Jayasree Subramanian
Mathematics education in general receives a lot of attention in the education policy documents as well in the curriculum frameworks because of the importance attached to the subject and also because of the difficulty it poses for learners. On the one hand, mathematics is becoming important in several higher education programmes – from the sciences including biological sciences and economics to finance, business management and social sciences as well. On the other, a large number of students from socio-culturally and economically marginalized background end up failing in the secondary school final examination because they fail in mathematics, thereby losing their opportunity for higher education or employment that require successful completion of schooling as a minimum requirement. So, mathematics functions as a gatekeeper for them. NEP 2019 is no exception to the importance it gives to mathematics education.
One of the members of the drafting committee of NEP 2019 is Prof. Manjul Bhargava, a Fields medallist (medal for outstanding achievement in mathematics) and as one can guess from his name, a person of Indian origin. Though he was neither born nor brought up in India, he visits India regularly, has a deep interest in Sanskrit, ancient Indian history and music. It is interesting to note that NEP 2019 makes repeated reference to Sanskrit as a language of importance, seeks to integrate a certain version of ancient Indian history in the school curriculum and wants everyone to learn music. In the context of mathematics education, Sanskrit, Indian history of mathematics and music get a special place. Even as one appreciates the fact that a renowned mathematician is involved in the drafting committee, it is difficult to ignore the absence of an equally renowned mathematics educator from India or abroad in drafting the policy. It is indeed a pity that India does not value inputs from mathematics education research engaging with the complex Indian reality as important for shaping education policy and curriculum frameworks in mathematics education and is willing to hide behind the stature of and settle for an established mathematician to do the job.
NEP 2019 brings in a lot of major changes, of which, its insistence on making early childhood care and education compulsory is very significant. Some of the changes suggested, however, may have very unfortunate consequences and much has been written about them in the mainstream media. The new NEP seeks to divide the school going years into four stages – five years of foundation consisting of 3 years of pre-primary and grades 1 and 2; three years of preparatory stage consisting of grades 3 to 5; three years of middle stage consisting of grades 6 to 8 and finally, four years of secondary stage consisting of grades 9 to 12.
Early childhood care and education (ECCE) receives a strong emphasis in the policy – the idea of preparing the child for school education gets a lot of recognition. Interestingly, rather than ensuring that pre-primary schools/anganwadis have specially trained teachers to teach the children, the document calls for community support and teacher volunteers to teach at this level, which may actually be counterproductive. As far as mathematics is concerned, at the ECCE level, there is a mention that the emphasis will be on play-way methods and activity-based learning (pp 75). However, there is no explicit mention that children should not be taught to write numbers or carry out operations with them. This is a matter of specific concern, because even some international schools boast about how they expect children to know to read and write numbers up to 300 or at least up to 100 before they join grade 1, ignoring questions such as whether children as young as five years can relate to large numbers in any meaningful way.
For the foundational stage, the policy suggests dedicated mathematics hours every day, ‘mathematics weeks’ and ‘mathematics melas’ every year, where children will participate in various activities and projects, weekly assemblies focusing on mathematics, puzzle solving sessions and activities designed to explore the link between ‘classroom mathematics’ and ‘real-life mathematics’. These suggestions are certainly appreciable, but unless planned well, they can end up being a set of assorted events that do not really amount to quality learning. These will be productive only when the mathematics curriculum at the foundational stage adopts an appropriate pedagogic approach and is carefully designed and sequenced, based on existing research and incorporates a research component to learn from experience. But unfortunately, this is missing. The chapter on foundational literacy and numeracy deals more with the organization of the ECCE class. It is not clear regarding the approach to the learning and teaching of numeracy, its curriculum and process of curriculum development.
At the preparatory stage, the policy suggests an integrated approach, calling for a generalist teacher and at the middle stage, specialist teachers will be introduced. At the secondary stage, students are expected to start taking board examinations, of which at least two will be in mathematics. Apparently, a student can take more advanced courses in mathematics at this stage. Unlike the NCF 2005 which laid a strong emphasis on constructivist approaches to learning mathematics, emphasizing the process more than the product, the NEP document says very little about an appropriate pedagogical approach for the preparatory and middle stages. One might argue that the policy document is not expected to spell out pedagogic approaches. But given that the policy document has suggested reorganization of the preparatory and middle stages, it should have deliberated upon how this reorganization should be realized. We are now left to wait for the curriculum framework to build the bridge between policy recommendation and classroom transaction.
The only suggestion the document makes is the need for building logical thinking and problem-solving ability, to do which it suggests providing opportunities for children to work with building blocks, solve puzzles, play games that call for logical thinking and so on. It also says logical games, puzzles and problem-solving activities will be incorporated in the curriculum.
By clubbing grades 9 to 12 as the secondary stage, the policy calls for a departure from the prevailing system of streaming after grade 10. However, from grade 9 there will be several choices made available including (one or many) courses in advanced mathematics as possible options for interested/capable students. The rest will take two examinations in mathematics; presumably comparable to the existing grade 10 level split into two parts.
In order to cultivate interest in mathematics for those who will eventually opt for courses in mathematics, right from the middle level, ‘talented’ students will be encouraged to participate in mathematical circles. These circles will consist of mathematically talented students and interested teachers from a neighbourhood who will meet during the weekends regularly to spend time solving challenging problems and honing their abilities. Similarly, mathematics clubs and project-based teaching will cater to the talented/motivated students who will be selected strictly on the basis of merit. It is clear that these students will be nurtured to pursue mathematics. The document does not consider the question of rural, semi-urban, urban divide, gender, caste and socio-economic hierarchies, difference in the kinds of schools to which students have access as factors contributing to who gets to be talented in mathematics and who does not. Students who belong to the margins of the society, under represented communities and religious groups, urban poor, transgender and special needs communities are seen as bringing in deficit and measures are suggested to try and improve their access to education, including mathematics education. There is no reference to the kind of knowledge and experience the students from the margins bring to the classroom to enrich the curriculum that is designed for the normative learner, who belongs to the middle /upper middle-class from an urban location and has educated parents and standard career ambitions.
In other words, the policy document takes a step back from the progressive approach taken in NCF 2005.
The document makes repeated reference to India’s past, its contribution to education and the approach adopted by the ancient education system without substantiating its claims by pointing to relevant literature. To quote an example, on page 2, it says, ‘The Indian education system produced scholars like Charaka and Susruta, Aryabhata, Bhaskaracharya, Chanakya, Patanjali and Panini, and numerous others. They made seminal contributions to world knowledge in diverse fields such as mathematics, astronomy, metallurgy, medical science and surgery, civil engineering and architecture, shipbuilding and navigation, yoga, fine arts, chess, and more’. Variations of this keep recurring in the document.
Promoting Sanskrit as a repository of ancient Indian knowledge, the document says wherever relevant, puzzles, poems and games from the Indian tradition should be incorporated in mathematics. Listing several achievements of ancient Indian mathematicians whose work did not/does not get the recognition their western counterparts do/did, in spite of the fact that the Indian work predates work from the west, the document calls for an inclusion of Indian achievement in mathematics in the curriculum.
There are several problems with this position. For one, while there is a rich body of current literature on Indian contribution to mathematics (see for example Kim Plofker’s book on Indian Mathematics which is considered a standard text), there were also several other ancient cultures that made significant contributions to mathematics – Greek, Chinese and Islamic traditions just to name a few. It would be appropriate and historically faithful to present the history of mathematics as having roots in diverse cultures. Secondly, there is no acknowledgement of caste and its role in knowledge production in India. Sanskrit as a language was available only to Brahmins and a few dominant caste members. On the other hand, there is also a range of mathematical knowledge created by communities engaged in different kinds of productive labour. Their mathematics does not figure as Indian heritage. Mathematical knowledge and culture of a small section of the population is passed off as Indian heritage, without paying any attention to the sense of alienation it will create for the large majority of learners.
To conclude, the policy document does not take the geopolitical, religious, gender, socio-cultural, economic, linguistic diversities and hierarchies and the position of the disabled learner as the complex reality of India and make any new recommendations about how to meet the challenge of providing equitable mathematics education. It sees the category of students as homogenous and seeks to provide specialized training in mathematics for a small minority, without raising and addressing the question of ensuring comparable participation across the multitude of differences. It is therefore clear that the policy is indifferent to the fact that only those who are already privileged are more likely to get better opportunities to learn higher level mathematics. At a time when equity issues have gained a significant place in mathematics education and when emancipation is emerging as one of the aims of mathematics education, NEP 2019 betrays ignorance of these developments. Rather than building on a more inclusive vision for mathematics education that NCF 2005 adopted, NEP 2019 resorts to tokenism. By adopting an approach that seeks to highlight only Indian contribution to mathematics rather than highlighting mathematics from across several ancient civilizations as well as forms of mathematics that are still alive in the practices of people engaged in productive labour, the document seeks to present a distorted image of the history of mathematics which is very problematic. More importantly, the policy document does not make any reference to an appropriate pedagogical approach that mathematics curriculum needs to adopt. Is the decision on the pedagogy going to be made by textbook developers or is the document leaving the choice of pedagogy to the schools and teachers? And if yes, what kind of support does it provide the teachers to make these choices and what measures will it adopt to study the effectiveness of the approaches adopted?
Policy documents often outlive the governments that brought them into effect. A careful reading of the document, particularly the sections that focus on curriculum and pedagogy and the section on teacher education, reveals that the document suffers from lack of engagement with education research. Simply saying ‘research shows’ without pointing to specific reference is one evidence of this shortcoming. Making drastic changes in the policy that will have serious consequences for classroom transaction, without well-designed research to support the changes is irresponsible and unethical.
The author is an independent researcher working in the area of mathematics education with a deep commitment to socio-political concerns in mathematics education. She was a Fellow at Eklavya Bhopal from 2005 to 2012, Associate Professor at TISS Hyderabad from 2012 to 2018 and a Visiting Faculty at Homi Bhabha Science Education, Mumbai from February to August, 2019. She can be reached at jayasree.subramanian@gmail.com.