Research in Mathematics Education

This research is aimed at developing a suitable model of professional development for teachers of mathematics in the context of the recommendations of National Curriculum Framework (2005) towards more learner-centred approaches. The components of the model are

1. Workshops that integrate different levels of processes connected with teaching and teacher development. These workshops aim to bring together teachers, teacher educators and researchers, as well as include student teaching in the form of lesson study. The aim is to create a shared understanding of what learner-centred approaches in the classroom look like.
2. Follow up through collaboration between teachers, and between teachers and researchers
3. Building an online network for teacher interaction

• Some specific issues being studied are:
• How do the teachers' knowledge and beliefs change in the course of (a) participation in the teacher development workshop and (b) the collaboration?
• What do the teachers take up from the professional development workshop as expressed in subjective reports and in their reflection on their classroom practice?
• What strengths exist in the classroom culture, teaching practice and teachers' knowledge, as reflected in the sample, that can be utilized for teacher professional development?
• What are the specific difficulties faced by the teacher in adopting learner centered practices and how can s/he be supported to overcome these difficulties?

• Publications
• Naik. S., (2008). Mathematics Teacher Education in India – demanding change and reform in teachers' professional development. In Proceedings of symposium on the occasion of the 100th Anniversary of International Commission on Mathematics Instruction (ICMI), Rome:ICMI.
• Naik. S., (2008). The measures for understanding teachers' mathematical knowledge for teaching fractions – how do they really work? In Proceedings of International Conference in Mathematics Education (ICME), Mexico:ICME.
• Naik, S. (2009) Understanding teacher's mathematical knowledge using non-typical examples, The Indian Educational Researcher (ISSN0974-2123), Stella Matutina College of Education, Chennai.

(K. Subramaniam, Ruchi Kumar, Shweta Naik)

School students everywhere find fractions a difficult topic. This research project aims at clarifying the role and importance of fractions in the mathematics curriculum as a whole, and at developing teaching learning approaches that lead from initial understanding of fractions to their use in solving ratio proportion problems.

Fractions in the school curriculum contribute three important conceptual functions: (i) the co-ordination of partitioning actions with the representations of measure (ii) providing symbolic tools for the manipulation of proportional relationships and (iii) preparation for the algebraic manipulation of rational functions.

In the teaching learning approaches being developed, we have focused on integrating students' actions of partitioning grounded in situations of equal sharing with their sense of measure. We are at present exploring how students' everyday experiences can be a powerful motor for learning about fractions. The use of fraction understanding in solving proportion problems provides a context for applying and strengthening students' understanding.

(K. Subramaniam, Shweta Naik, Smita Patil, Amol Parab, Arati Bapat, V.N. Saritha, Aaloka Kanhere)

• Publications:
• Naik, S. and Subramaniam, K. (2008) 'Integrating the measure and quotient interpretation of fractions'. In O. Figueras et al. (Eds.) International group of the psychology of mathematics education: Proceedings of the Joint Meeting of PME 32 and PME-NA XXX (PME29), Vol 4, 17-24, Morelia, Mexico.
• Subramanian, J., Subramaniam, K., Naik, S., Verma, B. (2008) `Combining Share and Measure Meaning of Fractions to Facilitate Students' Reasoning', International Conference of Mathematics Education: ICME-11, Monterrey, Mexico. Available online at http://tsg.icme11.org/document/get/823.
• Subramaniam, K. and S. Naik (2007) `Extending the Meaning of the Fraction Notation',Proceedings of Episteme-2, New Delhi: Macmillan India, 223-227.

• Presentations:
• Subramaniam, K. Issues for Research in the Teaching and Learning of Fractions, HBCSE, March, 2008.
• Naik, S. and Subramaniam, K. Integrating the measure and quotient interpretation of fractions. Presentation at PME-32 by K. Subramaniam. July 2008.

The problem of students' transition from arithmetic to algebra, and the associated theoretical issue of the relation of arithmetic to algebra have been active areas of research over the last three decades. This research project aimed at understanding and facilitating students’ transition from arithmetic to algebra using a teaching design experiment methodology with several batches of students over many cycles. The students were drawn from lower income groups from neighbouring English and Marathi medium schools.

One of the findings of the study was the elaboration of the topic domain of 'numerical' or 'arithmetic expressions' as a preparation for algebra. The approach, fine tuned over the several cycles of the teaching design experiment, led to an increasingly refined understanding of how students learn to 'reason about and with symbolic expressions'. In contrast in the traditional curriculum numerical expressions are treated only briefly, largely to introduce the operation precedence rules.

Key concepts essential to a structural (as opposed to a 'procedural') understanding of symbolic expressions, such as term, value, equality and transformation have been identified and linked to tasks that require students' reasoning. The approach is promising in allowing students to learn the conventions and concepts associated with symbolic notation in arithmetic and algebra in an integrated manner, using their knowledge of arithmetic as a springboard.

The phase of the work that was concluded focused on developing this approach in detail at the class 6 level. The subsequent phases of this work will involve further development of the approach, continuing evaluation of its effectiveness of, and the preparation of teachers in using this approach.

(K. Subramaniam, Rakhi Banerjee, Shweta Naik, Rashmi Jadhav, Pranali Bobhate, Manoj Nair – Video support)

• Publications:
• Subramaniam, K. and Banerjee, R. (under review) 'The arithmetic-algebra connection: A historical-pedagogical perspective'.
• Banerjee, R., Subramaniam, K. and Naik, S. (2008) 'Bridging Arithmetic and Algebra: Evolution of a Teaching Sequence', In O. Figueras et al. (eds.) International group of the psychology of mathematics education: Proceedings of the Joint Meeting of PME 32 and PME-NA XXX(PME29), Vol 2, 121-128, Morelia, Mexico.
• Banerjee, R. and Subramaniam, K. (2007) Exploring student's reasoning with algebraic expressions (Short oral paper). Proceedings of the 31st International Conference of the Psychology of Mathematics Education, Seoul, Korea.
• Banerjee, R. (2007) Developing a learning sequence for transiting from arithmetic to elementary algebra. Unpublished doctoral dissertation. Mumbai: Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research.

• Banerjee, R. and Subramaniam, K. (2005) Developing Procedure and Structure Sense Of Arithmetic Expressions, In H. L. Chick and J. L. Vincent (Eds.) Proceedings of the 29th conference of the international group of the psychology of mathematics education (PME29), Melbourne, Australia, 2005.

• Naik, S. S., Banerjee, R and Subramaniam. K. (2005) Understanding Student's Reasoning While Comparing Expressions, In P. Clarkson et al. (Eds.) Proceedings of the annual conference of the mathematics education research group of Australasia Inc. (MERGA), Melbourne, Australia, 2005.
• Subramaniam, K.(2004) "Naming Practices that Support Reasoning about and with Expressions" Proceedings of the International Congress on Mathematics Education (ICME 10), Denmark. Available online at http://www.icme10.dk /proceedings/pages/regular_pdf/RL_K_Subramanian.pdf
• Subramaniam, K. and Banerjee, R. (2004) "Teaching arithmetic and algebraic expressions". In M. J. Hoines and A. B. Fuglestad (eds.), Proceedings of the 28th conference of Psychology of Mathematics Education, Vol. 3, pp 121-128, Bergen, Norway.

• Journals
• G.C.Pal, Chitra Natarajan, H.C.Pradhan, `Gender and the Mathematical Mystique,' Indian Educational Review, January - June, 1997.
• G.C.Pal, Chitra Natarajan, H.C.Pradhan, `Logico-mathematical Errors - An Analysis,' School Science, XXXV(1), March 1997, pp53-59.
• Reports & Proceedings

• G.C.Pal, Chitra Natarajan, & H.C.Pradhan, (1996): `Difficulties in Mathematics among Primary Students: A Socio-Psychological Perspective,' TR No.32, June.
• Pradhan H.C., Bhagwat, R.M., Mavalankar, A.T., et.al. (1992): Mathematics For All, Preparatory Course on Mathematics (in Marathi). Y. C. Maharashtra Open University, Nashik, India. 
• Pradhan H.C., (Ed.) (1992): Proceeding of the Indo-US Workshop on Mathematics Education, Homi Bhabha Centre for Science Education, TIFR, Bombay.
• Pradhan H.C. & Mahajan, B.S. (1994): Proceeding of the Second Indo-US Workshop on Mathematics Education, Homi Bhabha Centre for Science Education, TIFR, Bombay.