 2006). Those students who accept to study mathematics do so as a last resort at the undergraduate level. The scenario at the department of mathematics, therefore, is a weak connectivity between students and the high expectations of the entry behaviours of the first two years of undergraduates in mathematics. Such students arrive on campus not prepared for what traditionally is university level mathematics. Mathematics educators in mathematics department will apply student-centred approaches that will popularize the teaching and learning of mathematics in the first two years of undergraduates in mathematics. Mathematics educators in mathematics department will also with their contacts with post-primary schools and their work with teacher organizations like; Mathematics Association of Nigeria (MAN), Science Teachers Association of Nigeria (STAN) and Curriculum Organization of Nigeria (CON), will try to bridge the gap in the entry behavior of their students.
“Mathematics Resource Centres”
Efforts to improve undergraduate instruction have led to some mathematics departments to develop learning resource centres. Such centres which vary in functions provide students with free walk-in tutoring, out-of-class testing, access to reference materials, calculators and other equipment. Mathematics educators are involved in developing and overseeing such mathematics learning resource centres.
Teaching and supervising graduate teaching assistants are major challenges facing large departments. Mathematics educators can assist the department in arranging orientation workshops for fresh students. Most departments must consequently invest in a certain number of departmental positions in mathematics education efforts. Such positions can be distributed on a part-time or full-time basis. In any event, the importance of these tasks and the demands placed on those who carry them out make it very necessary that they be assigned to sufficient number of interested mathematics educators on full-time basis. Major obstacles the departments may encounter, include resistance to appointing people according to the educational needs and difficulties in providing suitable condition of service, such as salary, promotion and job security to these mathematics educators. Nevertheless, mathematics department must surmount these obstacles standing in the way of their educational activities.
Nigerian universities are accepting a more diverse ability group of students than the case two decades ago. Consequently, universities must begin to adopt a role more like that of the school system and less the elite institutions of the past. The danger of creating a dichotomy between two approaches; teacher-centred and student-centred is highlighted. A healthy collaboration of mathematics educators and professional mathematicians in research efforts can be valuable to mathematics department. The presence of a mathematics educator in mathematics department will go a long way in this collaboration because some of the graduates of mathematics in the department are trained for the purpose of teaching mathematics at the post-primary school level.
Mathematics educators in the department of mathematics will teach special mathematics courses for teachers and curricular issues to pre-service and in-service teachers. They will also teach the first two years mathematics courses to the present crop of students of the department with poor entry behavior. Other services to the department like management of resource centres and supervision of teaching assistants will be an added benefit of the presence of mathematics educators in mathematics department.
While no single approach would suit all departments of the two tiers of education, viz post-primary and university levels, it is hereby recommended that:
- Mathematics teachers at the post-primary school level should not over estimate the abilities of the students in mathematics. It is common place to hear some teachers yell at students because they have not been able to answer correctly a question they perceive to be very simple!
- Mathematics teaching and learning at both levels must be student-centred but not teacher-centred. Infact, all teaching must be student-centred.
- Department of mathematics should maintain an active group of mathematics educators.
- Professional mathematicians should intensify meaningful collaborative research with colleagues in other universities.
- Government should adequately fund mathematics departments in Nigeria. Government, industries and wealthy individuals should be involved in establishing resource centres and also fund in-service training of mathematics teachers.
- The National Mathematical Centre (NMC) should increase its efforts at staff development in the field of mathematics.
- Universities should restore overseas training for their mathematics lecturers.
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