nime nrc formatted report

1 NATIONAL INITIATIVE ON MATHEMATICS EDUCATION NORTHERN REGION CONFERENCE – 21-‐23 November, 2011, Delhi

NATIONAL INITIATIVE ON MATHEMATICS EDUCATION

NORTHERN REGION CONFERENCE

21-‐23 November, 2011

Ambedkar University, Delhi & Shiv Nadar University

www.nime-‐nrc.webs.com

Contents Aims and History.......................................................................................................................................... 2

Speakers & Panelists .................................................................................................................................... 5

Summary of Events ...................................................................................................................................... 6

Inauguration ............................................................................................................................................ 6

Plenary Talk.............................................................................................................................................. 7

Invited Talks ............................................................................................................................................. 9

Parallel Sessions..................................................................................................................................... 10

Panel Discussions ................................................................................................................................... 15

Organisers .................................................................................................................................................. 24

Detailed Profiles of Speakers & Panelists .................................................................................................. 26

List of Participants ..................................................................................................................................... 31

Schedule .................................................................................................................................................... 35

Acknowledgements ................................................................................................................................... 38

Invitation.................................................................................................................................................... 40

Sponsors

• Ambedkar University, Delhi • Shiv Nadar University • Texas Instruments

• National Board for Higher Mathematics • Indian National Science Academy


Aims and History

In the 21st century, the world is increasingly dependent on Information technology. We see this in a

range of activities beginning from simple emails to commercial online transactions. Security of these communications is of grave concern. The encryption system used to secure these communications is based on a simple fact from mathematics: to multiply two numbers is easy and to factorize a number is

difficult.

Though mathematics either directly or indirectly plays so much of a role in our society, it is rarely acknowledged with any degree of comfort. Part of this lies in the fact that almost half of the literate world has experienced difficulties when they encountered mathematics in school. Children learn to

count objects with ease as toddlers. The switch from five oranges to the number five is a level of abstraction that the human mind copes well with. But somewhere along the line, particularly by the time children reach middle school, a fear for the subject sets in and leaves a lasting impression.

Mathematics Education seeks to examine all aspects governing the learning, teaching and assimilation of

mathematics from early childhood to formal degrees at the University level. The National Initiative on Mathematics Education (NIME) aims to bring under one umbrella a range of ideas, trends and research in the area of Mathematics Education. Practice and research, learning tools and teaching methods,

technology and local knowledge systems, history and cultural aspects, policy and curriculum design are some of the aspects that directly affect the study of mathematics. It is these concerns that we hope to understand through NIME.

Internationally, an active community of mathematics educators meets every four years through the

ICME (International Congress on Mathematics Education). The Congress will gather a broad spectrum of participants such as researchers in mathematics education, teacher educators, practicing teachers, mathematicians, and others interested in mathematics education*.

ICME is organised by ICMI, The International Commission on Mathematics Instruction. ICMI is an official

commision of the International Mathematics Union that was set up in 1952. The next chapter of ICME will take place in Seoul in 2012. India has an important role to play in ICME-‐12 as it will be making a `National Presentation’ during the Congress. The National Presentation will have lectures, exhibitions,

videos, panel discussions and other initiatives with the aim of acquainting the Congress to Mathematics Education in India. The Indian National Science Academy (INSA) has set up a steering committee to

facilitate the National Presentation. The steering committee and invited members have together created `NIME’.

* Taken from the website http://www.icme12.org/sub/sub01_05.asp.


Under the aegis of NIME, a series of regional conferences and a national conference on Mathematics Education are being organized. The networks formed by these conferences will not only help in creating

the National Presentation for ICME – 12 but will also make sure that Mathematics Education initiatives and innovations from far-‐flung areas are accessed. NIME would also help reclaim for Mathematics Education a central role so that the system of education in this country can benefit directly from the

shared learning gleaned through the conferences.

The broad themes that NIME has identified are:

a. Historical and Cultural aspects of Mathematics and Mathematics Education. b. Systemic and Policy aspects of education. c. Mathematics Curriculum and Pedagogy at Elementary, Secondary and Tertiary Levels. d. Teacher Education and Development.

Each of these themes covers a broad spectrum of ideas and aspects.

The National Initiative on Mathematics Education: Northern Region Conference (NIME – NRC) was co-‐hosted during 21-‐23 November 2011, by Ambedkar University, Delhi (AUD) and Shiv Nadar University

(SNU). It covered the states of Delhi, Rajasthan, Madhya Pradesh, Haryana, Uttarakhand, Punjab, Himachal, Uttar Pradesh and Jammu and Kashmir.

The purpose of the NRC was to

Bring together mathematics educators, mathematicians with a keen interest in mathematics education, school as well as college teachers from various parts of India to share their experience, practices, and expertise with each other.

Provide a common platform for diverse groups working towards the cause of improving mathematics education and provide them with the opportunity to showcase their activities.

Create a forum to deliberate upon various issues such as changes in mathematics education policy, catalyzing research studies on mathematics education, bridging research and practice, and bringing about an overall improvement in the practice of mathematics education in the country.

The NRC brought together on a single platform, the significant innovations and efforts in improving mathematics education in school and tertiary education from the northern region of the country and thus helped to identify the best practices which can be showcased at the National Presentation at ICME

– 12.

The NIME-‐NRC conference was held from 21-‐23 November 2011 at the India International Centre, Max Mueller Marg, New Delhi. The conference focussed on the Themes given in b., c. and d. above. The

inaugural session was followed by a plenary lecture. There were invited talks, panel discussions and parallel sessions in which participants presented papers. There were rapporteurs for the panel


discussions and the plenary session. The rapporteurs presented their report in a special session on the last day. This was followed by an open session for the participants.


Speakers & Panelists

Inaugural Session: • Chief Guest:

Professor Dinesh Singh Vice-‐Chancellor, University of Delhi

• Professor Madan Gopal Director, School of Engineering, SNU

• Professor Vijaya Varma Advisor Planning, AUD

• Professor Amitabha Mukherjee Department of Physics and Astrophysics, University of Delhi

• Professor Geetha Venkataraman Dean, School of Undergraduate Studies, AUD

Plenary Speaker • Professor Anita Rampal

Faculty of Education, University of Delhi

Invited Speakers • Dr Asha Mathur

Former Vice-‐Principal of Lady Shri Ram College, University of Delhi

• Dr Jayasree Subramanian Eklavya Foundation

Panelists • Professor Inder K Rana

IIT Mumbai • Ms V Sudha

Sanskriti School, New Delhi • Dr Jonaki Ghosh

Lady Shri Ram College, University of Delhi • Professor Parvin Sinclair

Indira Gandhi National Open University • Professor Amber Habib

Shiv Nadar University • Professor Fozia Qazi

Islamic University of Science & Technology, Kashmir • Professor Nargis Panchapakesan

University of Delhi • Ms. Usha Menon

Jodo Gyan

• Dr. Haneet Gandhi

University of Delhi • Professor Vijaya S. Varma

AUD • Professor Rohit Dhankar

Azim Premji University and Digantar, Jaipur. • Professor Farida Khan

Jamia Milia Islamia • Ms Anita Sharma

Principal, S.D. Public School, New Delhi • Dr. Rakhi Banerjee

AUD • Ms. Rashmi Kathuria

Kulachi Hansraj Model School, Delhi

Speakers in Parallel Sessions • Ms Shreya Khemani

Eklavya Foundation • Dr Jayasree Subramanian

Eklavya Foundation • Ms Sonia Mondal

TISS, Mumbai • Ms Anchal Arora • Ms Jasneet Kaur

Jamia Milia Islamia • Dr P K Chaurasia

NCERT • Mr Pramod Maithil

Eklavya Foundation • Mr Ghanshyam Tewari

Eklavya Foundation • Mr Nidesh Soni

Eklavya Foundation • Professor Rekha S. Sen

Jamia Milia Islamia • Mr R Srikanth

Welham Boys School, Dehradun • Ms Himani Asija

Delhi Public School, Vasantkunj • Ms Ashu Threja

Miranda House, University of Delhi


Summary of Events

Inauguration The inaugural ceremony took place at 9:30 am, November 21 5, in the Multipurpose Hall of the New Extension Block, India International Centre.

Prof Vijaya Varma welcomed the delegates and provided a brief introduction to the genesis and aims of Ambedkar University, Delhi and its vision of combining excellence with equity, in line with Dr

Ambedkar’s vision of social change through institutional mechanisms. While the university is committed to implementing the reservation policies it seeks to be more pro-‐active and to enable students from marginalized communities to be the best they can be. The university is made up of Schools which are

interdisciplinary in nature, and faculty are typically appointed concurrently in two or more Schools. The undergraduate programmes are disciplinary, but allow major-‐minor combinations with graduation in 4 years. Postgraduate programmes may be interdisciplinary.

Prof Madan Gopal wished the organizers and participants an exciting debate on the issues in

mathematics education. He described Shiv Nadar University’s uniqueness in seeking to blend research and learning, and integrating humanities and social sciences with the natural sciences and engineering. In particular, the mathematics programmes are designed to dissolve the barriers between mathematics

and other disciplines. Our students will be exposed to rigourous mathematical thinking, as well as to applications in diverse areas like medical research and financial management. They can additionally

choose specializations within their major discipline, or minors outside it.

Prof Amitabha Mukherjee introduced the conference and its context. He noted that of all the regional NIME conferences, this one had the biggest task in the sense that it covered the largest number of states – including not only UP but also Madhya Pradesh and Rajasthan. In spite of their best efforts, the

organisers were unable to attract participation from some of the states in the region. The time available for organising this conference was short. The NRC had taken up the following three themes:

1. Mathematics Curriculum and Pedagogy at various levels: elementary, secondary and tertiary 2. Teacher education and development

3. Systemic issues in relation to mathematics education

Of these, Curriculum and Pedagogy was, in some sense, the biggest theme – involving the largest number of people. Three plenary sessions have been devoted to it – a plenary talk for the Elementary level and two panel discussions for the Secondary and Tertiary level respectively. There is also a panel

discussion for each of the other themes – namely Teacher Education for Mathematics, and Systemic Issues in relation to Mathematics Education.


Prof Mukherjee felt that the purpose of the conference would be served only if a large number of people give their inputs. Plenty of time has therefore been allowed for questions and discussions. All

speakers have been requested to keep their initial presentations brief. In addition, there is an open discussion session on the last day. If people feel that there are issues which could not be raised due to lack of time, or which do not figure in the themes but are important, the open session would give an

opportunity to raise them. The discussions would be very important, and some of the most significant contributions to this conference may well come from people whose names are not listed in the programme.

The keynote address was delivered by Prof Dinesh Singh. He spoke of how the conference was an event

after his own heart, and his joy in seeing among the participants many of his colleagues and students. He raised the issue of why we need so many conferences on mathematics education, and why the state of mathematics education is a concern at gatherings all over the world. There does not seem to be any

success in setting out clear-‐cut tangible goals and charting our progress towards them. He felt that comparing notes at conferences, while important, could not suffice to resolve our problems. He expressed a sense of urgency that within the next 5 years mathematics must combine with science,

technology and industry to start contributing to an Indian resurgence. He asked the participants of the conference to suggest policies and paths and measures of success to government and to advocate for their adoption.

Prof Geetha Venkataraman gave the vote of thanks to the inaugural speakers and to all the

participants. She noted that one of the tasks before NIME was to prepare a roadmap for the future of mathematics education. She especially thanked the two host universities and the other sponsors for their financial and organizational support. She also thanked the DPS Society for providing

accommodation to the outstation participants.

Plenary Talk The main section of the conference began with a plenary talk by Prof Anita Rampal on Curriculum and Pedagogy at the Elementary Level. Her presentation focused on concerns underlying recent curriculum

design at the primary level, especially the work done in the context of the 2005 National Curriculum Framework which was a watershed in terms of the subsequent text and syllabi.

She started by recalling how, during the 1970s, university academics got associated with work in schools, and very often with remote schools in rural areas and learned on the job about diversity. This

kind of participatory curriculum development with children and communities is an area that needs to be strengthened and taken forward for advocacy in policy formulation.

Professor Rampal talked of the policy shift that was captured by NCF 2005: Right to access to quality elementary and maths education was stated even prior to the enactment of the Right to Education Act.

She talked about how half the children are participating in education and the other half keep getting pushed out at the elementary stage itself—and how Mathematics has an unfortunate role in failing and de-‐motivating children at the elementary level in India.


Professor Rampal observed that a large number of children get marginalised in their learning experience by the elite and abstract nature of knowledge taught in maths classes; and the need for a shift in focus

from achieving or realising narrow roles to the higher roles of maths education.

We need to take up the following challenges: curriculum is not a given, what should be taught at a certain level is not a given. Why do we go by the historical baggage we carry in terms of ideas of what and how maths is to be taught in schools – this affects participation and motivation for learning.

Liberating school maths from the tyranny of one right algorithm, one right answer, was a key desire of

the national curriculum framework. What was instead kept in focus was the emphasis within maths education, adopted in some countries like Japan, where the focus is not on the answer obtained but the nurturing of a process through which children can adopt multiple strategies towards solving a problem.

Another distinct feature or stand which NCF took was the emphasis on every-‐day and folk mathematics.

Science and Maths are usually presented as context free. The assumption is that there is no cultural context to Mathematics as an area of knowledge and hence to maths education. This makes maths education all the more alienating. In a developmental, cultural context, maths should be able to serve

and nurture a child’s curiosity.

There are several other problematic and blind spots in the curriculum work done in maths—she cited the example of art for children in comparison to which the maths texts are linear and straitjacketed. The NCF tried to look at the maths text as a non-‐linear visual space and to engage with artists to bring in the

child’s cultural context in order to represent and do justice to the cultural and social diversity that we live with.

Prof. Rampal made the following commendations to teachers and text book writers, and illustrated them with examples from an elementary level textbook she has authored:

a) Promote culture of learning outside classroom b) Focus on language — the text should have narratives, should be representative of diversity.

Must challenge the language of maths as plain algorithm.

c) Introduction of perspectives, ideas of symmetry, mapping, through interdisciplinary themes. d) A conscious break from the hierarchy implicit in educational discourse where application is seen

to come after the pure concept. An attempt to bridge this perennial problem was made in the

new textbooks. e) Attempt to overcome the divisions of discipline at the primary level and to integrate language,

EVS, and maths.

f) Understanding of spaces and places is not taken seriously in education. Children are not able to engage with the way maps or spaces get politically represented.

g) Some chapters should be deliberately introduced and included to demonstrate that any theme

could be used to illustrate concepts of maths. h) Introduce examples from the world of work and livelihoods, for instance on craft, masons

making different patterns of bricks


i) The example of the Fish Tale presented in Class 5 illustrates how children’s art, elements of design, observation, symmetries and pattern are dealt and dwelled upon in greater details,

which also address issues on environment. j) Several challenges still exist within the mathematics curriculum and text, for instance the case of

children’s probabilistic thinking in early maths—their understanding of chance, is not dealt with

in primary maths curriculum; k) The transition from primary to upper primary maths is too sharp.

(Rapporteur: Ms Manasi Thapliyal, AUD)

Invited Talks

The first day of the conference featured two invited talks on the theme of equity in mathematics education.

Dr Asha Mathur, in her talk on Mathematics Teaching for the Visually Impaired, highlighted the

learning needs of the visually impaired and how alternative approaches are required to support their learning. The teacher of visually impaired learners needs to be sensitive to their cognitive requirements and must organize her classroom accordingly. She needs to talk at a slow pace since the learners will

depend largely on listening and also develop teaching learning materials so they can learn through tactile experience. She briefly described the use of materials such as Abacus, Taylor Frame, Braille slate, Braille Paper & stylus, spur wheel, Geometry Kit, drawing boards and tape recorders. Learning

mathematics requires dealing with abstract concepts which leads to additional challenges for the teacher. Teachers need to be proficient in the use of the tools mentioned above and also need to

develop appropriate teaching learning materials which can help the learners to explore and understand concepts. She observed that textbooks developed for visually impaired learners are usually just textbooks for sighted learners which are translated into Braille. Thus images and diagrams which are

crucial to the understanding of concepts are often dropped since they cannot be re-‐created in Braille. She concluded her talk by emphasizing the need for the creation of appropriate materials and tools for visually impaired learners and suggested that technology can have a role to play in this regard.

Dr Jayasree Subramanian’s talk was on Gender issues in mathematics: what we need to investigate

about. She began her talk by raising questions like why women are not usually seen in serious academic or prestigious positions, especially in mathematics and the sciences. Is it due to discrimination against women, or does the nature of these disciplines force women out of such positions, or is there an

inherent lack of ability in women towards certain disciplines like mathematics and science? Her literature review suggested that this ‘inherent lack of ability’ hypothesis is applicable for children in pre-‐primary school as well as for school going children, worldwide. She pointed out that women scientists

and feminist thinkers have been trying to explain the exclusion not in terms of biology but in terms of sociological factors – facilities available in institutes, practices in academics, impact of matrimony on women. Other studies were conducted to see how textbooks, classroom dynamics, peer interaction,

self-‐concept of girls, teachers’ bias, attitudes towards mathematics, influences girls’ performance in mathematics. Cross-‐national studies revealed variability in performance of boys and girls, they are doing


equally well in some countries where status and welfare of women were taken into consideration. She pointed out that the scene in India with respect to representation of women in mathematics and

sciences is disturbing, but there is no research to explain the under-‐representation and discrimination at all levels. She referred to her study of science institutes in India (a large set of interviews of both male & female students and faculty) which indicated that the reasons for the exclusion are the same as

indicated earlier – peer interaction, attitude towards mathematics as male domain, the still prevalent belief in male faculty about women’s lack of ability to think and reason logically. She suggested that serious investigations need to be taken up to find the reasons for girls’ under-‐representation and

exclusion.

Parallel Sessions An important feature of the meeting was the set of parallel sessions on the second day, featuring talks by teachers and researchers, with a focus on actual classroom practice.

1. Ms Shreya Khemani, in her talk Tackling the Division Algorithm, presented joint work with Dr Jayasree Subramanian. The presentation was based on a longitudinal study conducted by the

Eklavya team to understand the ‘division’ processes in the teaching and learning of fractions. Ms Khemani first enumerated the challenges that students face in the division algorithm and highlighted the contrasting views expressed by various educators on the division algorithm. She

spoke in favour of an alternate approach to teaching the process of division as the standard long division algorithm, based fundamentally on the place value system, can be counter-‐intuitive to

children’s existing whole number sense. Further, introducing division solely through algorithmic procedures can reduce the process of division to a series of mechanical, unthinking steps which makes it difficult for a student to relate the taught procedure to the meanings that can be identified

with division. The study was an attempt by the authors towards finding some alternatives. Ms Khemani described their engagement with the students wherein they helped students in doing division by grouping and distributing matchsticks. Further, they helped students to choose 'chunks'

or 'partial quotients' and developed a gradual, more naturalistic approach, to introduce division. The authors believed that beginning with the partial quotients method would erase the problems of hybridisation and allow for a meaningful introduction to the formal division algorithm at a later

stage. 2. Dr Jayasree Subramanian gave a talk on Children’s reasoning skills in Fractions. The presentation of

Dr Subramaniam was based on the interventions of the Eklavya team in teaching fractions to

primary classes. The presentation elaborated on the challenges and possible solutions that the team evolved as they grappled with the issue of making students understand fractions. Their review of previous studies indicated a need to bring in multiple sub-‐constructs in designing curriculum for

fractions. Having understood the complexities and and Learning Trajectories that students face in fractions, it was established that there is a need to permit and respect complexity yet disentangle it; build from the cognitive resources that children bring to school from informal settings; recognize

that the “logical structure of mathematics and cognitive development in mathematics” are not


identical; and to view expertise as refinement of approach over time. After the initial attempts to introduce fractions (without appealing to subconstructs) it was realized that there is a pressing need

to fix the meaning of the fraction symbol and thus started the journey of introducing the subconstructs of fractions. Through students’ work and teachers’ notes the attempts made to teach fractions through these sub-‐constructs were accentuated upon.

3. Ms Sonia Ann Mondal in Genesis of number in young minds studied an alternative approach developed by Jodo Gyan to develop number sense among 3-‐7 year old children. She found that earlier exposure to numbers impacts children’s later formal learning. She found that the alternative

approach built around learning of numbers as a cultural activity, initiates the children into this act in a meaningful way. A ‘context-‐bound’ approach to counting and ample exposure to counting, learning and using counting with understanding helps in children’s development of number sense.

She emphasized the role of appropriate learning materials and the teacher in the whole process. 4. Ms Anchal Arora undertook a critical exploration of the National Curriculum Framework 2005 and

mathematics teaching in primary schools. Ms Arora’s presentation dealt with exploring and

analysing how the new mathematics textbooks were being implemented in schools and ways in which teaching and learning of mathematics was affected as a result. She conducted the study in a government school and a central government aided but autonomous school in Delhi. She observed a

section of class 5 in each of the schools when they were learning the topic ‘area and perimeter’. Her observations revealed that the interpretation and implementation of mathematics textbooks in the class was dependent on teachers’ content knowledge of the topic under consideration, their

selection of content from the textbook, their pedagogical beliefs and their beliefs about mathematics. The difference in the two teachers’ educational backgrounds and their beliefs and

content knowledge was reflected in the difference in children’s performance on the topic; data for which was gathered by a written test and interview. She felt that teachers genuinely faced academic and structural constraints in their inability to implement the textbook and mere change in the

textbook cannot bring in improvements in the teaching and learning of mathematics in the classroom.

5. Ms Jasneet Kaur presented joint work with Mr Mohd. Mamur Ali and Ms Ashu Threja on

Understanding of Geometrical and Algebraic Concepts at Elementary Level. The presentation was based on the premise that a piece of mathematics is understood if one can explain the concepts and facts and can draw logical connections between different facts and concepts. The presenters shared

previous studies that had been conducted in Indian contexts on the understanding of geometrical and algebraic concepts. Drawing from their own studies the authors delineated the details of their study that looked into the developmental changes in conceptual understanding, particularly in the

concepts of ‘Triangle’ and ‘Circle’ in Classes V and VII. The study focused in comparing the perceptual and lexical aspects, investigating the figural aspects, overall understanding of these concepts and the social factors (pedagogical practices in mathematics, support available at home,

resources available at school) that contributed to the understanding. The data was collected through several activities that began with simple drawing activity and graduated to brain-‐storming and concept-‐defining sessions. A similar study was done in the area of algebra.


6. Dr P K Chaurasia spoke on Dynamic Mathematics with GeoGebra-‐ An innovation. He began by focusing on the importance of technology tools in the teaching and learning of mathematics. He

explained that the traditional classroom scenario needs to change in order to integrate technology and use it effectively. This was followed by an introduction to GeoGebra, a free and increasingly popular dynamic geometry software. He highlighted the e-‐learning principles on which GeoGebra

was developed. Further he described how mathematics teachers can create instructional materials using this software. He showed that the algebra, geometry and spreadsheet features of the software can be effectively used for enabling students to explore and visualize concepts. He concluded the

talk by highlighting the ways in which Geogebra can be used to enhance pedagogy. 7. Mr Pramod Maithil presented The ‘Ganak’ based game as a tool to learn about Numbers. Mr

Maithil discussed a game developed by him based on the Ganak (the open abacus) to give children a

concrete understanding of the number system. The game is based on the idea of representing numbers in base 3. He conducted a study with children of grade 6 in a village school where the children were made to play the game for representing numbers. During the presentation he

discussed various numeration systems and then went on to highlight how the concept of place value can be challenging for young learners. The use of various place value TLM (Teaching Learning Materials) was also discussed. It was observed that the game gradually let the child experience the

properties of positional notation system without explicitly taking children into the complexity of different bases. Through the enactive experience the learners were able to discover the additive-‐multiplicative property on which the game is based. Since the learners were familiar with the

abacus, they could figure out the relation between the face value and place value of digits within a given number. The presenter also highlighted how the game also helped learners to develop a

symbolic understanding of “+” and “X” in expanded forms of numbers. The learners were also able to extend the game to other bases.

8. Mr Nidesh Soni and Mr Ghanshayam Tiwari gave a joint presentation on Shiksha Protsahan

Kendras and Mathematics. They focused on how mathematics is dealt with in the Shiksha Protsahan Kendras of the Eklavya Foundation. The approach to dealing with mathematical concepts is grounded in the constructivist approach and is largely activity based. The emphasis is on designing

activities which enable learners to explore mathematical ideas and concepts at their own pace. The activities relate concepts to the prior knowledge of the learners and are often enabled by the use of manipulatives which give learners a concrete, enactive experience. The presenters began by

highlighting some of the difficulties children face in learning arithmetic concepts in the primary years. These are related to the concepts of place value, ‘carry over’ in addition, ‘borrowing’ in subtraction, concepts of multiplication and division and understanding the use of symbols. They

described a game teen gutke chaar note which can be played by five children (where four are players and one is a cashier). The materials used in the game are play notes of Rupees 1, 10, 100 and 1000. Through the game learners explore the concept of place value and arithmetic operations

(principles of exchange and borrowing). The game encourages peer learning and learners are given the opportunity to explore ideas with minimum intervention from the facilitators. The presentation ended by highlighting some of the pitfalls of the activity approach to learning.


9. Prof Rekha S Sen shared her study on Effective mathematics classroom. She undertook this study to understand the dynamics in a mathematics classroom. She used Cobb and Yackel’s framework of

socio-‐mathematical norms to analyse a class 4 classroom over two lecture periods in an elite private school while she was teaching fractions. Her analysis revealed the classroom as one emphasizing procedures, algorithms, right answers and with a pace geared to the ‘brighter’ children. The use of

teaching aids was limited to introducing the topic, rather than as an integral part of the teaching process. Moreover, the classroom did not provide opportunities for discussing the rationale for doing procedures or sharing of alternate methods by students. The classroom also seemed to clearly

indicate segregation of the ‘brighter’ students from the ‘slower’ ones, with no acknowledgement given to children’s initiatives in solving problems.

10. Mr R Srikanth, in his talk on Negotiating evolving topographies in a mathematics classroom

discussed how differences in mathematical aptitude influence the classroom dynamics and his own efforts to bridge these differences in his classroom. He listed some reasons which cause ‘undulations’ in the classroom -‐ self-‐beliefs, perceptions of others who matter (peers, teacher),

motivation, aspirations, performance scores and the incongruities that exist between these. He shared some of his interventions in the classroom in order to get students to a common platform. Differential instruction to suit individual students’ needs, remedial teaching, peer tutoring,

transparency in assessment policies and collaborative classrooms are some measures which he thinks are useful for overcoming the barriers in the classroom.

11. Ms Himani Asija in Developing Project and Inquiry Based Learning in Mathematics at the

Secondary School highlighted how Project based learning can help students to connect mathematics to real world experience. She discussed a project that she conducted with senior secondary

students, titled Mathematical modelling in the diagnosis of Cancer. The project was undertaken with students who were given a basic knowledge of fractal structures such as the Koch snowflake. The idea behind the project was to make the students appreciate the applications of mathematics, in

particular fractals, to medicine. The project also helped students to appreciate how technology increases the applications of the mathematical content in its simplest form in complex scientific situations. The project is based on the observation that in the Koch Snowflake, the perimeter

increases in a geometric progression with common ratio more than 1 while the area increases in a geometric progression with common ratio less than one. Thus, as the number of stages tend to infinity, the ratio of squared perimeter and area approaches infinity. The students made two

hypotheses: Hypothesis 1 Ratio of the squared perimeter and area is the least for a normal cell and is maximum for a malignant cell.

Hypothesis 2 Higher the stage of malignancy, lesser is the fractal dimension. Their explorations were based on testing the hypotheses based on data collected by them from the internet.

12. Ms Ashu Threja advocated the need for Creating Constructive Environments in Mathematics Classrooms. Building a theoretical basis, the presenter listed the tenets of constructivism in Mathematics education which postulate that knowledge is actively created or invented by the child, not passively received from the environment and that learning mathematics should be thought of as


a process of adapting to and organizing one's quantitative world, not discovering pre-‐existing ideas imposed by others. In support of such views the presenter took snippets from the current primary

textbooks of NCERT and described how her pupil teachers use the examples, illustrations and problems of the book to create constructive mathematics classrooms.


Panel Discussions

1. Technology in Mathematics Education

Chair: Professor Inder K Rana, Department of Mathematics, IIT Powai, Mumbai

Panelist 1: Ms V Sudha, Mathematics Department, Sanskriti School, New Delhi

Panelist 2: Dr Jonaki B Ghosh, Department of Elementary Education, Lady Shri Ram College, Delhi University

Prof I K Rana gave a talk titled Technology in Mathematics Education – What? Why? How? Prof Rana took up the aims of the National Curriculum Framework 2005 and discussed how technology can be

used to further them, for example by creating an environment featuring interaction between motivated students and motivated faculty. He gave numerous examples of how technology can be used to raise and resolve non-‐trivial issues, whether they feature applications of school maths to real-‐life or the

conjecturing and solving of higher level problems within school mathematics (especially geometry).

The presentation by Dr Jonaki Ghosh focused on the various possibilities that technology tools have to offer in the teaching and learning of mathematics. She began her talk by describing the goals of mathematics education as envisaged by the NCF 2005. She went on to discuss the various issues in

relation to technology use which have concerned mathematics educators the world over; especially those related to the relevance of paper and pencil techniques in the presence of technology, the role of technology in enhancing conceptual understanding, the need to maintain a balance between technology

use and paper-‐pencil skills and the nature of assessment and setting of examinations. Technology has helped in improving the quality of instructions in a number of ways. If used efficiently, it can promote deep mathematical thinking by initiating analysis, problem posing, problem solving and rich conceptual

understanding. Technology increases the range of mathematical content by providing a dynamic environment for computation, construction and visual representation. She mentioned that some of the softwares available for mathematics instruction are

• Computer Algebra Systems (CAS) such as Mathematica, Maple and Derive • Dynamic Geometry Software (DGS) such as Geometer’s Sketchpad, Geogebra • Handheld technology in the form of scientific as well as graphic calculators.

She concluded her presentation by highlighting examples of specific activities which she has tried out with students at the secondary and senior secondary level which were aimed at investigating the role of technology in enhancing mathematical learning. These activities focused on

• Visualization and exploration of concepts using handheld tools • Exploring geometrical problems in a dynamic geometry environment • Simulation of problems in probability using spreadsheets.


• Investigatory projects based on mathematical modeling and applications of topics taught in the curriculum

The presentation by V Sudha highlighted that mathematics is perceived as a ‘tough subject’ by a large majority of students and the ability to grasp mathematical concepts varies among students. Also

mathematics teachers do not have access to adequate resources which enable them to communicate mathematical concepts efficiently to their students. Recent advances in computing and wireless networking have enabled development of educational tools for a networked classroom enabling real

time transfer of information between students and teacher enabling proper discussion and assessment of each students understanding. Such technologies help the students to discuss and share their ideas both with the teacher and among themselves thus making learning of abstract mathematical concepts a

pleasurable experience. They can experience and engage with mathematics on their own terms and simultaneously help the teacher to monitor their progress and also intervene on an individual basis. The presentation focused on demonstrating the TI-‐Nspire technology developed by Texas Instruments which

has been designed specially to provide a learning environment in the classroom which enables a great degree of interactivity among students and between student and the teacher.

(Rapporteur: Bhawna Chauhan, University of Delhi)

2. Curriculum and Pedagogy: Tertiary level

Chair: Prof Parvin Sinclair, Indira Gandhi National Open University

Panelist 1: Prof Fozia Qazi, Islamic University of Science & Technology, Kashmir

Panelist 2: Prof Amber Habib, Shiv Nadar University

Prof Fozia Qazi began the discussion by sharing the structure and content of mathematics courses in Jammu and Kashmir both at the undergraduate and post-‐graduate levels. She brought out the issues

and challenges the state is facing in its effort to increase the number of courses offered and enhance the quality of the programmes. Even though the state now has much better educational infrastructure facilities, it has failed to engage with issues of curriculum reform and pedagogic innovations. Today,

there are fairly many universities, state run and private colleges in the state. However, they do not offer an honours level programme in mathematics. Moreover, the state colleges suffer from systemic problems – they are affiliated to either Jammu University or Kashmir University but the administrative

control lies with the state government. Compared to the older universities, the new private universities are offering more innovative courses. Lack of faculty with appropriate expertise seems to act as a limiting factor for such innovations, both in the private as well as the government colleges. Introduction

of new courses/ programmes may simply mean addition of a few more courses over and above the existing ones or the location courses, like computer programming, is not well thought out to take


maximum advantage in teaching other mathematics courses. She took the example of her own university (Islamic University of Science and Technology) as one not only offering a full-‐fledged

undergraduate mathematics programme but also a very job oriented programme of Actuarial Mathematics. At least three other universities have taken initiatives to offer job oriented electives at the post graduate level. The panellist felt that there must be a more synergistic relation between students’

lives and the curriculum taught to them and its evaluation. Thus, she recommended courses which connect to the real lives of students by offering job oriented courses, a curriculum which includes project work, emphasises reading and writing skills in mathematics and enables them to think

mathematically and teacher training at the tertiary level so as to create a cadre of well-‐trained mathematics faculty.

Resonating with the earlier speaker’s thoughts, Prof Amber Habib raised issues about curriculum development and the need for more mathematical application courses at the tertiary level. He shared

his experience with students who are unaware of the utility of mathematics in shaping up challenging careers. He brought forth his reservation regarding the existing disconnect between mathematics and other disciplines. He highlighted the need to recognize the definition of rigour and knowledge

construction/ validation in different disciplines. He shared some ways in which Shiv Nadar University is making efforts to achieve this by allowing students to take courses outside their programmes and making all programmes of 4 years duration. He finally shared some interesting vignettes from his

experience with MTTS and MSF students.

Prof Parvin Sinclair raised issues that arise as a result of UGC determining what mathematics is to be taught at the tertiary level and tying the funding of universities/ colleges to following the UGC model curriculum. This makes the syllabus rigid and cannot respond to the needs to particular sections of

students. She expressed her concerns about how syllabus narrows down the efforts to make mathematics multidisciplinary or design mathematics courses with real world connections. She felt that

students’ readiness is not attended to while making mathematics syllabi at the undergraduate level. The gap between what they had learnt at school and the abstraction which is required for the formal mathematics at the undergraduate level in huge. She too agreed with the other panellists and

additionally stressed the need for developing mathematical thinking, communicating mathematically and using mathematical symbols precisely. Another of her concerns was how assessment decides the pedagogy in the classroom and gives no scope to develop mathematical thinking. She gave the example

of IGNOU and its efforts to change the curriculum as well as pedagogy. She felt that training of teachers is a must even at the tertiary level so as to be able to address students of various backgrounds and differential abilities as well as giving interdisciplinary support.

Discussion

Audience and panellists agreed on the fact that content from the syllabi is excluded when teachers find

it difficult to handle and particularly applications of mathematics are excluded or limited by avoiding their assessment. This is a problem and has to be dealt with both by changing our understanding of mathematics as well as by tackling the examination system. One of the panellists shared how they are

trying to make connections of mathematics with other disciplines, like art. Issues were raised about


students’ at senior secondary level lacking minimum understanding of basic concepts in mathematics and the need to offer mathematics courses at various levels in school or interest based courses.

However, it was also pointed out that offering different levels of courses is problematic in that it introduces class distinction. The better way is to reduce content and universities can do whatever is needed at that level. It was pointed out that mathematics departments often decide what mathematics

is to be taught and what is important in a manner which kills the spirit for any innovation.

(Rapporteur: Dr Rakhi Banerjee, AUD)

3. Teacher Education for Mathematics

Chair: Professor Nargis Panchapakesan, Ex Head and Dean, Central Institute of Education, Delhi University.

Panelist 1: Dr Haneet Gandhi, Central Institute of Education, Delhi University

Panelist 2: Ms Usha Menon, Jodo Gyan.

Dr Haneet Gandhi’s presentation Issues in Mathematics Teacher Education was divided into three parts: Issues in mathematics teacher education programmes, Teacher’s understanding of mathematical

concepts and Structure of teacher education programmes in Delhi University. While talking about the issues in mathematics teacher education programmes she briefly touched upon some of the issues faced by these programmes at the elementary, secondary and senior secondary levels. To highlight teachers’

understanding of mathematical concepts, she shared her experiences of teachers’ responses from workshops which she conducted on the topic of fractions. She reflected on how teachers’ limited notions of concepts and content knowledge can be a stumbling block in their classroom interactions.

Following this she discussed the structure of the mathematics education courses of the B.Ed and B.El.Ed programmes of Delhi University. She highlighted the fact that mathematics component of the B.El.Ed programme has four components, namely, the core content knowledge, pedagogy, practicum and

optional papers. Similarly she shared the structure of the mathematics course in the B.Ed programme and ended her presentation by focussing on the challenges teacher educators face in dealing with these courses.

Ms Usha Menon’s presentation was titled The Challenges of Transformative Education in which she

shared some insights from the in-‐service teacher education programmes conducted by Jodo Gyan. These programmes, according to her, can be divided into three categories, that is, Continuous – Intensive, Periodic – Intensive and Episodic. The last category is based on workshop based interactions. Over the

years through these workshops she has encountered various kinds of teachers with different levels of understanding and competence. She reiterated that the main challenge in teacher education is communication across different communities of practice in teacher education. She shared her learnings


from studies on teachers’ understanding about the nature of mathematics, their perception about mathematics as a subject and about pedagogy. She talked briefly about the TLM (Teaching Learning

Materials) prepared by Jodo Gyan which are regularly used by them in their teacher training workshops. She concluded her presentation by saying that PCK (Pedagogical Content Knowledge) is essentially a practitioner’s knowledge which can be enhanced only through interaction with other practitioners and

suggested that a curriculum developed in situ with practitioners is perhaps a reasonable solution.

The chair, Professor Nargis Panchapakesan concluded the session by sharing her own observations related to the discourse of mathematics teacher education. She emphasised that the education of mathematics teacher educators is a key issue which needs to be addressed in the formal system.

According to her the M.Ed programme does not equip a person to become a mathematics teacher educator and thus there is a pressing need for programmes which cater to specialized courses in mathematics education. This will help to legitimize and formalize mathematics education as an

independent field of study and universities across the country, especially the new ones, must address this issue. Further she highlighted the pressing need for a concentrated effort in developing in-‐service teacher education programmes with systematic follow ups. Although the DIETs and the SCERTs are

contributing to in-‐service teacher education, their lack of follow up is a critical problem. Finally she emphasised that lack of classroom resources for school mathematics teachers also continues to be a major lacuna in our system which needs to be addressed.

The participants made a few comments and suggestions in the open session at the end of the panel

discussion. Several participants felt lack of adequate in-‐service teacher education programmes for college mathematics teachers. Pedagogy of teaching mathematics at the college level needs is a key concern and needs immediate attention since there aren’t enough opportunities for college teachers to

upgrade themselves. At the end of the panel discussion a consensus was reached that mathematics education needs to emerge as a separate discipline in our formal system and it must address the issues,

concerns and demands of teacher education, both at the school and college level.

(Rapporteur: Dr Jonaki Ghosh, University of Delhi)

4. Systemic Issues in Relation to Mathematics Education

Chair: Professor Vijaya S. Varma, Ambedkar University, Delhi

Panelist 1: Professor Farida A. Khan, Jamia Millia Islamia

Panelist 2: Professor Rohit Dhankar, Azim Premji University, Bangalore and Digantar, Jaipur.

Prof Vijaya Varma began by putting forward three issues or questions for discussion.

• In the recent past, we have been advocating activity-‐based, child-‐centred learning at all levels. The question is: how is it possible to do this when the system is resource-‐strapped, in our


overcrowded, understaffed classrooms, and our teachers have no special training in such pedagogy?

• How does learning in a conceptually hierarchical subject like mathematics take place in a situation where no child has to sit for examinations until Class X and cannot be detained?

• How do you enable the agency of the school teachers, give them greater autonomy, make curricula contextual, while keeping all curricular policy and textbook development so highly centralised?

Prof Farida Khan pointed out that mathematics as a discipline has a gatekeeping capacity: it is the discipline that pushes children out of school. We may advocate that it should promote a way of thinking and shouldn’t be highly content-‐loaded. Yet it is this content that gives access to higher institutes linked

to high-‐prestige professions. A high value is attached to children who can clear entrance tests. The focal point is that mathematics is the foundation of all science and technology. The question is: how much mathematics should children learn? NCF 2005 got rid of some content loading. Eventually, the reality is

that children have to deal with a hierarchical system with inequity. The social structure is heavily loaded against the underprivileged. Where are the resources going to come from? Every child should have a choice to be able to compete for engineering etc. This raises the question of how to address larger

systemic issues. The task of bringing about changes in attitude has to be taken up more in social science classrooms. The onus can’t be on mathematics alone. Finally, Prof Khan raised the question of how mathematics classrooms are different. The answer, she felt, was in the language used in mathematics.

The symbolic language is foreign. In other subjects, even if the teacher cannot communicate with the learner, there is a possibility of learning by reading. Here it requires translation of the symbolic language, leading to a double disadvantage.

Prof Rohit Dhankar divided his comments into talking about the system, talking about mathematics, and

asking what happens when the system regulates the teaching of mathematics. According to him, the Indian school system is a power structure. The main purpose of schools, deep down, is to protect and uphold the power structure. The system functions on rote thought. It is bounded by authority, regulated

by procedures. It has a total incapability to understand and total disregard for truth and epistemic force. It works, not on well-‐thought ideas, but on manipulation. Hence it has a great capacity to be blown over by fashions, for example: no exams, no pass/fail. Talking about mathematics, Prof Dhankar distinguished

its highly visible form, common-‐sense mathematics, from what he called ‘received mathematics’. School and college mathematics at this point of time belong to this second category. When talking of change, we often get enamoured by common-‐sense mathematics, but both common-‐sense and received

mathematics are limited. Both can work only as long as there exists a strong disciplinary mathematics, which is powerful and widely applicable. It derives its power by bracketing out all context, all meaning, and has the canny capability to reintroduce context-‐specific meaning. For this reason it requires a lot of

on-‐the-‐feet thinking from the teacher, addressing how to build mathematical models to solve-‐real-‐life problems. The system, primarily concerned with the power structure, cannot allow the teacher to function this way. Books are concerned with received mathematics. Serious engagement with ideas is

going down. Instead of ideas, we have sloganisation and caricature. For example, no pass/fail was thought of in a context where each child has his/her own pace of learning, and therefore no grades. This

context is lost and we want a system with grades, yet no pass/fail.


Since all the panellists had voluntarily limited their time, there was time for a lot of discussion, with around a dozen people contributing. Some of the points which came up are listed below.

As soon as a child starts going to school, we train him/her to think: I am going to get a job, earn a lot of

money. The celebrities with which children identify are film stars, never mathematicians.

We shouldn’t club all Govt schools together. There are many where there are less than 40 children in a class. The role of the school leadership is important. Often when people say a particular school is good, they mean that the principal has a different approach. Another aspect of the Govt system is the

inspection: there is training for teachers, but none for school inspectors.

In in-‐service training, we generally have our own agenda. Teachers don’t own it. There should be a shared agenda. In informal discussions with teachers, many ideas come up. These can serve as entry points.

How can teachers engage in research? There is no motivation to do anything in-‐depth. There is a lot of

inertia, teachers see no need… However, we have to see how much freedom they have. Whether in Govt or private schools, everything is specified. In SCERT workshops, resource persons are asked to come for just two hours. There is no space to address what teachers say.

The issue of grade-‐specific processes came up in the context of NCF 2005. Some participants expressed

concern at the imposition involved in all children of a given age moving together. There is no space for individual differences. In the UK, for example, the existence of O and A levels provides some systemic support. Rohit responded to the question about NCF 2005, observing that the NCF document talks of

grades in a subdued manner. During the process of its creation, there was a lot of discussion on whether syllabi should be developed or not. In his view, NCF was diluted when grade-‐specific syllabi came in, but the real contradiction came with the Right to Education Act, which says every child should complete the

(grade-‐specific) course in one year.

It was pointed out that the condition of the schoolteacher in the Govt system is little better than that of a contract labourer. We are often talking of a teacher who is paid Rs 1200-‐1500 a month. Educationists

expect the teacher to be all-‐in-‐one: to conduct activities, teach language through theatre, perform experiments in science … The system, however, thinks of the teacher as a labourer who does an eight-‐hour shift. Even the holidays are taken away, since training programmes are now held during vacations.

Vijaya Varma quoted a Hong Kong survey, which found that no teacher could get more than 6 hours of sleep.

In response to a query about received mathematics, Rohit Dhankar compared it to received wisdom in religious contexts. What is addition? It is what Guruji says it is. What algorithm to use for addition is also

what Guruji says. There is no space to understand when it will work.

The final few minutes of discussion were on social issues and the mathematics classroom. It began with Farida Khan remarking that, in the mathematics classroom, there is the syllabus which the teacher is expected to complete. In addition, can we put on it the onus of sensitising children? There has been


work on it the UK for instance, but it requires us to question the larger educational system. She further pointed out that the workforce is largely female, mostly women from the middle and lower middle class

who also have to manage families, and yet SCERT decides to have weekend workshops. The question was asked whether social justice issues can be integrated with mathematics. The view which emerged is that people elsewhere are working on it, and it will be useful if we can take on small trials. A case in

hand was that of a tribal region in Orissa, where in 1992-‐93, most vendors were women and did the calculations, but around 2000, vendors had become mostly male. Recent data showed that between spouses, wives have more schooling, but between siblings, boys get more schooling than girls.

Prof Varma concluded the session by asserting that the future revolution in pedagogy would occur only

if you could subvert institutions like NCERT.

(Rapporteur: Professor Amitabha Mukherjee, University of Delhi)

5. Curriculum and Pedagogy at Middle and Secondary School Level

Panelist 1: Ms Anita Sharma, S D Public School, Delhi

Panelist 2: Ms Rashmi Kathuria, Kulachi Hansraj Model School, Delhi

Panelist 3: Dr Rakhi Banerjee, Ambedkar University, Delhi

Ms Sharma initiated the discussion by speaking on curriculum and pedagogic issues at the middle and secondary school levels. The highlights of the talk included: Critical attributes of a 21st century learner that includes a holistic view of the learner; The coherence of NCF and CBSE’s CCE pattern of assessment

through which a shift can be envisioned from ‘traditional schooling’ to ‘empowering schooling’; and the role of Project-‐work that may help in making classrooms communicative and reflective. This was demonstrated through some samples of student projects.

Ms Kathuria continued on the theme of CCE and explicated her understanding of continuous

engagement between the teacher and the learners. She discussed the problematic areas of secondary and senior secondary students that included lack of visualising shapes, narrow connectivity of application of concepts to real-‐life, and a curriculum that is not child-‐centric. In an endeavour to find

solution to her concerns, she talked of her own initiative of creating expanded classrooms by using common social websites like e-‐mails, blogs, wikis and other e-‐resources. She gave exemplars of how she uses the internet to remain connected with her students, and also to increase interaction among the

students.

Dr Banerjee shared her concerns of a heavily loaded content in middle school mathematics textbooks. She shared that students find difficultly in bridging the mathematical concepts as they transit from primary to middle school. According to her, success in middle school mathematics requires mastery of

rules and convensions in operating with symbols, without referring to anything in particular. By focusing


on the learning of algebra she listed the challenges that students face in understanding, or rather not understanding algebra. The challenges are of discerning letter or literals instead of numbers, non-‐

acceptance of non-‐closure, limited understanding of equal-‐to sign and the problem of transition from arithmetic to algebra. Post discussing these challenges, Dr. Banerjee introduced her approach of teaching algebra: Using and extending students’ experience with symbols in arithmetic in specific ways;

reasoning as a basis of learning; exploiting structural sense of expressions; and promoting structural concepts.

The discussions in this session ranged across panelists, leading to clarification on CBSE’s pattern of CCE, experimental approach of teaching mathematics and physical constraints of non-‐availability of

technological support in schools.

(Rapporteur: Dr Haneet Gandhi, University of Delhi)


Organisers

Academic Committee

Amitabha Mukherjee (Chairperson) Professor, Department of Physics, University of Delhi

Anita Rampal Professor and Dean, Department of Education, University of Delhi

Gurmeet Kaur Bakshi Professor, Panjab University, Chandigarh

Haneet Gandhi Assistant Professor, Department of Education, University of Delhi

Hriday Kant Dewan Vidya Bhawan Society, Udaipur

Kapil Hari Paranjape Professor and Dean, IISER, Mohali

Parvin Sinclair Professor and former Pro-‐vice Chancellor, IGNOU, Delhi

Local Organising Committee

Amber Habib Professor, Department of Mathematics, School of Natural Sciences, Shiv Nadar University

Amitabha Mukherjee Professor, Department of Physics, University of Delhi

Geetha Venkataraman (Chairperson and Convenor) Dean, School of Undergraduate Studies and Professor of Mathematics, School of Liberal Studies, Ambedkar University, Delhi

Haneet Gandhi Assistant Professor, Department of Education, University of Delhi

Jonaki Ghosh Assistant Professor, Lady Shri Ram College, University of Delhi


Rakhi Banerjee Assistant Professor, School of Education Studies, Ambedkar University, Delhi


Detailed Profiles of Speakers & Panelists

Inaugural Session

Professor Dinesh Singh is the Vice Chancellor of University of Delhi, Delhi. Professor Singh did his undergraduate and postgraduate degree in Mathematics at St. Stephen’s College, University of Delhi

and his PhD from Imperial College, University of London. Professor Singh’s area of research in mathematics is functional analysis and he has authored many research papers and books. Professor Dinesh Singh was Director of University of Delhi South Campus during 2005-‐2010. He is also the Director

of Mathematical Sciences Foundation, Delhi and Adjunct Professor, Department of Mathematics, University of Houston, USA. He is involved at the international level in many areas of mathematics research and education. He is a member of the Scientific Advisory Committee to the Cabinet, Govt. of

India, of the Academy of Scientific & Innovative Research. He is on the Steering Committees on Science & Technology and Higher & Technical Education, Planning Commission, Govt. of India. He is also a member of the Governing Body of the All India Institute of Medical Sciences, New Delhi and serves on

the boards/executive councils of many other universities, institutions and professional bodies.

Professor Madan Gopal is the Director for the School of Engineering, SNU. He has joined the Shiv Nadar University from the Department of Electrical Engineering, IIT Delhi. His teaching and research stints span three decades at the IITs. Dr. Gopal is the author/co-‐author of six books on Control Engineering. Some of

his works have been translated into Chinese and Spanish. In India, his books have been serving as a major source of learning for about three decades. Dr. Gopal is an eminent researcher in the area of Machine Learning. He is the author/co-‐author of over 135 research papers; the key contributions have

been published in high impact factor journals. He has supervised 16 doctoral research projects. His research interests lie in the areas of Soft-‐Computing Technologies, Pattern Recognition, and Intelligent Control.

Dr Gopal holds B. Tech (Electrical), M. Tech (Control Systems), and Ph.D. degrees from BITS, Pilani.

Professor Vijaya Shankar Varma taught in the Department of Physics and Astrophysics, University of Delhi for nearly 38 years. During this period he served as the Director, Computer Centre and of the Centre for Science Education and Communication and was Dean Planning of the University before

retirement. In addition to teaching and research he was active in curriculum development, design and teacher training in the Hoshangabad Science Teaching Programme, the School Mathematics Programme, the Elementary Education Teachers Research Network, and Scientific and Technological

Literacy for All. Since its inception, he has been Advisor Planning at the Ambedkar University, Delhi.

Professor Amitabha Mukherjee is a professor in the Department of Physics and Astrophysics of the University of Delhi. Amitabha Mukherjee did his doctorate in physics at the Tata Institute of Funadamental research, Mumbai. He was the chairperson of the academic committee for NIME-‐NRC.


He has been the Director of the Centre for Science Education and Communication, University of Delhi and has a deep and abiding interest in science and mathematics education at the school level.

Professor Geetha Venkataraman is a Professor of Mathematics and Dean, School of Undergraduate

Studies at Ambedkar University Delhi. She did her undergraduate degree at St. Stephen’s College, her masters and PhD at the University of Oxford. Her research interests centre on various aspects of finite group theory, including questions related to enumeration of finite groups. Popularising mathematics,

mathematics education at schools, undergraduate education and questions related to gender and mathematics are also areas of interest. Her publications include research papers, articles related to undergraduate education and a co-‐authored research monograph titled Enumeration of finite groups

published by Cambridge University Press UK. Before joining AUD, she taught mathematics at St. Stephen’s College. She is also a founding member and treasurer of the Mathematical Sciences Foundation, New Delhi.

Plenary Speaker

Professor Anita Rampal is Head and Dean, Faculty of Education, Delhi University. She has been a Nehru

Fellow, UGC Research Scientist, Chairperson of the NCERT Textbook Development Teams at the Primary Stage, and is a member of several national task forces including the Steering Committee of the Planning Commission for Elementary Education and Literacy. She has been associated with the People’s Science

Movement and the National Literacy Campaigns, and her special interests include participatory curriculum development, cognition and communication of science and mathematics with a focus on indigenous knowledge, and policy analysis for equity in education. Her publications include research

papers and books, such as Numeracy Counts! and Zindagi Ka Hisaab, and she has produced films on women’s education and political participation.

Invited Speakers

Dr Asha Mathur is the former Vice-‐Principal of Lady Shri Ram College, University of Delhi. She is currently also Chief Advisor for the placement Cell at LSR. Dr Mathur was responsible for initiating,

conceptualising and actualising a Teacher Education Programme at LSR in the form of a Bachelor’s in Elementary Education in LSR. Dr. Asha Mathur is teaching “Methodology of Teaching Mathematics” to the students of B. Ed. (special education) at Durga Bai Dheshmukh College, Blind Relief Association at

present. Dr. Mathur started her teaching career as mathematics teacher at Lady Shri Ram College and retired from that position in 2006. Her research interest initially was in General Topology. Besides published research work in topology, Dr. Mathur has also participated in course writing projects as

member of course writers team at IGNOU and SCERT. She has edited a series of mathematics books published by Navdeep Prakashan for Classes I to V. Currently she is interested in understanding the challenges of teaching learning process in mathematics and is engaged in activities that provide space

for exploring in that area.


Dr Jayasree Subramanian is a Fellow at the Eklavya Foundation, Hoshangabad. She has a doctorate in Mathematics from the University of Hyderabad. She is interested in the issues of gender and social

justice and has worked in the areas of teaching and learning of mathematics for primary and upper primary school children, teacher education, and curriculum development for the upper primary level.

Panelists

Professor Parvin Sinclair is a Professor of Mathematics at the Indira Gandhi National Open University (IGNOU). She is now the Director of NCERT. She is also a former Pro-‐Vice Chancellor of IGNOU. Professor

Sinclair is an Algebraist by training. She did her undergraduate degree at Lady Shri Ram College, her masters at IIT Delhi and her PhD at the Tata Institute for Fundamental Research, Mumbai. Her research interests include algebra, distance education and mathematics education. She has many research

publications, and has also developed audio-‐visual and course material for mathematics. She has worked closely in an advisory capacity with NCERT on shaping mathematics curriculum and pedagogy. She is a member of the Steering Committee for the Indian National Presentation at International Congress for

Mathematics Education-‐12, and a member of the Steering Committee on Elementary Education and Literacy for the 12th Five-‐year Plan of the Planning Commission.

Professor Fozia Qazi is the founder and Head of the Department of Mathematics at the Islamic University of Science & Technology, Kashmir. She has an MSc and MPhil from Kashmir University, and a

PhD from Syracuse University. She taught for many years in the United States of America. She is also an artist and is a former fellow of the Center for Women’s Intercultural leadership. Her current focus is in interdisciplinary research that examines the role mathematics plays in cultural expression, and she has

used tools like symmetry analysis to understand cultural patterning in Kashmir.

Professor Amber Habib is a Professor of Mathematics at Shiv Nadar University. He has an MS from IIT Kanpur and a PhD from University of California, Berkeley. He has recently authored a book titled `Calculus of Finance’ on Mathematical Finance. He is especially interested in how projects and

applications can enrich mathematics education in both school and college. He has helped organise various efforts in this direction, from summer schools to certificate programmes, and is now engaged in developing the undergraduate curriculum at SNU. Prior to joining SNU, Amber Habib was professor with

the Mathematical Sciences Foundation, New Delhi.

Professor Inder K Rana teaches at the Department of Mathematics IIT Powai, Mumbai. He obtained his Masters in Mathematics from Bombay University and his PhD from the Indian Statistical Institute. He has been a research fellow at various premier institutes such as the Centre of Advanced Studies at Bombay

University, IIT Delhi and ISI Delhi and has taught mathematics at Universities in India and Abroad. Professor Rana’s special area of interest is Analysis, he has authored many books and research papers. He is the founder of the Mathematics Resource Centre at IIT Powai and has a keen interest in

Mathematics Education and Technology.


Mrs Sudha Venkatramanan teaches mathematics to senior students at the Sanskriti School, New Delhi. She has worked towards integrating technology into the mathematics classroom and to this end she has

used extensively ‘Geometers Sketch Pad’ and ‘Graphic Calculator – Texas Instruments’ in her class room teaching. She completed her formal Mathematics training (BSc, MSc and MPhil) from the Avinashilingam University for Women, Coimbatore, Tamil Nadu. This was followed by a BEd and MEd from the

University of Madras. She has been teaching Maths at the senior school level since 1995 She has also been associated as a Faculty with the BElEd Program of the University of Delhi (Vivekananda College for Women) during 1999 and 2000.

Dr Jonaki Ghosh is an Assistant Professor in the Dept. of Elementary Education, Lady Shri Ram College, University of Delhi where she teaches courses related to mathematics education. She obtained her PhD in Applied Mathematics from Jamia Milia Islamia University, New Delhi and Masters in Mathematics from Indian Institute of Technology, Kanpur. She also taught mathematics for 13 years at the Delhi Public School, R K Puram, New Delhi where she was instrumental in setting up the Mathematics Laboratory & Technology Centre. She has set up a Foundation for teacher training and regularly conducts professional development programmes for mathematics teachers. Her primary area of research interest is in use of technology in mathematics instruction. She is a member of the Indo Swedish Working Group on Mathematics Education and has been a recipient of the CASTME (Commonwealth Association of Science Technology and Mathematics Education) award.

Professor Nargis Panchapakesan is ex-‐head and dean of the Department of Education, Delhi University. After completing her doctoral degree from the United States of America, she joined the Department of Education, Delhi University and served as its head twice during her career. She was instrumental in

setting up the Maulana Azaad Centre for Elementary and Social Education (known as MACESE), which, with her efforts together with many others’, in 1994-‐95 started one of the most interesting and innovative programmes in teacher education: the four year bachelors degree in elementary education,

offered by the University of Delhi. She has designed and taught courses in education for many years, educational psychology being one of her core disciplines, mentored and guided numerous students in education. She continues to actively participate in education reforms and initiatives and serves in

committees to look into teacher education, curriculum designing, textbook writing.

Ms Usha Menon, is a graduate of IIT-‐Madras. She served as a scientist with the Council of Scientific and Industrial Research’s Delhi-‐based National Institute of Science, Technology and Development Studies. In 1995-‐96 following a World Bank initiated literacy campaign she became directly involved with

education. She established Jodo Gyan — a charitable trust and an organization working to find workable solutions to the problems in classroom practices. She is deeply interested in mathematics education, has been trying to develop innovative curriculum for primary and upper primary level using the philosophy

of Freudenthal: the realistic mathematics education. She conducts workshops for in-‐service as well as for trainee teachers; designs, produces, procures and distributes low-‐cost teaching and learning materials (TLMs) for promoting activity-‐based education in the classroom.


Dr Haneet Gandhi is presently an Assistant Professor in the Department of Education. She has earlier worked in the Department of Elementary Education, University of Delhi. Her specialization is in

Mathematics Education in which she was awarded her Doctoral Degree.

Professor Rohit Dhankar is Professor of Philosophy of Education at Azim Premji University, Bangalore. He also teaches a philosophy of education course in TISS, Bombay. He has been part of many NCERT initiatives in developing material and curriculum through various committees. He was an integral part of the National Curriculum Framework 2005 process as a member of the National Steering Committee. He is also a part of the collaborative group of institutions that developed the M.A. Elementary Education programme of TISS. He has also been involved with capacity building of educational functionaries at the national level and with various states. He trained as a teacher under David Horsburgh in the Neelbagh School, and taught at the elementary level for about 15 years. Prof Dhankar is the founder secretary of Digantar, a voluntary organization in Jaipur engaged in providing alternative education to rural children. Digantar endeavours to nurture self-‐motivated and independent learners equipped with the ability to think critically. His current interests are in epistemology of education, curriculum studies and teacher education. Professor Farida Khan is a professor at the Department of Educational Studies, Jamia Millia Islamia, New Delhi. Her training is in psychology and she earned her doctoral degree in developmental psychology

from City University, New York. She has been associated with various departments/ centres of education, JNU, DU and JMI and is interested in issues of society and education. For the past many years, she has been working in the area of mathematics education – mathematics in the street,

classroom transaction of mathematics, to name a few areas in which she has worked.

Ms Anita Sharma has been the Principal of S.D. Public School, BU-‐Block, Pitampura, Delhi, since July 2002. Since 1991 she has been involved in teaching mathematics at the senior school level. Anita Sharma did her BSc Honours and Masters in Mathematics from the University of Delhi. This was followed by a BEd and MEd from the Central Institute of Education, University of Delhi. She has been involved with the CBSE in many capacities including training of teachers and principals, preparation of material, involvement in examination reforms etc. She has appeared on television programmes and has written in newspapers about teaching and learning of mathematics. She was conferred the Aryabhatta award for contribuition in field of Mathematics teaching by All India Ramanujan Maths Club and Shiksha Uthan Nyas in December 2011. Dr Rakhi Banerjee is currently a faculty at the School of Educational Studies, Ambedkar University, Delhi.

She has earlier been a faculty at the Tata Institute of Social Sciences, Mumbai. She has a doctoral degree in mathematics education from the Tata Institute of Fundamental Research.

Ms Rashmi Kathuria is a passionate Mathematics teacher working as a P.G.T in Kulachi Hansraj Model School, Ashok Vihar, Delhi. She is associated with CBSE, NCERT, CTSA and DAVIIER as a resource person

for more than a decade for material development, teacher training programmes, workshops, seminars, teleconferences etc. She has created online Maths classrooms through blogs, wikis and social networks for students and teachers. She received the `National Best e teacher award’from Dr. APJ Abdul Kalam in

2007 for her initiatives on using technology in Mathematics teaching and learning. She received the National Best teacher award (2010-‐11) from the All India Ramanujan Maths Club for her extraordinary


contribution in the field of Mathematics teaching. She was awarded First place during BTPC 2008 for paper presentation for her paper on e Mathematics. She was awarded First place in the paper

presentation competition for teachers organised by AIRMC.

List of Participants Consolidated List of Participants, Speakers, Chairs & Organisers

Name Affiliation Email 1 Aabad Mushtaq Islamic University of Science & Technology,

Awantipora, Kashmir [email protected]

2 Abhinav Verma IISc [email protected]

3 Aishna Kejriwal BA (Hons) Economics, II year, AUD

4 Ajay Kumar University of Delhi

5 Ajay Kumar Dean, Research, DU

6 Akha Mao AUD, School of Education Studies

7 Akhil Veetil Pudiyathil BA (Hons) Sociology, I year, AUD

8 Amber Habib SNU [email protected]

9 Amitabha Mukherjee DU [email protected]

10 Anand Saurabh AUD, Academic Fellow, SLS

11 Anchal Arora [email protected]

12 Anima Nagar IIT Delhi [email protected]

13 Anita Rampal DU [email protected]

14 Anita Sharma S D Public School, Pitampura [email protected]

15 Ankita Ahuja Jesus & Mary College, DU [email protected]

16 Anup Sharma DPS Bulandshar [email protected]

17 Arindam Bannerjee AUD, SLS

18 Aruna Ummat DPS Society [email protected]

19 Ashish Gupta

20 Ashok Gogia Mathematics study Centre [email protected]

21 Ashu Threja Miranda House, DU [email protected]

22 Bhavana Chauhan Central institute of Education [email protected]


23 C M Upadhya Gargi College, DU [email protected]

24 Chanchal Yadav PhD Student, DU [email protected]

25 Charu Sharma Shiv Nadar University [email protected]

26 Chirashree Dasgupta AUD, SLS

27 Dinesh Singh DU

28 Farida Khan Jamia Millia Islamia [email protected]

29 Fozia S Qazi Islamic university of science & technology, Awantipora, Kashmir

[email protected]

30 Geetha Venkataraman AUD, SUS/ SLS [email protected]

31 Ghanshyam Tiwari Eklavya, MP

32 Haneet Gandhi DU [email protected]

33 I K Rana IIT Mumbai [email protected]

34 Jasneet Kaur JMI [email protected]

35 Jatin Anand Mathematical Science Foundation, Delhi [email protected]

36 Jaya Goel TGT (Maths) DPS Rohini [email protected]

37 Jayasree Subramanian Eklavya, MP [email protected]

38 Jonaki Ghosh LSR, DU [email protected]

39 Kathy Hargrove Visiting Professor, AUD [email protected]

40 Komal Jodo Gyan [email protected]

41 Komal Arora Assistant Professor, Institute of Home Economics, DU

[email protected]

42 Kuriakose Mamkootam AUD, SBPPSE

43 Madan Gopal Director, School of Education, SNU [email protected]

44 Manasi Thapayal AUD, School of Education Studies [email protected]

45 Manisha Goyal PGT(Maths),DPS ,Rohini [email protected]

46 Minati Panda JNU [email protected]

47 Mohd. Mamur Ali Deptt. Of Education Studies, JMI [email protected]

48 Mohmad Rafiq Wani Islamic University of Science & Technology, Awantipora, Kashmir

[email protected]

49 Monojeet Chakravorty Texas Instruments [email protected]

50 Mukund Madhav Misra Dept. of Mathematics, Hanraj College [email protected]

51 Nammulene Edith BA (Hons) Economics, I year, AUD


52 Nargis Panchapakesan DU

53 Navin Tiwari Darshan Academy [email protected]

54 Neha Joshi BA (Hons) Economics, II year, AUD

55 Nidesh Soni Eklavya, MP [email protected]

56 Nidhi Goel Aditi Mahavidyalaya, DU [email protected]

57 Parul Saxena JP Institute of Information Technology [email protected]

58 Parvin Sinclair IGNOU [email protected]

59 PK Chaurasia NCERT [email protected]

60 Pooja Keshavan Singh Gargi College, DU [email protected]

61 Pramod Maithil Eklavya, MP [email protected]

62 R Srikanth Welham Boys School [email protected]

63 Rakhi Bannerjee AUD, School of Education Studies [email protected]

64 Rashmi Kathuria Kulachi Hansraj Model School [email protected]

65 Ravindra Babu Texas Instruments [email protected]

66 Rekha S. Sen JMI [email protected]

67 Riddhi Shah JNU [email protected]

68 Rohit Dhankar Azim Premji University, Banglore [email protected]

69 Sagar Jain BA (Hons) Mathematics, I year, AUD

70 Sameer Malik BA (Hons) Mathematics, I year, AUD

71 Sanjeev Agarwal SNU [email protected]

72 Saroj Malik Faculty, Hindu College, DU [email protected]

73 Savan Kumar Khanna DPS Bulandshar [email protected]

74 Savita Mehta Darshan Education Foundation [email protected]

75 Shanta Laishram ISI, New Delhi [email protected]

76 Shashi Aggarwal Faculty, Miranda House, DU [email protected]

77 Shobha Bagai Cluster Innovation Centre, DU [email protected]

78 Shreya Khemani Eklavya, MP [email protected]

79 Shyam Menon AUD [email protected]

80 Shyamolima Ghosh Choudhary

AUD, Research Assistant, SUS

81 Sona V Andrew Jesus & Mary College, DU [email protected]


82 Sonam Ambastha BA (Hons) History, I year, AUD

83 Sonia Mondal TISS [email protected]

84 Srajan Agadi BA (Hons) Economics, I year, AUD

85 Sudha V Dept. of Mathematics, Sanskriti School [email protected]

86 Sunil Verma Eklavya, MP [email protected]

87 Swati Nayak Teacher [email protected]

88 Tarun Vohra BA (Hons) Economics, II year, AUD

89 Tavpritesh Sethi Institute of Genomics & Integrative Biology, CSIR

[email protected]

90 Usha Menon Jodo Gyan [email protected]

91 Uttara Dhawan BA (Hons) Psychology, II year, AUD

92 Veena Ahi Darshan Academy [email protected]

93 Vijay Varma AUD

94 Vinod Kumar Singh Banaras Hindu University, Varanasi [email protected]

95 Ziaur Rehman SNU [email protected]

96 Radha Mohan St. Stephen’s College


Schedule Day 1: Monday, November 21, 2011

Time Programme

9:00 am REGISTRATION OF PARTICIPANTS

9:30 am INAUGURAL FUNCTION

10:30 am HIGH TEA

11:00 am

Curriculum and Pedagogy at the Elementary School:

Issues and Challenges

Plenary Talk by Professor Anita Rampal Head and Dean, Faculty of Education, University of Delhi

12:00 pm

Technology in Mathematics Education

Panel Discussion Chairperson: Professor Inder K Rana, Department of Mathematics, IIT Powai, Mumbai Panelist 1: Mr. Sanjay Sinha, Head, Mathematics Department, Sanskriti School, New

Delhi Panelist 2: Dr. Jonaki B Ghosh, Department of Elementary Education, Lady Shri Ram

College, Delhi University

1:30 pm LUNCH

2:15 pm

Mathematics Teaching for the Visually Impaired

Invited Talk by Dr. Asha Mathur &

Gender Issues and Mathematics Invited Talk by Dr. Jayasree Subramanian

Eklavya Foundation

3:15 pm TEA

3:30 pm

Curriculum and Pedagogy: Issues at the Tertiary Level Chairperson: Professor Parvin Sinclair,

Professor of Mathematics, Former PVC, IGNOU Panelist 1: Professor Amber Habib, Department of Mathematics,

Shiv Nadar University


Day 2: Tuesday, November 22, 2011

Panelist 2: Professor Fozia Qazi, Head, Department of Mathematics,

Islamic University of Science and Technology, Srinagar

Time Programme

9:30 am

Paper Presentations

(Parallel Sessions)

11:00 am TEA

11:30 am

Paper Presentations

(Parallel Sessions)

12:30 pm LUNCH

2:00 pm

Teacher Education for Mathematics

Panel Discussion

Chairperson: Professor Nargis Panchapakesan, Ex Head and Dean, Faculty of Education, University of Delhi

Panelist 1: Ms. Usha Menon, Jodo Gyan Panelist 2: Dr. Haneet Gandhi, Faculty of Education, University of Delhi

3:30 pm TEA

3:45 pm

Systemic Issues in Relation to Mathematics Education

Panel Discussion

Chairperson: Professor Vijaya S. Varma, Advisor Planning, Ambedkar University Delhi

Panelist 1: Professor Rohit Dhankar, Azim Premji University, Bangalore and Digantar, Jaipur.

Panelist 2: Professor Farida Khan, Faculty of Education, Jamia Milia Islamia


Day 3: Wednesday, November 23, 2011

Time Programme

9:00 am

Curriculum and Pedagogy at the Middle and Secondary School

Chairperson: Anita Sharma, Principal, S.D. Public School, New Delhi

Panelist 1: Dr. Rakhi Banerjee, School of Education Studies, Ambedkar University, Delhi

Panelist 2: Ms. Rashmi Kathuria, Kulachi Hansraj Model School, Delhi

10:30 am TEA

11:00 am

Rapporteur’s Session

Concluding Remarks by rapporteurs of all panel discussions

12:30 pm LUNCH

1:30 pm

Open Discussion Session

2:30 pm VALEDICTORY SESSION

3:30 pm TEA


Acknowledgements The conference would not have been possible or successful without the contributions and support of

the following.

1. Funding agencies: a. Ambedkar University, Delhi b. Shiv Nadar University

c. National Board for Higher Mathematics d. Indian National Science Academy e. Texas Instruments

2. Delhi Public Society, who hosted the outstation participants in their Dwarka campus

3. Local Organising Committee: Amber Habib (SNU), Amitabha Mukherjee (DU), Geetha Venkataraman (AUD) – Chair & Convenor, Haneet Gandhi (DU), Jonaki Ghosh (DU), Rakhi Banerjee (AUD).

Academic Committee: Amitabha Mukherjee (DU) – Chair, Anita Rampal (DU), Gurmeet Kaur Bakshi (Panjab University), Haneet Gandhi (DU), Hriday Kant Dewan (Vidya Bhawan Society),

Kapil Paranjape (IISER, Mohali), Parvin Sinclair (IGNOU) The organisers put in a lot of work beyond the obvious – in preparing the website; handling

emails; short-‐listing participants; co-‐ordinating speakers, panelists, and chairs; arranging accommodation; designing and mailing the invitations; etc.

4. AUD administration and faculty: a. Vice-‐Chancellor Prof Shyam Menon b. Registrar Prof Chandan Mukherjee c. Controller of Finance Ms Asha Rani Rungta d. Professor Salil Misra, Dean, School of Liberal Studies, AUD e. Mr Anand Saurabh, Academic Fellow, School of Liberal Studies, AUD f. Ms Divya Bhambri, Academic Fellow, School of Undergraduate Studies, AUD g. Ms Shyamolima Ghosh Choudhary, Research Assistant, School of Undergraduate

Studies, AUD

5. SNU administration and faculty:

a. Vice-‐Chancellor Prof Nikhil Sinha b. Director, School of Engineering, Prof Madan Gopal c. Head, Department of Mathematics, Prof Sanjeev Agrawal


6. The speakers, panelists and chairs, especially Prof Dinesh Singh (inaugural speech).

7. AUD Staff: a. Ms Asha Vijay, Office Assistant, School of Undergraduate Studies, AUD b. Mr Sita Ram Sharma, Care taker, AUD c. Dr R D Sharma, Assistant Registrar, Finance Division, AUD d. Mr B K Somyajulu, Assistant Registrar, Finance Division, AUD e. Mr Laxmikant, Junior Executive, Finance Division, AUD

8. AUD student volunteers: Aishna Kejriwal, Akhil Veetil Pudhiyatil, Edith Namuleme, Neha Joshi,

Sagar Jain, Sameer Malik, Sonam Ambastha, Srajan Agadi, Tarun Vohra, Uttara Dhawan. They were vital to the conference running smoothly, and their effort is all the more appreciated because it came so close to their final exams!

9. Participants

10. India International Centre, Max Mueller Marg, New Delhi


Invitation

nime nrc formatted report

Documents

shiksha protsahan

prof dinesh

professor

ms rashmi

ms usha menon

dr haneet

dr rakhi banerjee

shiv nadar