Mathematics Curriculum and Pedagogy at the Tertiary Level: A Perspective from J&K

Fozia S. Qazi

Islamic University of Science and Technology, Awantipora, J&K

fozia.qazi@islamicuniversity.edu.in

National Initiative on Mathematics Education

Northern Region Conference, Nov 21-23, New Delhi

Abstract: This talk will present a summary of the current status of tertiary education in J&K with a

focus on mathematics and the teaching of mathematics in the colleges and universities of the state. In

spite of significant progress in the domain of education in J&K there is a gap between its quantitative

and qualitative dimensions. Drawing from some personal experiences of starting a new actuarial

mathematics program in J&K, the talk will touch upon the need for reform in mathematics

curriculum and the necessity of introducing subject-specific orientation programs for faculty.

Overview:

The higher education field in Jammu and Kashmir has, over the last 60 years, made

significant progress. But even though this progress has resulted in an increased literacy rate

and better educational infrastructure and facilities, it did not evolve in tandem with

curricular reforms or appropriate teaching methodologies to the extent one would have

liked. There has been minimal reform in higher education in Jammu and Kashmir,

especially at the UG level: whether in terms of curriculum, or pedagogy. This applies, in

particular, to mathematics education.

The quantitative information regarding tertiary level institutions in J&K is as under:

Institutions of Higher Education Number

Universities (including two recently opened Central Universities,

and two ‘deemed universities’)

11

Government colleges that offer 3-year degrees post 10+2 (some of

them also offer PG courses)

76

Government professional Colleges 12

B. Ed Colleges that offer a one-year program 145

Private Colleges 119

There are six universities offering programs in mathematics at the UG or PG level through

their main campuses or satellite campuses. They are University of Kashmir (KU), University

of Jammu (JU), Islamic University of Science and Technology (IUST), Baba Ghulam Shah

Badshah University (BGSBU) and Shri Mata Vaishno Devi University (SMVDU). The new

Central University Kashmir has also started M.Sc. program in mathematics while as Central

University Jammu is yet to start its operations. There is a lack of coordination or

collaboration between the universities and their respective mathematics departments.

The colleges, both state and private, are academically affiliated with either Jammu

University or Kashmir University. However, administrative control of state colleges lies

with the state government. This dual nature of management often makes it difficult to

monitor the standards. In 2009-2010 the student enrolment in state colleges was 115,552

with corresponding faculty strength of 2060, thus giving a faculty-student ratio of 1:56.

Curriculum:

Undergraduate Level

At this level students do not graduate with a degree in mathematics but rather a B.A.

or B.Sc. and take mathematics as one of the four or five subjects every year. This

translates to a total of roughly 10 math courses during the three years – some year-

long (Real Analysis and Abstract Algebra) and others of 6 months duration. There

are no Honors programs in mathematics. The curriculum in state colleges has gone

through some revisions but not at a level that would qualify it as a reform. A new

stream labelled ‘Applied Mathematics’ was introduced in Kashmir in 2005 in some of

the newly established government colleges. However, all it meant was that three new

courses were added to the regular 3-year math curriculum while keeping all of the

existing courses. The three new courses are Descriptive Mathematics (a review of

high-school level mathematics), Discrete Mathematics and Probability and

Optimization (no statistics). The enrolment in this stream has been low.

Islamic University of Science and Technology has become the first institution in J&K

to not only offer a full-fledged mathematics program at the UG level but that too in a

very job-oriented of actuarial mathematics. Our 3-year program in actuarial and

financial mathematics is the first on its kind in the state and one of the very few in

the country.

Postgraduate Level

The curriculum offered by the various universities at the PG level has seen some

recent updates and would be considered a positive move. Courses like operations

research, coding theory, mathematical biology etc have been introduced – many of

them as electives. However, in many cases, the faculty is not available to teach these

courses thus limiting the pool of electives for students. In some cases courses like

computer programming are offered late in the program and thus reducing the

effectiveness of some applied math courses offered earlier in the program. It would

be fair to say that the three new universities on the scene – SMVDU, BGSBU and

IUST have taken the lead in introducing innovative courses and programs relevant to

today’s job market whether at the PG or UG level. At the PG level, SMVDU offers a

good collection of electives

Pedagogy:

The teaching of mathematics leaves a lot to be desired. Little no project work is included in

the curriculum and as such students often lack a broad understanding of applications.

There is a disconnect between what the student learns in the classroom and their daily

experiences. Real-world applications of mathematics are rarely discussed and students often

see no ‘purpose’ in mathematics other than solving exercises.

Mathematical writing is not taught. At the UG level assessment is only through written

examination focused on problem solving. Paper writing (even expository) is not required or

encouraged. This leads to a tendency for rote learning in some cases and serious gaps in

mathematical comprehension and reasoning.

Teacher orientation programs offered by Academic Staff Colleges are general in nature and

not discipline specific. They are also not frequently offered.

Recommendations:

1. Teacher training:

a. Discipline-specific orientation programs for faculty should be offered that

have a focus on pedagogy. These need not be month-long and can be 2-3 days

long and focused on teaching of mathematics. There is a critical need for well-

trained mathematics faculty especially at the undergraduate level.

2. Curriculum:

a. The curriculum needs to change in order to include applications of

mathematics to the world around us. Project work should be included.

b. The curriculum needs to incorporate the use of technology in the classroom.

However, this can be implemented only if the faculty is trained appropriately

beforehand. The orientation programs should include such components.

c. The curriculum should include job-oriented courses at the undergraduate

level also e.g. mathematical finance, computer programming, statistics etc

3. Mathematical Communication:

a. Writing to learn mathematics should be encouraged as a pedagogical tool.

b. Project work (or senior thesis) even at the undergraduate level, should be

encouraged.

c. Student seminars and conferences should be encouraged

4. Assessment:

a. Mathematical writing should form part of student assessment.

b. Project work should be encouraged and included in student assessment.

References:

1. Anthony, G., Walshaw, M., (2009) Effective Pedagogy in Mathematics, Educational

Practices Series 19, International Academy of Education.

2. Kamal, A., Wahid, S. (2011), Educational Opportunities: Cooperation across the Line of

Control in Kashmir, Conciliation Resources, UK

3. J&K Government Higher Education Department website