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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.
1.
TEACHER TRAINING IN MATHEMATICS
Md. Azhar
Department of Mathematics
Hussain
Veer Kunwar Singh University, Arrah 802301, Bihar, India
email- [email protected]
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.
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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
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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.
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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.
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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
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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,
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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
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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
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
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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.
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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
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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
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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
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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
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
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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.
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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.
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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.
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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
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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
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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.
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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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