The physically active mathematics classroom
Pooja Keshavan Singh
As part of the recent developments in the school curriculum, Physical Education (PE) has been made compulsory for all years of formal schooling. This is a welcome step as most children are facing consequences of sedentary lifestyles. Moreover, with urban spaces becoming lonely and insecure, it is important that schools respond to this urgent need of the current generation of school going kids to grow up healthy. As per a recent data, when compared to 195 countries in the world, India has 14.4 million obese children, second only to China which has 15.3 million obese kids. We must realize that a huge percentage of our school going children have become obese only over the last few decades. This can be attributed to the kind of food that students eat and the lack of physical activity. In this scenario schools need to step up their act in order to help students live a healthy life today and in the future.
In this article, I will share how teaching of mathematics and PE can be combined together easily. I will discuss some activities that can be taken up in the mathematics classroom in which students can be engaged with mathematics and be physically active as well. Most of them have been tried in the classroom and I have briefly discussed students’ mathematical responses here as well.
In my years of work with schools and with my own children I have realized that children love to be active and agile. They simply want to be moving physically and mentally. With a little careful planning, we can incorporate mathematics lessons in physical exercises and it’s a win-win situation for children’s physical well-being and their math learning. I shall begin with some activities that were taken up in primary and secondary classes and then discuss some existing resources that can be used by teachers.
The first example is an activity on ‘visualizing solid shapes’. As an introduction, the teacher brought many solid objects into the classroom and placed them on an elevated position on her table. For instance, cubes, cuboids’, cylinders, spheres and cones. She discussed each one of them with their names and characteristics and she also asked the students to think of examples of objects that have those shapes. After familiarization, the students were taken into the school field. Now the task given to the class was to form groups of two and in as little time as possible, they had to locate three examples of the solids they had discussed in class in the school’s campus and return to the starting point. Since time was an important factor to be considered in this activity, students had to run, discuss and co-ordinate within the groups. During this activity students not only got to observe solid shapes in their vicinity, they also got to be physically active in the process. During this activity, students reported some interesting examples that even the teacher had not thought of. For example, a student asked the teacher if the steps of the stairs were cuboids placed one on top of the other, slowly reducing in size. Another child remarked that the drainage pipe running down the building was like a long cylinder.
Another example of a physical activity where mathematical ideas can be incorporated is a common game called ‘corner-corner’. In this game there is one “den” and four others who have one corner each in the room. Players have to carefully exchange their corners while the den has to grab one of the corners. The one who loses his/her corner becomes the den now and the previous den now gets a corner in the game. When this game was played in a rectangular room, students were seen to figure out that the width of the rectangular room was the smallest distance they had to cover to exchange their corners and the length was longer than the width. They also found out that the diagonal corners of the rectangle take the maximum time because it is the longest distance between any two corners.
After discussing these observations, the teacher gave them a meter tape to verify these. Any mathematics teacher will tell you that this understanding about the length, width and diagonals of a rectangle is hard to build with simple paper-pencil tasks. Most importantly, it can be extended to other quadrilaterals as the case may be. For instance, a square has all sides equal but the diagonal is still the longest distance to be covered for exchanging corners. The children in this process remain physically active and mentally engaged while playing the game.
Another example could be an activity on understanding integers. Just like students use stairs for going up and down school floors, in order to discuss integers, we take the first floor of the school as the ‘base floor’, the ground floor as the ‘underground’ floor and the second floor of the school as the ‘above ground’ floor. Students can stand on any number stair, and the teacher can call out numbers to move under-ground or above ground and write simultaneous expressions for it. Students can jump on the stairs in groups of 4-5 as the space permits.
Later their movement can be connected to ‘positive numbers’, ‘zero’ and ‘negative numbers’. This activity serves two important purposes besides keeping children physically active. First, they build an understanding about integers which is a new domain in numbers introduced to them in class VI, and second they also learn to write respective expressions for the operations on integers. This is important because other than learning the concept of integers, the students also need to be introduced to the language of mathematics. The same activity can be taken up with primary classes for introducing and practicing addition and subtraction.
For senior classes (class VIII onwards) there are many ideas to combine physical education and mathematics. Some of them are discussed here. One example could be to keep a record of the scores in basketball or cricket matches played during the schools’ sports sessions over a period of two to three months. The teacher can use the data generated during these matches to teach students about measures of central tendency. These can be connected with national and international matches played. Students can be given suggestions on improving the team’s performance and how individuals can contribute to their own team. Students can be taught about the techniques of analysis used by various teams around the world to improve their performance.
A second example could be a ‘Treasure Hunt’ for students learning coordinate geometry. In this activity, the school ground can be mapped on to a grid just like a coordinate axis. This has been shown in the Figure 1 below. Students can be handed out a map of this grid and they can be introduced to the tools of coordinate geometry like a point, its coordinates, distance formula, equation of a line through a point satisfying a condition, the point of intersection of two lines, etc. Then they could be sent on the ‘Treasure Hunt’ during which they have to find exact locations on the ground to find the treasure. The coordinates and the equations of the lines can be used as clues for student teams to find the hidden treasure. Students are seen to make new discoveries about the co-ordinate plane and how to use various tools associated with them. All this learning happens in addition to keeping them physically active.
I must reiterate that students learn better when their entire body is involved and engaged in the process, this is also called the bodily-kinesthetic learning. This learning is better than when only their eyes (visual learning) and ears (auditory learning) are involved and this is also addressed as multimodal learning.
Besides these activities there are some resources that I would like to share with the readers through this article. There are some PEC cards that have been developed by the Physical Education Congress and they are available online for access. Just Google ‘pec cards for class 1- Make sports a way of life’ and one can find many pdfs that can be downloaded. There are suggestions for classes I to V on the website. If we click on the class I PEC cards we find many activities on agility, balance and coordination. There are 20 cards in the collection for class I, each having explanations about the physical activity and the related English vocabulary that can be developed as well as the mathematical idea that can be discovered during these activities. The activities on these cards can be used liberally for teaching English and mathematics along with physical education in the primary classes. I have given a sample of the card in Figure 2 below.
To conclude I would just like to bring the reader’s attention to the ease with which even a mathematics classroom can be made physically active. It requires small tweaking in our planning and a small change in our attitude towards teaching mathematics. The best gain in this proposed transformation is the increased activity and improved agility of the mathematics teacher who is also required to be on his/her toes both physically and mentally.
The author has been a mathematics teacher and teacher educator for many years. She is currently pursuing her Ph.D from the University of Delhi in mathematics education. She has been researching on the use of storytelling as a pedagogic tool in teaching of mathematics. She can be reached at keshavansinghpooja@gmail.com.
