A Report
The Department of Elementary Education organized an online workshop for school mathematics teachers titled Pedagogical Opportunities for Technology Enabled Explorations in the Mathematics Classroom in collaboration with Internal Quality Assurance Cell (IQAC), from 22nd to 26th March 2021.
The aim of the workshop was to bring together school mathematics teachers, mathematics educators and individuals interested in mathematics education to deliberate on the role of explorations and investigations in the mathematics classroom. Eminent mathematicians, who have made significant contributions to mathematics education in India, conducted the sessions of the workshop. The sessions focused on the nature of mathematical explorations, on creating meaningful tasks for exploration and on empowering students to develop their mathematical thinking skills. About 100 mathematics teachers participated in the workshop. A majority of the participants were from Delhi NCR, Mumbai and Pune. The sessions were conducted on Google meet.
Professor R Ramanujam, Institute of Mathematical Sciences, Chennai, Professor K. Subramaniam, Director, Homi Bhabha Centre for Science Education, TIFR, Mumbai, Professor Inder K Rana, Retired Emeritus Professor from IIT Powai, Mumbai, Dr. Shailesh Shirali, Director, Sahyadri School, Sahyadri, Pune and Dr. Jonaki B Ghosh, Department of Elementary Education, LSR conducted the sessions of the workshop. Each speaker conducted a two hour session from 3:30 to 5:50 pm. All sessions were interactive and participants were invited to work on problems and also share their views on the theme of the session.
The first session of the workshop was held on Monday, 22nd March at 3: 30 pm. Dr. Suman Sharma, Principal LSR, welcomed the participants and the speaker and set the tome of the workshop. Prof. K Subramaniam spoke on the theme Data literacy as an educational goal: Setting the agenda which highlighted the fact that an important goal for education aimed at social transformation is widespread data literacy among the citizens of the country. He explicated terms such as datafication, data dominance and data literacy, which is linked to quantitative thinking and statistical literacy and is an important part of mathematics education. He facilitated an exploration of data based on distances between various bus terminuses in Maharashtra acquired using Google maps and enabled the participants to make inferences from the data. This helped to illustrate the kind of exploratory activities which may be conducted with school students to enhance their data literacy.
The second session titled From 2 D to 3 D making boxes and cones was conducted by Prof. Inder Rana. The session began with making a box using an origami sheet followed by finding its area and volume and the relation between them. Different ways of making the same box without wastage of paper was demonstrated and analysed mathematically. To develop the understanding of 2D and 3D, the unfolding of boxes were done, and the relation between attributes such as surface area, volume and area of the 2D layout of the box was illustrated. Overall the session was very engaging.
In the third session, on Adventures in problem-solving (with some help from technology) Dr. Shirali discussed several problems (from geometry and algebra) which lend themselves to very interesting investigations. His approach was to get the participants to think and propose a solution after which he discussed the problems in depth. He demonstrated the problems visually on GeoGebra and enabled the particpants to make conjectures and prove them.
The fourth session on the theme Thinking about algorithmic thinking by Prof. R Ramanujam was truly thought provoking. By citing examples he differentiated between algorithmic and computational thinking. He discussed well known algorithms such as the Rhind Papyrus algorithm for multiplying two numbers and illustrated how the algorithm of long multiplication can be converted into an investigation for children. He pointed out that children must be encouraged to think about why algorithms work rather than just practice the procedural steps. Refering to the conceptual vs procedural debate in mathematics education, he emphasised that we must think of an inseparable blend between conceptual and procedural knowledge. The talk provided a rich source of explorations based on procedural algorithms that are taught as a part of the school mathematics curriculum.
In the last session on Enhancing students’ engagement in mathematics through explorations Dr. Jonaki Ghosh talked on the role of mathematical explorations in providing opportunities to students to formulate problems, discover patterns, make and test conjectures and approach solutions via multiple paths of inquiry. She cited examples of students’ investigations on the topics of Fractals, Genetics and integer partitions and demonstrated that the appropriate use of technology can help to enhance students’ mathematical thinking and also sustain their interest in the subject over a longer duration. The participants were given the opportunity to explore some of the problems on MS Excel during the session.
The feedback taken from participating teachers at the end of the workshop was very encouraging. They expressed that the sessions provided them with a plethora of innovative ideas for integrating mathematical explorations in the classroom and they hoped that more such workshops will be organised in the future.
