TEACHER TRAINING IN MATHEMATICS

1. TEACHER TRAINING IN MATHEMATICS Md. Azhar Hussain Department of Mathematics Veer Kunwar Singh University, Arrah 802301, Bihar, India email- hussainazhar@yahoo.com Abstract Mathematics is a part of our glorious heritage and it is in the fitness of things that we keep up to our old traditions of excellence in this field. Mathematics as a discipline has grown very fast in the last twenty-five years and has become an essential component of all sciences. The rapid use of mathematics at different levels of our development makes it all the more necessary to have a critical appraisal of mathematics education in our country. That training of teachers is an essential component of any process of mathematics education cannot be overemphasized. Teacher training is increasingly seen as a continuum, of which pre-service and in-service programmes form integral related parts. So that the future pr4ogrammes can be meaningfully planned, it is necessary to look back and take stock of what we have been doing, how far we have been able to achieve our objectives, and what have been the major problems faced. The present paper is an effort in this direction dealing with various facets of the problem of teacher training in India at all levels.

2. OBJECTIVES Inservice training programmes are probably more important than pre-service programmes. In the pre-service programmes, the prospective teacher learns about teaching, while in the class-room, the beginning teacher learns how to teach. Inservice education for teachers consists of those programmes of professional study in which teachers are involved after they are actively employed. If the educational enterprise is to be fully effective, it is imperative that teachers be involved in inservice activities on a regular and continuing basis. Many teachers need to change their teaching either in style or in content, or in both. Increased knowledge boosts confidence. We would like to have class-room teachers who know mathematics in considerable depth, who are so well—prepared academically that they are comfortable with the role of mathematics in society, who understand students and communicate with them well, who would lead the students to the powerful goals of independence and self-esteem, who will provide moral and

3. intellectual models for their students. Also teaching technology is constantly changing. This makes old skills and content obsolete. Educational and psychological research continues to provide new insights into the ways in which students learn mathematics and these new understandings needs to be translated into class-room practice. How is the teacher to cope with the constant problem of day-to-day teaching and also of simply keeping abreast of the times? The need for teacher-training is apparent. In a nutshell the aims of training programmes for mathematics teachers are: • to keep teachers aware of recent developments in mathematics • to keep teachers abreast of recent trends in teaching of mathematical subjects • to keep teachers aware of fast developing applications of mathematics.

4. to help teachers in communicating the students the style, the structure and concepts in mathematics, in developing the students the ability to solve mathematical problems, to mathematize a situation, and to achieve computational skills • to come to their aid in writing texts • to enable them in acclimatzing with change in curricula that might be introduced in institutions. Teachers have to be actively involved in inservice activities and not to passive recipients. A training programme has to provide support in bringing out the best in an individual teacher. Also, one has to remember that teachers are professionals capable of solving their own problems. You cannot change a teacher, all you can do is to create an environment in which change is possible.

5. STATUS Our education system just after independence was a hangover of the British system. In the present system, schooling consists of 12 years (5 years primary, 3 years middle, 2 years secondary and 2 years senior secondary (or plus two)). One needs 3 years for graduation and 2 years for post-graduation. The post-independence era called for gigantic efforts in terms of training of teachers at all levels. The idea of summer-institutes, refresher-courses etc. was conceived as far back at the late fifties of this century, largely due to the enthusiasm of a group of college and university teachers of mathematics. The entire programme started with a big bang and on a massive scale in the early part of sixties. The University Grants Commission (UGC), in co-operation with the National Council of Science Education (NCSE), resolved to help solve the problem by providing necessary finances for organizing teacher-training programmes at all levels in different parts of the country. Subsequently summer-schools became a regular feature. The collaboration of the National Science Foundation of USDA and CEDO of UK provided additional strength by giving necessary advice and services of experts.

6. The last few decades have seen the rapid expansion of primary, secondary, higher-secondary, college and university education without proper preparation in terms of personnel infrastructure and with paucity of funds. This has brought in enormous deterioration in the standards of mathematics instruction at all levels. The need for teacher training programmes today is recognized more than ever before. The programme of summer-schools organized by the UGC has taken the shape of refresher-courses and orientation programmes organized under the ambit of academic-staff colleges established at chosen university-centres and institutions spread all over the country. These are responsible for holding refresher-courses in major disciplines for inservice teachers to update and enrich their knowledge in the respective field of specialization, and orientation programmes for newly appointed teachers in teaching methodology, pedagogy, educational psychology, etc. at the under4graduate and postgraduate level systematically throughout the year. Some training programmes have been organized off and on as part of activities under the UGC schemes of University Leadership Projects, COSIP and COHSIP programmes.

7. At the school level, the National Council of Educational Research and Training (NCERT) is a government agency responsible for school education. It has initiated a number of training programmes for school teachers at all levels during the past three decades. Its much talked of document ‘Programme for Improvement of Mathematics Education (PRIME)’ prepared for the eight plan, recognized that inservice training programmes are not effective without a package of specially designed, need based instructional materials. It also emphasized the training of resource-persons who would in turn orient more resource-persons to help organize training programmes on regional and local basis. The NCERT thus basically organizes training programmes to train resource-persons. State units called ‘State Councils of Educational Research and Training (SCERT)’ have been set up to do the job in the respective States. Further, ‘District Institute of Education and Training (DIET)’ have been set up to take care of respective districts. Some of these are doing good work. All categories of schools are covered under these programmes,

8. such as Govt. Schools etc. At the primary level, there is the ‘District Primary Education Programme (DPEP)’ aided by the World Bank. However, there is no systematic plan of training teachers at the school level and the total output of various efforts is only a drop in an ocean. As regards recruitment qualifications, theoretically, for school teachers, pre-service training of one year in education is compulsory. This is a professional degree awarded by Departments of Education or training institutions where the emphasis is more on lesson-planning, test construction, teaching methods than on the subject-content. Many institutes award these degrees by correspondence also. However, in practice one finds that in 90% schools at primary and secondary level, those teaching mathematics are totally unsuitable to do the job. They do not have formal training in mathematics. They had mathematics up to secondary or higher-secondary level and were recruited to teach other subjects, but are required to teach MATHEMATICS also. Instead of creating interest in mathematics these teachers have done just the opposite. In case of schools meant for girls only, the situation is worse. At leas 50% of the teachers of mathematics at the secondary level are either not qualified or

9. not competent to teach the courses they are teaching. At the higher-secondary level, there is acute shortage of trained mathematics teachers. The result is that many of the fresh M.Sc.’s are given the job without any formal training to teach. Many of time these new entrants do a better job than trained teachers. They are of first-rate caliber, well motivated towards their work and capable of reaching a high level of performance. But more often, a fresh M.A. with very good marks and good understanding of the subject still proves to be a bad teacher. At the undergraduate level, teachers re not required to have received any pre-service training. However, in recent years, UGC and the Council of Scientific and Industrial Research (CSIR) have started a National Education Test (NET) which is a pre-requisite for regular appointments as lecturers in colleges. Several states have also started similar tests for recruitment of college teachers. Also, for promotions to higher grades, every teacher is expected to have attended a certain number of orientation and refresher courses such as those organized by the Academic Staff Colleges established by the UGC. To that extent, inservice training for college teachers is compulsory.

10. For example in India, there are about 6000 colleges and about 150 universities teaching mathematics. Not more than 10 universities are getting special assistance from UGC to improve the quality of mathematics instruction. India is a big country. Efforts made by the NCERT, UGC and other organizations have not yet been able to cover a sizeable segment of the total teacher-population. Reasons are many. We make an attempt to identify our problems.

11. PROBLEMS One of the reasons why we have failed in our pre-service training programmes is the declining number of students available to be trained. Low salaries and low status given to teaching attracts few students willing to take up a teaching career. Best students flock to medicine and engineering courses. One rampant malady afflicting the Indian educational set-up is the wide-spread practice of private tuitions by school teachers. It makes the teacher less than whole-hearted in class-teaching and completely averse to spending any time on training programmes as time is money for him. Particularly at the higher secondary level the situation is becoming worse day by day because of the importance students attach to the entrance examinations for the medicine and engineering courses. The business of private tuitions is flourishing and is becoming more and more lucrative. Even in some of the very prestigious schools, at the plus two level, students are just not going to the classes and the teachers are just not interested in teaching (in class!). Instead, coaching-classes are flooded for which the students pay heavy fees and the teachers are teaching in coaching-schools

12. where they are handsomely paid. Of what relevance is any training programme under such circumstances; unfortunately, the situation even at the undergraduate level is taking this turn in as much as students are preparing for entrance-examinations to MBA/MCA courses etc. Another reasons why we have not been able to derive maximum benefit from our training programmes seems to lie in our social and educational set up. Entire teaching in our country is examination oriented and it is no wonder that both the teachers and the students are happy with the traditional methods and courses which have ensured better success to the students. Even when the teachers are convinced that training is necessary and worth the effort, they have first to unlearn what they have been traditionally teaching before they can be ushered into the new and unfamiliar ways of modern approach. The routine class-room method of lecturing in a training programme makes the participant feel that he is being treated as a school-child and gives to the trainer the impression that the participants are not interested in learning. This creates a climate of distrust between the participants and the teacher and is disheartening to those associated with the programme.

13. An alternative method suggested would be that the teacher may give a set of expository lectures which should be supplemented by reading from the books supplied and then be followed by free and frank discussions to remove the difficulties of the participants. However, experience has shown that participants hardly ever participate in such discussions. The reason is that this method is foreign to them and that they are apprehensive lest the questions they ask may betray their ignorance. It is needless to emphasize that for discussions to be illuminating, the trainer must have mastery over the subject and should encourage the participants. In fact, we suffer from the lack of qualified teacher-educators. Research in mathematics education is negligible. Most universities do not have a department in mathematics education. Normally, the job of training in a programme is assigned to a motivated teacher of mathematics faculty in addition to his normal duties and obviously this makes heavy demand on his time and energy. Programme quality is directly related to the time spent in planning the programme. Teachers often complain that the training programme did not help them to deal with the day-to-day problems of class-room management, that the content was too much, and the faculty was too much concerned with developing their mathematical

14. knowledge and too little with showing them worthwhile methods of teaching. The teachers have to be exposed to a variety of teaching approaches – problem solving, investigations, reading contemporary sources – which they must take as examples for their subsequent work. Good mathematics and good methods can be studied simultaneously to the benefit of both. Another major problem is the lack of resources; we have a large number of teachers to be trained. The finances available do not match our needs. Normally, there are large classes of participants which make a completely heterogeneous groups. The increases the task of meaningful planning on the part of the educator. Probably, the younger generation of teachers is in less need of the inservice training programme than the older ones who are usually unable to attend for some unavoidable reasons. Finally, our training programmes have suffered more on account of the callousness on the part of principals and governing bodies than the lack of interest on the part of the teachers. Many principals are not very enthusiastic about granting duty-leave to the teachers to attend a programme as they feel it might affect adversely the teaching/examination/evaluation work required of a teacher.

15. ACTION PLANS It is clear from the above that what we have been trying to do in the realm of training programmes may be said to be marginally small. We have yet to arrive at a take-off stage. Co-ordination amongst the exiting efforts suffers from the lack of information. There is need for systematic national surveys on a continual basis. The information should be publicized through proper channels. The workable system of pre-service training of prospective teachers must be evolved. For prospective teachers, a special teacher-training programme should be instituted in select universities. Such teacher-trainees should be selected on all India basis and only talented ones should be given training for an adequate period. Future teachers should be recruited from this list. There has to be an inbuilt system for making available a continuous supply of competent and enlightened teachers.

16. A committee should be constituted to formulate standards for curriculum evaluation and instruction in the pre-service training programmes. The curriculum and instruction should evolve in such a way that content and methodology are not separated from each other, and the teaching methods which a student-teacher team learns are relevant to the actual class-room teaching which they may take up at the end of their training. It is advisable to build up local teachers’ centres with good library and other facilities, to which teachers from the immediate neighbourhood could come at week-ends and discuss relevant class-room materials and problems. It is only enlightened teachers of mathematics, acquainted with problems of school mathematics, who can teach in an imaginative manner what school teachers would need particularly at the elementary level.

17. More inservice work that is based in the school should be encouraged rather than taking teachers outside the school. School-based support services should be provided by professional organizations. Expert help can be provided to motivate teachers. Polya’s discovery approach to teaching of mathematics is well-known. With a large number of students and the pressure to complete the syllabus, it is hardly possible to try this method in a usual class-room. It can be tried, however, with a small batch of students in a lab where they can be encouraged to find patterns and guess results. Besides attempts at the state level, an organization may be set up at the national level so as to reinforce inservice programmes in collaboration with state authorities. Such an organization may carry on the programmes of summer-institutes and correspondence courses through universities in each state selected in consultation with state departments of education. Financial incentives in the shape of increments and promotions to higher scales should be given to teachers based on their performance and participation in training programmes. Also, the teachers should have the benefit of duty leave with full pay and allowances for the duration of the programmes.

18. Generally, few schools and colleges have cared to possess a decent library. A good library in such school and each college helps to inservice training of teachers better than periodic workshops or summer-institutes. Good libraries should be set up in teacher training institutions and various teaching aids relevant to mathematics teaching be made available at these institutions. A sample of students at the concerned level should be involved to form a test section for suitability of methods. Also, enthusiastic teachers at the same level and at a slightly higher level should be identified who could take the leadership in these programmes. The UGC should make the academic staff college programme more effective by ensuring, among other things, that competent teachers of the selected topics/subjects from the region (not necessarily belonging to the host university) are involved as faculty members and that topics/subjects to be covered are so chosen in orientation courses that these have some bearing on what the participants are required to teach.

19. There is need for some system of evaluation after the completion of a training programme. Any formal testing doesn’t seem to work. The work of a participant should be judged from the interest he takes and the understanding be exhibits during the discussions. Further, each participant should be called upon to deliver a number of lectures on topics covered in the programme and he should be assisted in the preparation of these lectures. This should also form a basis of judging his achievements. A way should be found to supervise the teaching of mathematics with a view to improving its quality. It mathematics appears to be a difficult and dry subject to some students, there is something wrong with the method of teaching. Very often, teachers fail to provide the right motivation for the for the study of the subject. Today, mathematics is respected not only for its aesthetic charm and abstract contents, but more so for its applications in different fields of human activity. The teaching of mathematics can certainly be made more meaningful for the raw student by emphasizing its immense practical value. A mathematics teacher needs a foundation in the subject which he can continue to expand and modify throughout his working life. But he requires more than a good knowledge of a number of parts of mathematics. He requires an overview of how the parts fit together; he

20. needs a perspective into which he can fit fresh knowledge as he acquires it. This involves the history of the subject, the philosophical foundations and a knowledge of where the current expanding frontiers are to be found. The history and the foundations of the subject need to be taught in such a way that their social relevance and their relevance to the school class room are clearly seen. Finally, reforms through the training programmes could be supported through awareness building programmes among mathematicians, mathematics educators and administrators. We are living in a world that is rapidly changing. Educational, psychological and technological research continues to provide new insights into the ways in which students learn mathematics and these new understandings need to be translated into classroom practice. That we need inservice education and continuing staff development activities for teachers is evident. The need to know and to keep abreast of the time is dramatic and compelling. What is urgently required is to build up the adequate infrastructure that may carry on not only the programmes with a fairly reasonable speed on a continuing basis, but

21. also the follow up activities that are so essential in sustaining the enthusiasm and initiative of teachers who are likely to communicate the same to others, so that the tempo of curriculum reforms in the realm of mathematical education is kept up. A good teacher of mathematics is one who uses his knowledge and love of the subject as well as his love and respect for his students to lead these students to enjoy the study of mathematics. Training programmes in India have not been very successful because the teachers for whom they are meant have not generally taken them seriously. Good teaching requires the maintenance of a high level of enthusiasm on the part of the teacher. Only an enthusiastic teacher can inspire the students. Mathematics teachers continually need mathematical enrichment experiences for themselves and obtaining such experience is worth the expenditure of time and effort. Demands that modern life makes on our time and energy poses a difficulty. But the price is worth the cost and for the teacher who would stay alive and active, the price simply must be paid.

22. Nobel laureate Rabindra Nath Tagore had summed up the matter very well when he wrote: “A teacher can never truly teach unless he is still learning himself. A lamp can never light another lamp unless it continues to burn its own flame. The teacher who has come to the end of his subject, who has no living traffic with his knowledge but merely repeats his lessons to his students, can only load their minds; he cannot quicken them, Truth not only must inform but must inspire. If the inspiration dies out and information only accumulates, then truth loses its infinity and the teacher loses his effectiveness”. THANK YOU