Ankita had just moved into her new house and was very excited about it. Bereft of any furniture her room was totally empty. She closed the door, blindfolded herself and started moving across the room, tracing the walls with her hand. She traced one wall after the other and continued doing this for some time.

She then removed her blindfold, opened the door and rushed to her mother and asked her to close her eyes and started describing how her new house was. She described one room after the other in great detail. She even told her that if the lengths of the four walls of her mother’s room were added, it would be more than that of her room.

Her mother was astonished at Ankita’s observations. She had seen her visualising things earlier too, but this time she was amazed by her ability to not just visualise the rooms but also feel them with some degree of accuracy. This was Ankita!

Ankita was a little late for school the next day. When she reached her class, she didn’t find anybody there and was informed by another teacher to go to the audio-visual room as her entire class was there. She had no clue what was happening there. She slowly opened the door, took permission and took a place on one side. Initially she could not figure out what was going on. There was a tripod stand on which was fixed a movie camera, a mike, a projector, a computer that was connected to it and a screen on which was projected the following question.

There were a few people who were eliciting responses from students, some related to the question and some not. They kept repeating that they were not interested in the correct answer, but the reason/s for choosing a particular option and therefore to think for a while and be ready with their reason. Ankita went through the question and thought for a while.

Interviewer, “Those who think the answer is A, raise your hands.” More than half of the students raised their hands. “Option B” and almost all of the remaining ones went up with their hands. “Option C” and there was no one apart from Ankita. Initially, she was reluctant to raise her hand. But the interviewer asked her to relax and told her that it was quite alright to think in a given way. She raised her hand for option C. Hardly any hands went up for option D.

Manan, who had raised his hand for option A, was called to come up to the screen. The first question that was asked to him was “Do you know what a perimeter is?” He replied, “Yes”. They asked him to explain what it means. He said, “Perimeter is the length of the boundary of a shape.” It indicated that he knew what a perimeter was. He was then asked to explain the reason why he thought A was the answer. He said, “Since we are removing a square of perimeter 20 cms from a triangle having a perimeter of 80 cms, we have to subtract 20 from 80 and so we will get 60 cms as the answer.” His answer showed that although he could define a perimeter he had not not actually understood it.

Priya, had raised her hand for option B. She was also asked to explain what a perimeter meant. She too gave a fairly satisfactory answer as far as the definition of a perimeter was concerned. Then came the reason for her answer. She said, “The square that is cut out has a perimeter of 20 cm. So each side will be 5 cm long. Now, the piece that is remaining had a perimeter of 80 cms. Three sides of the square are left out in that piece. So, if we subtract 5+5+5 from 80, the answer will be 65 cms.” It seemed that she also knew what perimeter was, even knew how to calculate the perimeter of a given shape but was not able to apply it correctly in this context.

What do you think was the error that these two kids were making? Do let us know by emailing us at misconceptions.dh@ei-india.com.

Ankita was listening to all their reasons. She was pretty sure what the answer would be. We shall discuss her response along with those of other students, in the next issue.

Educational Initiatives is an Ahmedabad-based 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 2,500 students on over 30 questions from ASSET.