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Teacher Training in Mathematics

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Md. Azhar Hussain
Department of Mathematics
Veer Kunwar Singh University, Arrah 802301, Bihar, India
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 inservice 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.
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
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:
пЃ¬ to keep teachers aware of recent developments
in mathematics
пЃ¬ to keep teachers abreast of recent trends in
teaching of mathematical subjects
пЃ¬ to keep teachers aware of fast developing
applications of mathematics.
пЃ¬ 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
пЃ¬ to come to their aid in writing texts
пЃ¬ to enable them in acclimatzing with change in
curricula that might be introduced in
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.
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 postindependence era called for gigantic efforts in terms of training of
teachers at all levels. The idea of summer-institutes, refreshercourses 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 cooperation 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
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.
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 resourcepersons. 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,
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
not competent to teach the courses they are teaching. At the highersecondary 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.
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.
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
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.
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
knowledge and too little with showing them worthwhile methods of
teaching. The teachers have to be exposed to a variety of teaching
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.
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 teachertrainees 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.
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 classroom 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.
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.
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.
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
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
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.
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”.
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