MTA Regional Conference Kochi 2024

In this talk we will trace one of the trajectories that lead to the development of modern group theory. The trajectory we follow starts with solutions of quadratic equations. Students learn to solve quadratic equations in school whereas solutions of cubic and quartic equations have formulae that are difficult to express.

Sixteenth century Italy was the setting for the drama and intrigue that surrounded the discovery of solutions to cubic and quartics. The question then shifted to whether a general formula existed which could express the roots of a quintic equation in terms of the coefficients.

It was not until the early nineteenth that the Norwegian mathematician Neils Henrik Abel was able to show that no such formula existed for the quintic. Evariste Galois, a young French mathematician, showed soon after that this was the case for any general equation of degree five or higher. To prove this, he invented groups and was able to settle the question of solutions of equations in its most general form.

For the most part this talk will be accessible to anyone with a background of high school mathematics.

This talk gives a brief sketch of the evolution of the mathematics curriculum of schools in Keralam from the 1960’s and some highlights of the ongoing revision of the curriculum.

Technology enabled explorations: A rich context for integrating computational and mathematical thinking

(Workshop session for secondary school and college mathematics teachers)

There is widespread acknowledgement that computational thinking needs to be integrated in the school curriculum. Mathematical thinking (MT) and computational thinking (CT) are mutually supportive and Mathematics as a fundamental school subject therefore becomes the likely choice for integrating CT practices. However, developing tasks, which integrate MT and CT is not straightforward and poses a major pedagogical challenge. This workshop session will illustrate that CT skills can be developed if students engage in appropriately designed tasks which illustrate the practical significance of mathematics as a discipline and also enable them to apply mathematical concepts to real world phenomena via computer-based explorations. Participants will be given the opportunity to explore a range of problems from topics such as fractals, simulation of problems in probability and application of matrices. The spreadsheet MS Excel will be the primary vehicle for exploration. Participants will engage in processes of visualization, generalization, recursion, iteration, and analysing algorithms, which are important from computational as well as mathematical standpoints.

Note: Participants should preferably bring a laptop to this session.

This workshop introduces teachers to some applications of square and circular geoboards in school mathematics. Participants will explore how these simple yet powerful tools can enhance the teaching of key concepts such as shapes, fractions, circle theorems, transformations etc. The session will highlight hands-on activities that demonstrate the geoboard’s use in problem-solving and mathematical explorations. The workshop aims to equip teachers with new strategies to integrate geoboards into their lesson plans to foster deeper mathematical understanding and student participation.

Paper presentations on Day 1 (21st Sept, 11.45 am to 1.15 pm)

1. Nisha, C. “Comparative study of primary maths textbooks of four Southern states”
2. Kamalee, P. “Enhancing Primary-Level Arithmetic Abilities Through Magic Squares”
3. Manimegalai, M.K. “Live Learning of Pythagoras theorem using Geogebra”
4. Singh, G., Thakkar, J. & Jain, M. “A Cucumber in the Classroom- Understanding 3D Shapes in a Playful and Meaningful Approach”

Paper presentations on Day 2 (22nd Sept, 10.15 am to 11.15 am)

1. Amrita. “Towards bringing change in the classroom: Focusing on the development of number sense”
2. Sreerekha, U. “Innovative practices in mathematics education through design thinking”
3. Selvan, U. (Vizhiyan). “Deck Card Mathematics: An Easy-to-Use Tool for Learning Fundamentals of
   Mathematics”
4. Iyer, A. “Number Systems: From Tribe to Machine”

All posters will be presented on Day 1 (21st Sept, 2.30 pm to 3.30 pm)

1. Bansal, S. “Inquiry-driven approach of visualizing similarity between curves of conic sections”
2. Garg, N. “Puzzles and explorations in math classrooms”
3. Khan, I., “The art of geometrical design”
4. Farhat, A., “Decrypt secrets to celebrate mathematics: on attaining the essence of NEP through excellence in teaching mathematics”
5. Selvakumar, G. “Innovative activities for teaching mathematics”
6. Kumaravelu, K. “Teaching and learning volume of a solid using GeoGebra”
7. Thakker, J. “Experimental mathematics in high schools using GeoGebra: Sliding ladder as a first introductory assignment”
8. Rajeev, N.J. “Conceptual literature review of mathematical reasoning and reasoning abilities”