Gaming math on the board!

Sandeep Yadav, Anveshna Srivastava and Koumudi Patil

Math: the only place where you have to figure out the ratio of yellow candy to blue candy when all you are thinking about is eating them! (stolen from Google)

It is the same old, boring story that math is hard and that one has to be extremely sharp and intelligent to get it correct. Of course, we know about thousands of coaching classes running in every nook and corner to help train young minds to get their math right. But, as educators, parents and well-wishers of the young generation, we have to ask ourselves – what makes math appear so hard in the first place? Of the multiple reasons, math is difficult because our textbooks are full of examples which are not just hard to relate to but are also a practical challenge to process. So, for instance, one can always wonder why would anyone buy 80 cars and the other 60? Can’t comparison be taught in a more relatable and practical way?

Impractical and unfamiliar examples are likely to cause cognitive stress to students who are then forced to rote memorize not just concepts but also examples that they have guessed to be their teachers’ favourites. However, there is a silver lining to this cloud. Passionate teachers, thoughtful parents, active researchers are doing their bit to make math fun, and their efforts have to reach far and wide to make a strong societal impact. Aligned with this perspective, National Curricular Framework (2005), published by the NCERT, suggested that math should be activity oriented so that students can learn the basics by experiencing it.

Taking cognisance of the above, we wanted to design an activity that would seamlessly connect fun and basic math learning. For the fun part, we designed a physical manipulation game and for basic math, we zeroed in on area-perimeter as the conceptual theme, given its significance as a gateway to understanding complex mathematical equations and its general relatability to practical life. Our work is built upon multiple efforts made in math education that have worked to bring about learning through games. However, this also makes us aware of the flip side that games are usually not taken seriously and that using games as part of regular class curricula is a distant dream. That said, we remain undeterred and did design a basic manipulation game thinking that students will at least have some fun.

We modified the game mechanism of an existing paper-pen game built on area-perimeter by transforming it into a board game while adding a number of fun elements to let learners relate to mathematical concepts in an amicable fashion. Our modification involved introduction of dice which had ‘0’ as a value on one of its face that would reduce area/perimeter to null values during the game. To let students mark the boundary of a space, we introduced push pins to help them mentally visualize the concept of fencing, the physical referent for understanding perimeter. We also introduced shapes other than square to make learners familiar with other expressions of area-perimeter. However, in this article, we are just reporting the game we have designed using square shaped units for the sake of simplicity. We tested the efficacy of our game by reaching out to limited number of young learners from grades 4, 5 and 6 from schools catering to both lower and higher socio-economic background. Through this article, we share our basic game with the teaching-learning community.

The Game
Our two-player board game includes a rectangular cardboard piece, stuck upon styrofoam sheet, which has uniform 10*10 (100) square grids made on it (see Fig. 1). Each square side is equivalent to 1 unit. The game includes a set of two different coloured square units which easily fit on top of the cardboard square grids and a set of two different coloured push pins, where each pin is meant to define the boundary of one unit side of the square. The two players choose the colour of their square units and the push pins at the beginning of the game.

This is a dice game where the dice is improvised to include numbers from 0-5. With every dice rolled, players have the opportunity to either pick farming or fencing as their option. Farming involves computing the area of the square which is side*side and fencing involves computing the perimeter of the square which is 4*side. The value of side is determined by the number that appears on the face of the dice when it is rolled. For instance, if one rolls the dice and the face value appears to be 3, and the participant decides to farm, then the participant has to calculate the area for a surface where the corresponding side is equivalent to 3 units, which computes to 9 (3*3). The player can then put 9 square blocks on the grid. In another case, when the player rolls the dice and the face value appears to be 2, and the participant decides to fence, then the participant has to calculate perimeter for a surface where the corresponding side is equivalent to 2 units, which computes to 8 (4*2). The player can then add 8 push pins, one each pinned on the boundary of the cardboard square unit. Figure 2 illustrates the game in action.

During the process of the game, participants record for each of their turn, the value of the dice and the computed value for farming or fencing (see Fig. 3). At the end of the game, which we capped at 10 turns, the winner of the game is decided based upon the total number of farmed and fenced square units on the board. This means that the square units which are farmed and not fenced or vice-versa are not included in calculating the overall score.

Our learning
We found that participants were eager to play the game again and again and a possible reason for this could be the fun competitive element and the ability to bring the concept of area-perimeter into a familiar zone. We also believe that the target of winning the game made the process of repeated calculation of area/perimeter more efficient for the students. We could also see that the demand of the game to simultaneously compete and compute area/perimeter enabled participants to develop specific plans and strategies during the process. This work has shown various ways of taking the game forward, like using different methods for playing the game or using different shapes to compute area/perimeter. These tweaks may enhance learning by adding both complexity and fun to the game. That brings us to our next agenda which is to see if students particularly do well in their regular school exams on area-perimeter because of this little intervention. For now, this is a tiny success which is quite encouraging for us as educators.

Reference
National Curriculum Framework (2005). New Delhi: National Council of Educational Research and Training.

Sandeep Yadav is a mathematics educator working for Pratham Education Foundation, Delhi. He specializes in designing learning tools, games, activities and educational videos. He can be reached at salimyadav43@gmail.com.

Anveshna Srivastava is a science education researcher. She is interested in understanding the how of learning and how this can lead to improvement in the outcome of learning. She can be reached at anveshna.sriv@gmail.com.

Koumudi Patil is an Assistant Professor in the Department of Humanities and Social Sciences and the Design Programme in the Indian Institute of Technology, Kanpur. She works in the areas of creative thinking, vernacular design, frugal innovation and gamification of education. She can be reached at kppatil@iitk.ac.in.