The draft undergraduate curriculum for Mathematics proposed by the University Grants Commission (UGC) seeks to create mathematical knowledge and skills that are contemporary and, at the same time, rooted in Indian heritage, in alignment with the goals articulated in the NEP, 2020. Unfortunately, as has been pointed out by a large group of mathematicians and teachers of Mathematics, it does not come anywhere close to achieving such lofty goals. It is termed a Learning Outcomes-based Curriculum Framework (LOCF) but it is hard to see what learning outcomes it assures.
Considering that the proposals will have an impact on what will be taught in thousands of colleges and universities to lakhs of students, it is important that the UGC provide a forward-looking curriculum, one that develops strong mathematical foundations, enables students to face the uncertainties of 21st-century life and contribute to socio-economic development. But the proposal compromises even the current strength in core Mathematics, adopts a mechanical attitude to applications and fails even in its attempt to provide rootedness in Indian heritage.
Any curricular proposal needs some unifying curricular and pedagogical purpose in deciding what is taught, why and how it is to be taught, and how such knowledge is to be assessed. Teachers and educational systems should have the capacity (or be able to quickly build the capacity) to implement the proposed curriculum. The draft offers no such clarity of purpose and possible implementation.
Educational researchers point out that an understanding of the historical development of mathematical ideas helps students’ learning. It would be welcome if this were attempted, pointing to global achievements across cultures and placing Indian contributions in context. One well-designed course, backed by well-presented material, would achieve this. Instead, the draft proposes a long list of courses, each with mathematical content that would need, at most, a couple of classes of teaching. In fact, the content of the proposed courses on “Indian Mathematics” is all at a high-school level, ignoring further developments, and little of it can be meaningfully integrated with contemporary Mathematics courses.
In terms of curricular structure, it is certainly welcome to offer a range of options for students to choose from. But it is ridiculous to choose between one such “historical” course and a mathematical one such as calculus of variations or a skill-based one such as computer programming. What rationale can be provided for such a grouping to choose from?
It is also worth asking what an exam on such “Bharatiya” Mathematics would look like. The calculations are at school level, so perhaps information items are expected to be memorised and recalled (Note that the emphasis is not on historical analysis either). Why then would a student choose calculus of variations where getting a good grade would surely be more difficult? Implementing such choices will seriously weaken Mathematics education.
On the other hand, core mathematical competence has been compromised. In the draft structure, students learn “real analysis” in their fourth year, hence building on it for future courses is not possible. The emphasis needed on linear algebra and abstract algebra is missing. Mathematics of machine learning may be a welcome addition, but linear algebra simply cannot be relegated to be a part of machine learning. How can one hope to understand the contributions of a great mathematician like Ramanujan (offered as a course) without an in-depth study of analysis and number theory?
A mechanised approach to applied Mathematics, presenting applications in a long list of courses titled “Mathematics in X” is also problematic. There is a structural and conceptual unity to Mathematics that needs appreciation. A great deal of Mathematics was formulated to address questions arising from Physics, and fields such as the Life Sciences, Engineering, Computing and Economics lead to new Mathematics even today. The interplay between the internal disciplines of Mathematics (such as algebra and geometry) as well as between Mathematics and other disciplines is best learnt in their contexts. Many courses such as complex analysis, differential equations, discrete mathematics, probability and statistics, mathematical logic, algorithms and programming offer core techniques that help such cross-fertilisation, and elective courses such as stochastic processes, cryptography, optimisation theory and machine learning lead students towards new and exciting directions. We only get disappointed when we look for such coherence in the proposed draft, and instead find a touch of the bizarre in a proposed course on “Mathematics in Meditation”.
A course on “Mathematics in Drama and the Arts” looks promising and welcome, but where would we find teachers (and culturally rooted material) for this course? In this sense, the proposed material for most new courses is abysmally poor in quality, in contrast to the availability of excellent texts for core mathematical areas.
No curricular reform can be implemented without its ownership by the teaching community in the country and the UGC seems to have little regard for this. Good Mathematics curricula existing in the country have not been utilised either.
We need a Mathematics curriculum that prepares the student to meet the challenges of the future by fostering problem-solving, theory building, adaptability, and the ability to apply mathematical concepts to real-world contexts. For this, it is imperative that the UGC drop the proposed draft curriculum in its entirety, and formulate one that is forward looking and builds a strong future for our students.
The writer is professor, Azim Premji University, Bengaluru, and faculty (retired), Institute of Mathematical Sciences, Chennai
