‘Body mathematics’ is a technique that requires the student to physically experience the mathematics that they are learning about. This is also known as ‘embodiment’, or giving concrete form to an abstract concept. The concept of embodied cognition is that of using the body to shape the thinking of the mind (Dreyfus, 1996; Gibbs, 2006). Embodying mathematics can:
In Activity 2 you worked with your students on large measurements. The next activity takes this a step further: working outside with large measurements again, but also requiring students to be the mathematics – to represent mathematics in a bodily form. Students will be asked to represent a point on the circumference of a circle and then to construct the centre of that circle precisely. Consequently each student/point has to be convinced they actually are at the same distance from the centre as all the others. The activity requires students to stand up for their rights and let their voice be heard when they think they are being discriminated against by not being the same distance from the centre as all the other circumference points. This type of activity is not easy to manage the first time you try it, but if you persist your students will gain more sense of mathematical properties.
For this task you will need enough space for all of the students to hold hands and stand in a circle, with some more space outside the circle to be able to enact the construction of its centre. This task is to embody constructing the centre of a circle using ‘a perpendicular bisector of a chord pass[ing] through the centre of a circle’, as discussed in the textbooks for Class IX. If you think the group is too large to be able to complete the discussions they are asked to have in this task, it might be a good idea to ask them to discuss their ideas first in groups of three before sharing them with the whole class. You might need some rope or string, a ball, and a whistle.
Oh, they loved the competition element of this task! It made them so eager to think and come up with ideas. They all thought it would be so easy and simple to find the centre of the circle.
It was real problem solving – there were problems to be solved, both by thinking and by coming up with ideas to enact/embody the construction. There was a lot of getting stuck, and thinking about how to get unstuck. When they realised after several goes at placing the ball in the centre that it was difficult to be exact, they were kind of stunned. They did find it hard to come up with a fool-proof method, and again, I was tempted to walk them through the chapters relating to circles.
But the hint of the bisector did the trick – although thinking of using a chord or tangent to act as line segment took some time. But they got there on their own, and the sense of achievement, joy and pride, that they had thought of it themselves, was so much worth waiting for. I think that self-discovery and the ‘struggle’ to get there will also help them remember it much better – perhaps even in the exam.
Actually, in that process of thinking of what method would work, they came up with nearly all the different properties and theorems related to the circle. So it was good revision at the same time, together with the realisation that these theorems and properties might help them solve the real problem they were facing in the playground.
![]() Pause for thought
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