A Program of quality mathematics education for bright
students in schools
PROLOGUE: No one will deny the fact that a country which aspires to be world
leader in science and technology, must have quality education in mathematics at
school level. There is no need to elaborate this point. India does have compulsory
mathematics education up to class 10 and both, the course curriculum and its
teaching in a large number of schools is quite good (thanks to NCERT books).
However, serious concern has been raised about the quality of examinations in
which both average and very good students score almost same marks. Hence the
examination results are unable to distinguish a bright student from an ordinary
student. This has very bad effect on mathematics education:
1. Good (especially talented and this number is very large in India) students
have no motivation of learning mathematics deeply but to simply practice
for high marks.
2. Various institutions for higher education (and even some companies) hold
their own examinations as a part of selection processes for admissions /
employment. Preparation for these examinations, with uncertain future,
throws the present education out of gear. This results not only in wastage of
time but also of resources (both manpower and money), and creates
tremendous physical and mental pressure on the students and their parents.
Can we assess the bad impact of all these on Indian citizens?
I think, it would be very difficult for any one to change the present trend in
question paper setting and evaluation even in one state but this trend is not a big
evil for average students. Therefore, we must provide scope for full growth,
utilization of the capacity of good and talented students,
(i) attract them to study mathematics deeply and then
(ii) inspire them to work hard to learn it in such a way that it is enjoyable.
If we ask a good student of mathematics, he will never say that it is boring to study
of mathematics. In fact he will say that it is full of joy.
Suggested plan of action: It is quite simple to achieve both aims (i) and (ii) and, in
addition, give recognition of their talent by the following programme – an optional
mathematics programme:
(a) providing excellent books in optional mathematics1 at appropriate levels from
class six or even earlier2 up to class twelve,
(b) having special two classes3 per week for good (not for all) students of
mathematics in optional mathematics from class seven up to twelve and
(c) having a continuous evaluation all through the year and then annual
examinations4 in this optional mathematics curriculum and finally having
final examinations4 at 10th and 12th level.
(d) For the procedures (b) and (c) CBSE5 and all state examination boards should
introduce optional papers in mathematics in the final examinations 4 at 10th
and 12th level based on special enrichment material. The question papers in
optional mathematics would test deeper understanding of mathematics and
ability to solve challenging problems. These papers in mathematics need not
be taken by all students but only those who have interest in learning deeper
aspects of mathematics. The marks scored in these papers must be recorded
in the mark card (transcript).
(e) In order to prepare the syllabus for optional mathematics course from class
seven, for setting question papers and for evaluation of answer books in final
examinations at 10th and 12th level, there should be a special autonomous Cell
in CBSE7, headed by a professor of an institute / university. The Cell would
choose group of teachers (which may involve college and university teachers
also) to set the papers and evaluate the answer books.
Availability of books: Since the initiation of Mathematics Olympiad activity in
India, a large number of excellent books by Indian mathematicians have been
written for students at various levels and many such books are also available from
abroad (some of them have been reprinted in India). Hence the item (a) is quite
easy to organize.
Why optional papers only in mathematics: There may be some questions like
“why optional papers only in mathematics and not in other subjects?”. It is quite
easy to give answers to this question. I just mention some of them:

A majority of the students, who would take these papers, would eventually
choose a career in a discipline other than mathematics and the enhanced
capability in mathematics will help them to do better in their areas of
specialization.

The students, who miss good mathematics up to class eight, are not likely
to learn mathematics later on, even for their professional work. This is not
true for any other science subject.

Success of bright students in optional mathematics program in every
school will instill confidence and will provide an excellent opportunity to the
children of the unprivileged members of the society to compete with other
students in admission to national institutions, an opportunity which probably
no other existing program can provides.

When USSR (former Soviet Union and other neighbouring countries)
launched the first ever satellite in space in 1957, USA traced a great
weakness in their education system – weakness of mathematics teaching in
schools and attempts were made to rectify it immediately.
Nobel laureate, Sydney Brenner emphasized in a lecture recently8 the importance
of teaching probability theory to every student of biology. Later in a private
discussion with me, Prof. Obaid Siddiqi, FRS, reiterated this point and added that
only necessary parts of mathematics should be presented in a very interesting way
in schools. One great advantage of having an optional mathematics paper for bright
students is that in a regular mathematics curriculum for all students there is no
need to burden every student with too many deeper and difficult concepts.
IIT JEE, ISI admission test and KVPY Programme: The JEE of IITs is a
national examination but probably it does not test deep understanding in
mathematics and its difficult problems in the mathematics paper tests practice,
speed and tricks they learn, mainly in private coaching classes. In fact, I have
gathered from some IIT mathematics teachers that a large number of students in B.
Tech. courses in IITs, are unable to learn deep mathematics - probably their
capacity to do so is lost due to drilling they go through in the preparation for JEE.
The JEE results are of no use to any one else other than IITs because the actual
marks are not disclosed and probably, they are too low and of little use. On the
contrary the entrance examination papers for B. Stat. and B. Math courses of ISI
test aptitude in mathematics and the questions are published later.
There is a serious attempt by the Government of India in nurturing talent in
science, for example the nation wide examination conducted under KVPY. But in
this and other programme (such as Olympiads), the attempt is to spot and nurture
talent but there is no arrangements for students to learn various subjects (including
mathematics) deeply in a regular curriculum from an early age. In USA (and I
believe in many developed countries) there is a provision for bright students to
learn subjects of their interest at their own pace9. In India students miss this
opportunity. Optional mathematics will provide this opportunity at least in one
important subject.
One great advantage of an optional mathematics paper in mathematics at 12th level
will be a decrease in the number of examinations, at least in mathematics,
conducted by various institutions of higher education and KVPY itself. This will
actually decrease the wastage mentioned in item 2. above. One of the greatest
beneficiaries of the optional mathematics examination by CBSE will be the
Mathematics Olympiad (MO) activity in India. I know how the Olympiad
organizers struggle in conducting the Regional MO (like the KVPY). The top
scorers in optional mathematics at the 10th and 12th level can be directly selected
for the International MO Training Camps.
An appeal: I request that my suggestions (a) – (e) be considered and implemented
with suitable modification. I am not just making a suggestion but I am prepared to
work for a few years, if it is really needed, on the above suggestion with the same
intensity as I did for 15 years for Mathematics Olympiad during my involvement in
it for 20 years from 1978 to 1997. However, I would prefer to continue doing
research and book writing in which I am involved now.
Phoolan Prasad
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NCERT: National Council of Educational Research and Training, which has done
excellent work in production of good quality text books.
KVPY: Kishore Vaigyanik Protsahan Yojana
CBSE: Central Board of Secondary education
……………………………………………………………………………………….
1
The NCERT may take some initiative in production of some more books for
bright students of mathematics at various levels.
2
I quote from the introduction of the book “Arnold’s Problems”, Edited by V. I.
Arnold, Springer & PHASIS, 2000: “Mathematical training in Moscow usually
begins before the school age.”
3
To provide appropriate learning material and to guide them in learning and
problem solving on their own.
4
Examination here means an innovative method of evaluation.
5
CBSE is one of the finest organizations, coordinating a difficult work of framing
curriculum and conducting examinations of many types in this vast country. It is
fully capable of taking care of the suggestions with the help of innovative methods
of paper setting and evaluation using sophisticated software.
6
Problems, which require step by step mathematical deductions and not those
problems which require tricks and only practice.
7 Setting up a separate organization outside an existing one would require new
infrastructure, money and is not likely to have control over the all examinations in
the country. This will also require an additional arrangement and time table for the
examinations in optional mathematics like that for JEE, adding additional burden
on students. These examinations should be a natural part of regular examinations.
In a lecture on “How to Read Human Genome” at IISc on 15th December, 2008 at
the Indian Institute of Science, Bangalore.
8
9
For a bright student this means at an accelerated pace. I know a student in USA,
who was admitted to BS at the age of 11, completed his undergraduate curriculum
at the age of 16 and immediately joined Ph. D. program of the University of
Chicago. He has turned out to be a good mathematician. In India in a normal
course of study, this student would have taken many years to do Ph. D. and quite
likely would have remained just a bright smart student without much success. I
am not suggesting such an accelerated pace but an accelerated pace for a normal
bright student, a programme of this type does not exist in India.