## Harita Raval

#### Scientific Staff

Harita Raval is a scientific staff in Mathematics Education at HBCSE. She has received a bachelor’s degree in Mathematics and in Education from Saurashtra University. Harita also has a master’s degree in Mathematics from M.S. University of Baroda. She pursued her post graduation diploma in computer application (PGDCA) from Saurashtra University. She has been engaged with various programs on mathematical enrichment, such as Mathematical Training and Talent Search Program (MTTS), teacher conferences of Gujarat Ganit Mandal and Satellite conference on various aspects of Dynamical Systems. She is a recipient of the Rashtrapati Guide Award (2006) from Dr. A.P.J. Abdul Kalam for her social work.

Before joining to HBCSE, Harita was teaching mathematics at the Kendriya Vidyalaya School in Rajkot and at the Shakti Higher Secondary School. During these teaching years that Harita understood some fundamental challenges of teaching and importance of knowing the students’ ideas and learning trajectories. She holds key interest in teaching mathematics in connection to real life and developing conceptual depth in milestone topics such as basic arithmetic, integers, fractions and problems of Geometry.

- Tel: 022 2507 2106

## Jeenath Rahaman

#### Research Scholar

Jeenath Rahaman is a doctoral student at HBCSE, working in the field of Mathematics Education and Cognition. Her research interests revolve around students’ understanding of measurement, multiplicative thinking, proportional reasoning, spatial thinking, geometry and fractions, which she is studying through the lenses of cognition, visualisation, gestures, embodied cognition, physical and practical resources of learning. These research interests have a major impact on her doctoral study, where she is examining students’ understanding of area-measurement through various lenses. Jeenath’s work is attempting to integrate the perspectives from the field of cognitive science to understand students’ learning of the mathematical concepts.

Presently she is analysing students’ data from two perspectives. In the first perspective, she is trying to understand the concept of area as a network of several other subconcepts in maths and how the network components impact students’ learning. While in the other perspective, she is trying to understand the cognitive nuances that might have an effect in students’ understanding of area measurement.

Jeenath is also an active resource person for conducting workshops on learning mathematics through Geogebra for teachers and students.

- Tel: 022-25072218

## K. Subramaniam

#### Professor

My main work for the last decade and a half has been research and development on improving the learning and teaching of school mathematics. I have studied, along with my colleagues, how children can be helped to make the transition from arithmetic to algebra, how they can be supported in learning fractions and multiplicative reasoning, and how out-of-school mathematical knowledge can be related to school learning. I have also worked on developing models for in-service teacher professional development. I have authored text-cum-workbooks and teacher books on mathematics for students of Class 3. I have contributed to formulating education policy through my participation in the focus group on the teaching of mathematics, the syllabus committees for NCF-2005, the curriculum and textbook committees for the state of Maharashtra (since 2011). I am a member of the National Council of Teacher Education (2013-present). I have a B.Tech in Aeronautical engineering and an M.A. and Ph.D. in philosophy. My Ph.D. dissertation was on aspects of the philosophy of history, with a focus on the Continental Philosopher Heidegger. Before joining HBCSE, I taught mechanical engineering at the college level. Publications

- (2006). Sarvaansaathi Ganit, Sikhshak Hastpustika. Homi Bhabha Centre for Science Education, Class 3.
- (2005). Maths for every child: Teachers’ book to accomapany text-cum-workbook. Homi Bhabha Centre for Science Education, Class 3.
- (2001). Maths for every child: Text-cum-workbook. Homi Bhabha Centre for Science Education, Class 3.

- (2013). Research on the learning of fractions and multiplicative reasoning: A review. In S Chunawala (Ed.), The epiSTEME- 4 reviews: Research Trends in Science, Technology and Mathematics Education. Macmillan.
- (2012). The preparation and professional development of mathematics teachers. In R Ramanujam, & K Subramaniam (Eds.), Mathematics Education in India: Status and Outlook (pp. 151-182). Homi Bhabha Centre for Science Education.
- (2011). The arithmetic-algebra connection: A historical-pedagogical perspective. In J Cai, & E Knuth (Eds.), Early Algebraization: A Global Dialogue from Multiple Perspectives,Springer (pp. 87-107). Springer.
- (2000). Geometrical examples from real life. In A. G Bhalwankar, K Modi, & S Rawool (Eds.), Pathways in Mathematics Education: Colloquim in Mathematics, World Mathematics Year 2000. SNDT University.
- (). Professional development of In-service mathematics teachers in India. In B Sriraman, J Cai, K. H Lee, F Lianghuo, Y Shimizu, L. C Sam, & K Subramaniam (Eds.), Abstracts of the First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India (pp. 207-211). Information Age Publishing, Inc.

- (2013). When you don’t know the solution to a problem?. At Right Angles, 2.
- (2012). Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics.
- (2010). Culture in the learning of mathematics. Learning Curve: Special Issue on Mathematics, 26-28.
- (2009). Visualisation and reasoning in explaining the phases of the moon. International Journal of Science Education, 31 (3), 395-417.
- (2005). What is mathematics education research and why is it important?. Learning Curve.
- (2003). Elementary mathematics: A teaching learning perspective. Economic and Political Weekly, Special Issue on the Review of Science: Perspective on Mathematics, 37 (35), 3694-3702.
- (2002). Working with fraction, Unit for course on teaching of primary mathematics. Indira Gandhi National Open University.

- (2013). Characterising work-context from mathematics learning perspective. In G Nagarjuna, A Jamakhandi, & E. M Sam (Eds.), epiSTEME-5: International Conference to Review Research on Science, TEchnology and Mathematics Education (pp. 173-179). Cinnamonteal publishing.
- (2013). Elementary teacher’s belief about teaching of mathematics. In G Nagarjuna, A Jamakhandi, & A. M Sam (Eds.), epiSTEME-5: International Conference to Review Research on Science, TEchnology and Mathematics Education (pp. 247-254). Cinnamonteal publishing.
- (2013). From relational reasoning to generalization through number sentence tasks. In G Nagarjuna, A Jamakhandi, & E Sam (Eds.), epiSTEME-5: International Conference to Review Research on Science, TEchnology and Mathematics Education (pp. 336-342). Cinnamonteal publishing.
- (2012). Profile of the students’ arithmetical knowledge acquired in and outside school. In Proceedings of the 12th International Congress on Mathematics Education (pp. 7386). ICME.
- (2012). One teacher’s struggle to teach equivalent fractions with meaning making. In Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (pp. 290).
- (2012). Understanding teachers’ concerns and negotiating goals for teaching: Insights from collaborative lesson planning. In Proceedings of the 12th International Congress on Mathematical Education (pp. 5157-5166). ICME.
- (2012). Interaction between belief and pedagogical content knowledge of teachers while discussing use of algorithms. In Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (pp. 246).
- (2012). A network model of the mathematical concept of area. In G Nagarjuna, A Jamakhandi, & E Sam (Eds.), epiSTEME-5: International Conference to Review Research on Science, TEchnology and Mathematics Education (pp. 300-306). Cinnamonteal publishing.
- (2012). Exploring the connection between multiplicative thinking and the measurement of area. In Proceedings of the 12th International Congress on Mathematical Education (pp. 1964-1973). ICME.
- (2012). Does participation in household based work create opprtunities for learning mathematics?. In Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (pp. 107-112). PME.
- (2012). Measurement modes and units: The Indian context. In Proceedings of the 12th International Congress on Mathematical Education (pp. 1974-1983). ICME.
- (2012). Understanding teacher’s knowledge of and responses to students’ mathematical thinking. In Proceedings of the 12th International Congress on Mathematical Education (pp. 4906-4915). ICME.
- (2012). Towards conceptualising a teaching sequence to promote early-algebraic thinking. In Proceedings of the National Meet on Celebration of National Year of Mathematics. NCERT.
- (2011). Exploring school children’s ‘everyday’ mathematical knowledge. In E Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (pp. 477). PME.
- (2011). Collaborative approach for continuous in-service teacher professional development. In Abstracts of National Seminar on Current Issues in Teacher Education, CASE, Department of Education and Psychology (pp. 39-40).
- (2011). Connecting to the folk of mathematical culture through puzzles. In B Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (pp. 396). PME.
- (2010). Attending to language, culture and children’s thinking as they learn fractions. In M. M. F Pinto, & T. F Kawasaki (Eds.), Proceedings of the 34th International Conference for Psychology in Mathematics Education. PME.
- (2008). Briding arithmetic and algebra: Evolution of a teaching sequence. In O Figueras (Ed.), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX 29 (pp. 17 — 24). PME.
- (2008). Integrating the measure and quotient interpretation of fractions. In O Figueras (Ed.), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX 29 (pp. 17 — 24). PME.
- (2008). Drawing from cognitive studies of mathematical learning for curriculum design. In Proceedings of the International Conference of Mathematics Education. ICME.
- (2008). Combining share and measure meaning of fractions to facilitate students’ reasoning. In Proceedings of the International Conference of Mathematics Education. ICME.
- (2007). Exploring student’s reasoning with algebric expressions. In Proceedings of the 30th International Conference for the Psychology of Mathematics Education. PME.
- (2007). Mathematical literacy and situated social knowledge: Understanding revolving credit. In Indian Social Science Congress.
- (2007). Reasoning processes underlying the explanation of the phases of the moon. In Proceedings of epiSTEME-2: International Conference to Review research in Science, Technology and Mathematics Education (pp. 121-125). Macmillan.
- (2007). Is school mathematics all about recipes for calculation?. In Proceedings of the Conference on Technology and Innovation in Mathematics Education.
- (2007). Extending the meaning of the fraction notation: A teaching Experiment. In Proceedings of epiSTEME-3: International Conference to Review research in Science, Technology and Mathematics Education (pp. 223-227). Macmillan.
- (2005). Developing procedure and structure sense of arithmetic expressions. In H. L Chick, & J. L Vincent (Eds.), Proceedings of the 29th Conference of the International Group of the Psychology of Mathematics Education. PME.
- (2005). Designing an instructional sequences for transiting from arithmetic to algebra in the middle school. In Proceedings of epiSTEME-2: International Conference to Review research in Science, Technology and Mathematics Education (pp. 218-222). Macmillan.
- (2005). Understanding student’s reasoning while comparing expressions. In P Clarkson (Ed.), Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia. MERGA.
- (2004). Term as a bridge concept between arithmetic and algebra. In Proceedings of epiSTEME-1: International Conference to Review research in Science, Technology and Mathematics Education (pp. 76-77). Homi Bhabha Centre for Science Education.
- (2004). Students’ use of language and symbols in reasoning about arithmetic expression. In Proceedings of epiSTEME-1: International Conference to Review research in Science, Technology and Mathematics Education (pp. 92-94). Homi Bhabha Centre for Science Education.
- (2004). Naming practices that support reasoning about and with expressions. In Proceedings of the International Congress on Mathematics Education. ICME.
- (2004). Innovative practices in mathematics education: An overview. In Proceedings of the National Conference on Enhancing Learning in Elementary Schools. Azim Premji Foundation.
- (2004). Teaching arithmetic and algebric expressions. In M. J Hoines, & A. B Fuglestad (Eds.), Proceedings of the 28th Conference of Psychology of Mathematics Education (pp. 121-128). PME.
- (2002). The Homi Bhabha curriculum in primary mathematics: Background and overview. In Proceedings of the Science Technology and Mathematics Education for Human Development. Homi Bhabha Centre for Science Education.

- (2008). What mathematics does everyone need to learn. In Proceedings of the Core Group Workshop on Science Education in India, Peoples Council of Education. Homi Bhabha Centre for Science Education.

- (2005). Mathwiki: A Resource for Problem Solving.
- (1999). Threads in time: Historical connection to school mathematics.
- (1999). Exploring mathematics: Dissections and graphs.
- (1997). Geometry through collage: Boosting performance in school geometry.
- (1997). Activities for school mathematics laboratory.
- (1996). Evaluation of Gammat Jatra (educational fun fair).

- Tel: 91-22-25072228
- Location: Mumbai
- Website: Link

## Manoj Nair

#### Scientific Officer

Manoj Nair works on creating web interfaces where mathematics group’s curricular and research work could be hosted. He is also involved in designing educational materials, such as, posters, textbooks, instructional material and proceedings. He has developed the existing website of the mathematics education group at HBCSE and looks after its maintenance.

- Tel: 022-25072119
- Website: Link

## Rossi D’souza

#### Research Scholar

Rossi is pursuing a PhD in Mathematics education at HBCSE-TIFR. His research interests include exploring how ableism operates in Mathematics education. Prior to working as a Research scholar, Rossi completed his M.Tech in Modeling and Simulation from Pune University, specializing in and then working in the field of Computational Genomics. He has also worked as a visiting lecturer in at Govt. Polytechnic Mumbai, a medical instrument repairman at Narayana Hrudayalaya Hospital, Bangalore and as a Science Communicator on the Science Express train.

Rossi teaches Music and Mathematics along with curricular subjects at the Vivek Education Foundation, School for the blind, Mumbai.

- Tel: 022-25072219

## Shikha Takker

#### Research Scholar

Shikha Takker is a doctoral candidate in mathematics education at HBCSE. She holds a bachelor degree in elementary education from Delhi University and a masters degree in elementary education from TISS, Mumbai. Shikha has also taught mathematics to elementary school children for over three years, where she began to realize the issues of learning with understanding and legitimacy of students’ ideas in orchestrating their learning. This made her pursue research in mathematics education.

For her doctoral work, Shikha is examining teachers’ understanding of students’ mathematical thinking in decimal fractions, mainly to investigate and enhance teachers’ on-task decision making and its relationships with their knowledge of students’ mathematics. Currently, she is analyzing classroom data to understand the characteristics of the connection between teacher knowledge of students’ ideas and their practice.

Shikha actively works in taking sessions on mathematics teacher professional development. She supports teacher learning from studying their own practice: analysing teaching, using artefacts from classroom, unpacking student’s case studies, etc.

Shikha’s key areas of interest in mathematics education are understanding teacher knowledge through the lens of practice, designing and implementing students’ cases, mathematics teacher education and professional growth, decimal fractions, proportion, and early algebra.

- Tel: 022-25072221

## Shweta Shripad Naik

#### Scientific Officer

Shweta Shripad Naik is a Scientific staff in the mathematics education group at HBCSE. She holds a bachelor degree in mathematics from Mumbai University and a masters degree in mathematics from Pune University. Currently, Shweta is pursuing her doctoral degree in mathematics education at School of Education, University of Michigan. Shweta has been an active researcher and instructor in developing teaching trajectories for bridging arithmetic and algebra, understanding fractions, ratios and proportions, teaching area measurement, representing word problems and understanding decimals. As part of the trajectory development work, she has taught for two educational years in the nearby schools. Shweta has also been one of the active resource persons for teacher education programs at HBCSE. She has been focusing on teachers’ mathematical knowledge required for teaching that facilitates learning with understanding. She conducts workshop that involves practice-based sessions for teachers, such as studying live teaching, videos of teaching, learning to solve mathematics problems, studying students’ work, reading research, etc. For her dissertation work, Shweta is investigating teachers’ use of mathematical practices, for the role they play in developing the knowledge needed for teaching. Her study, involves working with in-service and pre-service teachers, and examining their engagement with the mathematical practices while solving problems. Shweta’s key areas of interest in the mathematics education are mathematical knowledge for teaching, teaching and learning of mathematical practices at the school level, developing teacher learning communities and designing practice-based tasks for teacher education.

- Tel: 022-25072106
- Website: Link

# Former members

## Aaloka Kanhere

Aaloka Kanhere was a post-doctoral fellow with the mathematics education group from 2009 to 2012. She is at present with Ekalavya, Hoshangabad.

## Arindam Bose

#### Research Scholar

Arindam Bose is an advanced doctoral candidate in Mathematics Education. He holds a Master’s degree in Mathematics and five years of teaching experience at the undergraduate level in Patna University, India. During this teaching stint, Arindam’s involvement in the curriculum development of school education as a member of the mathematics focus-group of the Bihar Curriculum Framework 2006 motivated him to move into research in mathematics education.

For his doctoral dissertation work, Arindam explored the nature and extent of everyday mathematical knowledge possessed by middle grade school students living in an urban low-income settlement that has embedded in it a thriving micro-enterprise economy. The objective of the study was to unpack and document the connections between students’ mathematical knowledge, work practices and identity formation, and inquire into the implications of these connections for school learning. His study argues that experiences from everyday work-contexts makes students familiar with artefacts and practices that represent a crystallised and embodied form of mathematics, which can be resources to make potentially powerful connections with school mathematics. The study further argues that school mathematical knowledge represents a form of generalisation or abstraction consisting of ideas or constructs that illuminates diverse instances in the everyday settings.

Arindam’s key areas of interest in Mathematics Education are connections-disconnections between out-of-school and school mathematics, language diversity and math learning, and ethnomathematics.

- Tel: 022-25072218

## Arun Mavlankar

Arun Mavlankar (deceased in 2014) was Scientific Officer with the mathematics education group. Arun was an active teacher educator with wide experience of schools and teachers in Maharashtra and outside. He was also a curriculum designer and textbook writer.

## H. C. Pradhan

#### DAE Raja Ramanna Fellow, HBCSE,TIFR and UM-DAE CBS, Mumbai

H. C. Pradhan retired in July 2011, as Senior Professor and Centre Director, Homi Bhabha Centre for Science Education (HBCSE), TIFR. His areas of work include physics and mathematics education. Many of the current programmes were inspired or directly initiated by Pradhan. Together with Arun Mavlankar, he also pioneered mathematics education research at HBCSE.

- Website: Link

## Hari Mishra

#### Research Associate

Hari Mishra is a research associate in mathematics education research group at HBCSE. He holds a degree in Information Technology engineering from RGTU, Bhopal. After his degree, he taught for two years to undergraduate level in Vashi. During his teaching career, he realized the challenges of the work of teaching, which pursued him to join the research group in Mathematics Education at HBCSE.

Currently Hari is engaged in investigating teachers’ own voices in the forms of teacher diaries, logs and other records of teaching and exploring opportunities, where prospective mathematics teachers could have a dialogue with such materials. Moreover, he is supporting other research related activities run by the group through helping them in data analysis.

Hari is also an active resource person for workshops on mathematics laboratory for teachers and students.

## Rakhi Banerjee

#### Associate Professor, Azim Premji University, Bangalore, India

Rakhi has a Bachelor’s and Master’s degree in Mathematics from Delhi University, a Bachelor’s and Master’s degree in Education from Delhi University and a Ph. D in Mathematics Education from Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai.

She has taught at various levels of education: school, undergraduate programmes and postgraduate programmes. Prior to joining Azim Premji University, she has held faculty positions at Tata Institute of Social Sciences, Mumbai and Ambedkar University, Delhi. She has been developing and teaching courses in Child development, Cognition and Learning and Mathematics Education.

Her doctoral work, carried out at the HomiBhabha Centre for Science Education, Mumbai, was on developing a learning-teaching sequence for grade 6 students to help them understand beginning algebra based on their prior understanding of arithmetic. Subsequently, her work has focused on looking at curriculum, textbooks and their transaction in the classroom, highlighting students’ and teachers’ role in the process.

## Ruchi Kumar

#### Research Scholar

Ruchi is an advanced doctoral candidate in Mathematics Education. She holds a masters degree in Biology from Delhi University and a bachelor and masters degree in education from CIE. She taught for six years in a primary school in Delhi; during her teaching career, Ruchi felt systemic constraints, isolation present in the job of teaching and problems of teaching that are inherent to content knowledge required to teach. Her sensitivity to educational issues and students’ learning persuaded to join PhD in mathematics Education.

For her doctoral dissertation work, Ruchi explored the nature and extent of teacher knowledge and beliefs in, a professional development setting, during collaborative lesson planning meetings with peers and in their classroom practice. Her work examines what conceptual meanings are constructed when teachers encounter interactions that consist of theories from research and experiences of other teachers.

Ruchi’s key areas of interest in Mathematics Education are teacher beliefs, knowledge and practices, teacher education and designs for professional development programs.

## Tuba Khan

#### Project Scientific Officer

Tuba Khan is a research associate in the mathematics education group at HBCSE. She holds a bachelor degree in Chemistry from Mumbai University, a bachelor and masters degree in education from Mumbai University, and a masters in Urdu from Varanasi University. For her masters degree thesis, Tuba studied secondary school teachers’ attitudes towards the use of technology. Her experience as a researcher during masters brought her to the mathematics education research group. Currently, she participates as a teacher and co-researcher on multiple projects. Her research interest are around teacher learning to teach – mainly at pre-service level, and connecting students’ out-of-school knowledge in classroom teaching. Tuba is also an active resource person for workshops on mathematics laboratory and teacher professional development.

- Tel: 022-25072106