The Mathematics Team, CRMD, Eklavya
The mathematics team at Eklavya broadly works in the area of primary and upper primary mathematics. By engaging continuously with students, teachers, and the mathematics education community, we hope to find ways in which school mathematics can be made fun, relevant, and meaningful for children.
Mathematics in schools is often characterized by fear and anxiety, it invariably functions as a gatekeeper that serves to exclude, rather than include. Recognizing this, the teaching and learning of mathematics has been an area of much concern over the last few decades. The work of several individuals, institutes and organizations – in India and abroad – has contributed greatly to our understanding of mathematics education at the primary school level.
In the mid-80s and early 90s, Eklavya ran a primary education project called Prashika (Prathamik Shiksha Karyakram) after conducting a series of surveys in Shahpur and Harda, MP. Taking into account the socio-economic conditions and cultural traditions of the learners, the local environment and the physical and administrative conditions of schools at the time, a primary school curricular package was developed, which included the Khushi-Khushi textbook series. It sought to integrate mathematics and language learning, bringing them together through an exploration of the child’s environment. Eklavya worked closely with teachers, empowering them to create similar appropriate materials for children.
Today, in context of the work already done, NCF 2005 and RTE 2009, the work of the mathematics team can be characterized under the following broad areas:
Curriculum Research
With a hope to develop teaching-learning trajectories for particular topics in school mathematics, we design and conduct teaching experiments in government and private schools in Hoshangabad district. By reading existing mathematics education literature and engaging with the mathematics education research community, we find ways of linking research to actual classroom practice, allowing for us to identify the problems that characterize the teaching and learning of mathematics and to build an organic relationship between theory and practice. Our work is documented in the form of articles, films, modules and academic papers.
Some of our recent work includes the following:
Fractions: We conducted a three year longitudinal study on the teaching and learning of fractions from Class 3 to Class 5 at Raipu
r Girls Government School, Hoshangabad District, MP. The study offers a curricular alternative to the teaching of fractions. Departing from the standard practice of introducing fractions as a part of a whole, we propose a teaching-learning trajectory that begins with the share meaning of fractions and moves on to the measure meaning at the second level. The study draws from the Realistic Approach to Mathematics Education that believes in creating appropriate 'model situations' to facilitate conceptual understanding. It has been documented in the form of a six-part documentary entitled ‘Bato, Napo, Bhinn Batlao’. Copies of the film can be obtained by writing to
Division: We conducted a three week study with students of Class 6 at Raipur Girls Government School, Hoshangabad District, MP, attempting to understand how division is learnt. We worked with an alternative to the standard division algorithm – the partial quotients method – that builds upon students’ intuitive notions of sharing and distribution. This method had been used by the Delhi SCERT textbooks and is currently being used by the NCERT as well. The study resulted in a paper entitled ‘Tackling the Division Algorithm’ that was presented at the International Congress of Mathematics Education (ICME-12) held in Seoul, South Korea. It argues (as much research on teaching division suggests) that the standard long division algorithm, based fundamentally on the place value system, can be counter-intuitive to children’s existing whole number sense and doesn’t relate in a natural way to children’s intuitive notions of division. It describes the outcomes of our teaching experiment and suggests that the partial quotients method enables students to carry out division with understanding and much fewer errors.
The work done is preliminary, and we hope to extend it in order to develop a teaching-learning trajectory for division. We would like to include the grouping meaning of division and build on children’s informal strategies while working with meaningful contexts. We would also like to probe teachers’ understanding of the algorithm by conducting teacher interviews and observing classrooms. We invite researchers, teachers and interested educators to collaborate with us to develop this further.
Working with Teachers
We have recently started a mathematics teacher forum, so as to engage directly with teachers to explore the issues and challenges of teaching primary school mathematics. We often find that there is a disconnect between the theory and practice of mathematics education, but believe that neither can exist without the other. We hope that by initiating a dialogue with teachers, we are able to bridge the gap between research and classroom practice. On the one hand, we hope that the concerns of teachers motivate and form the vocabulary of future research, while on the other, we hope that teachers are able to appreciate the value of research that has already been done. Together, we hope to find ways in which mathematics education can be made more meaningful.
The Team as a Resource Agency
As a part of our work, we also serve as a resource agency, working closely with governments and organizations to develop mathematics curricula and textbooks. Over the past year, we have collaborated with the SIERT, Rajasthan and ICICI Foundation to develop the mathematics syllabus for Classes 1 to 5 for the State of Rajasthan. So far, we have developed textbooks for Class 1, 3 and 5, and will be working on Class 2 and 4 in the coming year.