Our days at Aavishkaar starts with an engaging energizer followed by a math or science charchaa. One of our facilitators leads this space igniting us with curiosity and a sense of exploration. Today was Sandhya Madam’s turn. She had come across an interesting and fun math problem which she was excited to share with us. The problem or rather the puzzle is a picture given in figure 1. She drew it on the board, and gave us options, either to share the complete problem, or share it in small parts, step by step. Both ways have their own perks, either to realise that we can handle challenges or to build on every step and finally see the big picture and get surprised! We chose the first option, the sun soaked winter morning felt to have made us open to new challenges. What is the quest? To find the ratio of shaded and unshaded regions in the square in figure 1.
Figure 1. The problem: Find the ratio between shaded and unshaded area in the given square.
From a conventional point of view, this is a math class and we are all expected to solve it individually at the quickest. But here it is different; here we also do things in groups. Why? That is something we are going to witness soon. So, we split into groups of 3 and (some of us, on our own) started pouring our ideas on what this problem is and how to approach it. Some of us had trouble figuring out where to start, or what to measure. Identifying which attribute to measure, the right and most efficient tool to use in one particular math problem, is an important skill. Here, the key was in identifying the measurable quantity, area of the square, and how it can be expressed as we see it. In the last few weeks we have done so many things to visualise fractions, so our facilitator brought a problem in which fraction is applied. Now it is our turn to find out how we can implement our understanding. Recently we have also been learning algebra; how to catch what is repeatedly growing. We could see that today’s problem had a repeatedly progressing pattern.
As I looked at the team some learnings got underlined in my mind; that math can be made visual, and when the brain struggles with a new problem, it thinks, and that way it grows. All our senses work together when we read the picture, think, and express it at the same time. It gets engraved in our memory better and builds confidence: ‘I can do this and any problem which appears complicated’, and that felt incredible. These are also the things to strengthen in every member of the team or every student in the classroom. Making mistakes is an essential part of learning and we do not categorise any responses or point of views as right or wrong rather we look for multiple responses and debates. Today also eventually we realised that we all looked at the problem differently, and broke it down differently, as shown in figure 2 below. The perspectives were so varied. It was fun!
Figure 2. Different ways of seeing the square.
Once the puzzle is understood, we tried calculating the fractions of shaded and unshaded regions, again in groups. Some of us were able to express it in an algebraic expression while some of us solved it numerically, and some of us kept the fractions in tact and proceeded further (figure 3). It felt that doing math is not easy but if we keep going with one step at a time it starts making sense. I could see that our belief is getting stronger that anyone can do math. We have experienced it in so many charchaas, made it happen with various groups, and it is also our vision. We want anyone to believe that they can handle complication and rigor. Today’s charcha felt like a self reflection of our facilitator upon us.
Figure 3. Different ways of solving the problem.
Often, whenever we do group activities, within a group some participants move ahead and some are left behind, they need more time to think. This happens very naturally and none of us hesitates to help eachother or more importantly to push each other. That does not mean that we force our understanding upon our fellow participants. We believe that if one has solved a problem first, their celebration is helping the fellow group members see it their way. Helping others this way hones one’s skill of asking the right questions at the right moment. As a facilitator working with a group, one knows that everyone can do it. But the facilitator also understands the levels of each student. We are all teacher trainers, teachers/facilitators and students. Be it a teacher or a participant, it is in our practice to keep an open mind in classrooms, curious to find new ways of solving anything, and to get surprised.
As a team we still have a lot to learn. Today also many of us were on different pages in some aspects. One major gap identified in today’s problem solving was ‘how to bring out the commonality’ between the shaded and unshaded areas in the square. For sure practice and interactions with fellow participants helps in developing the visualisation ability which in turn deepens one’s understanding of any concept.
Here is a fun fact: Have you ever thought about it? Math is a language?!
– By Athira, STEM Lead
