The problem 25×5=? was given to a group of government school children in standard 3 by their teacher in the class.
Out of a class of 30, only 10 got the right answer, viz, 125. Another 7 got 105 as the answer, 3 gave 30 as the answer, 5 gave 1025 as the answer. The remaining wrong answers were random.
The teacher was appalled! Only 1/3rd of her class had got such a simple problem right.
The teacher made the students memorize and repeat the 5 times table.
Would that have made a difference to their ability to solve the problem? Not in a significant way!
If one analyzes the wrong answers, there is a clear pattern. A large number – 7 – got 105 as the answer. In this sum, they would have got 105 if they forgot to add the carried over ‘2’. So this is what had gone wrong in their case.
Another 3 have got 30 as the answer: obviously, they thought that they had to add the 2 numbers or they did not know multiplication, so decided to add.
5 students got 1025. They would have got this answer if they did not understand the concept of carry over, and thus wrote the whole product of each of the 2 numbers.
In 12 out of the 20 ‘mistakes’, the students had got their 5 times tables right. What they did not know was the operation involved in doing a multiplication!
Hence, if the teacher had spent time going over these, it would have been of greater help than getting the children to learn the 5 times tables, since if at all, only 8 of the class of 30 may have had problems with that!
Shri Kartikeya Sarabhai, Director Centre for Environment Education, often quotes this example from his experience with a school he was working in, to groups of teachers and teacher educators. He used to tell us why teachers needed to pay more attention to students’ mistakes than to what they got right. It was never a matter of just marking things with a tick or a cross, but looking at patterns in the answers, and analyzing these to understand what the children had missed or misunderstood and thereby re-aligning teaching.
And indeed this is true. Whether it is language or math, or social science, or science, the teacher needs to understand what children don’t know. Only this will lead to effective teaching-learning.
Sometimes, it may be obvious, but at other times, the teacher has to probe hard to understand what the children have not understood. It might be that the children have not understood a concept. Or it may be that while they understand the concept in abstract, they don’t know how to apply it, or they are not able to perceive when to apply it. A teacher has to push the students to more and more advanced questions so that she can make out where they are dropping off.
For instance, a very common confusion that persists with most students (and adults, for that matter!) is the difference between mass and weight (also see Let’s Experiment! in this issue). Your students may be able to say the definitions, but don’t be satisfied with that! Ask them questions that will tell you a little more about their understanding of these concepts. For instance, ‘If you go to the moon, will your weight be the same or change? Will your mass be the same or change? Why?’ This will help them apply the definitions, and help you see if they have understood. And then you will have to tailor your explanations based on the feedback from their answers.
It is thus important to ask the right questions, and in a sense get the wrong answers, to be able to teach right!
The author is Director, Community Services, GMR Varalakshmi Foundation, Hyderabad. She can be reached at Meena.Raghunathan@gmrgroup.in.