Rahul was visiting his grandmother in their native village. He held on to his dad’s hand as they walked fast through the small bylanes of the village. Women were washing clothes, a few of them were going to draw water from the well. For Rahul this seemed like a scene from his picture books. He believed these things belonged in pictures and was in all probability what the entire world looked like some 100 years ago.
His dad showed him a huge tree where some kids were playing hop and skip which, he said used to be his favourite hangout in summer. Rahul was lost. He wondered what could be done with a tree. Finally, they came to a huge white gate. His father took the knocked on the door with the handle and they heard Rahul’s grandmother run to the door with excitement.
As the door flung open his grandmother stood with a diya in her hand and put a small tilak on their foreheads to welcome them. As Rahul walked inside he saw a huge ground filled with patterns made in white. It looked similar to the rangoli his Mom made outside their door during Diwali. But this was different and something about the patterns made him curious. They looked like small diamonds on the floor filled with other shapes. He was wondering how they had managed to make such perfect designs and such perfect diamonds at that.
While travelling back to his home he asked, “Dad does dadi have a geometry box like me?” His dad smiled. “How did she manage to draw those perfect circles? and how does one make diamonds?” wondered Rahul aloud. His dad made a diamond like shape with his hands and said, “This way”.
Rahul was not convinced and decided to ask his teacher. The next day his teacher put the following question on the board (See box on left hand side).
Rahul felt shapes were haunting him. He wondered if squares could be made and turned around to look like diamonds. Staring at the question he made a square-like shape with his hands and tried to turn it a bit.
His teacher saw this and asked him to select his answer from the options. Rahul said he was confused but thought B was the correct answer. His teacher asked him why he thought so. Rahul said that when you turn the square it becomes a diamond. All the corners change so it does not remain a square.
His teacher went back to the ASSET results and looked at how other students had answered this question. The results can be seen in the graph in the last column.
More than 6,655 students were asked this question and this is what the results show. A lot of students tend to believe that if we turn a particular shape around it becomes another shape. Research shows that students tend to believe that shapes need to be in a particular orientation or size for them to be defined as a square, circle, triangle and so on, much like what Rahul thought of the village being a part of his picture books. We will explore the reasons of these misconceptions next week but if you have interesting responses to this question or have come across misconceptions about geometrical shapes then do write to us at misconceptions.dh@ei-india.com
Educational Initiatives is an organisation working at the forefront of driving change in education through research, large-scale assessment and the development of new learning technologies. Student responses in this article are taken from a series of interviews by a special team that travelled to 28 schools across the metros and interviewed over 2500 students on over 30 questions from ASSET. Please visit www.ei-india.com for various ideas like this.
Rahul was visiting his grandmother in their native village. He held on to his dad’s hand as they walked fast through the small bylanes of the village. Women were washing clothes, a few of them were going to draw water from the well. For Rahul this seemed like a scene from his picture books. He believed these things belonged in pictures and was in all probability what the entire world looked like some 100 years ago. 
