Priyanka, Keshav and Shreyas have been spending the past hour over the following question.
Priyanka and Keshav think the answer is C, 6 cms while, Shreyas thinks it’s B, 5 cms.

But can we conclude that both Priyanka and Keshav had the same reason for selecting option C? Here is a brief of the conversation they had with their parents.

Priyanka: I think the answer is 6 cms.
Parent: Why?
Priyanka: See, the pencil is starting at 1 cms but its lead is ending at 6 cms and so the                  answer will be 6 cms.
Parent: Ok. So what will be the length of the pencil if it starts from 5 cms and ends at 10             cms?
Priyanka: Then it will be 10 cms because the lead would end at 10 cms.
Keshav: The answer will be 6 cms.
Parent: Ok. Is it because the lead is ending at 6 cms?
Keshav: No. It’s not because the lead is ending at 6. See. If we count from 1 - 1, 2, 3, 4, 5, 6, we have to count 6 numbers and so the length will be 6 cms.
Parent: Oh! Then what will be the length of the pencil if it is starting from 2 cms and ending at 5 cms?
Keshav: Then it will be, 2, 3, 4, 5 – 4 cms as we will be counting 4 numbers.
Shreyas: The answer will be 5 cms.
Parent: Ok. Can you explain why it will be 5 cms?
Shreyas: Yes. When we move from 1 to 2 it’s 1 cm and from 2 to 3 again its 1 cm. So, that way, as the pencil is starting from 1 and ending at 6, it will be 5 cms.
Parent: Ok! So what will be the length of the pencil if it is starting from 1 cm and ending at 3 cms?
Shreyas: It will be 2 cms.

Their parents were taken by surprise. Conversations like these reveal what’s going on in a child’s mind. As seen, though Priyanka and Keshav had selected the same wrong answer, the reasons they gave for selecting that option were clearly different.

These were just two of the common wrong answers students give when showed this question. This is a question that class 4 students are expected to answer correctly provided they have understood the concept of length measurement.

So where does the problem lie as in the case of Priyanka, Keshav or other kids of their age and how do we handle it?

One of the possible misconceptions that should be looked for while teaching measurement is whether students have understood the linear nature of length measurement. They are familiar with counting discrete objects and hence end up counting the markings instead of measuring the length which is a continuous property. 

It is important to check specific procedures and practices implemented in our classrooms. A simple strategy used by most students to find the length of an object, is to look for the end point on the scale. In addition, students generally see the starting point as 0, but what would happen if it does not start from 0?
Students are unable to deal with unfamiliar situations. It is very important that the concept of a reference point and an ending point is taught to students.

Several such factors could lead to incorrect answers. It is important to identify, understand and cure these unclear concepts before they become the cause for other misconceptions.

Anar Shukla & Nishchal Shukla

(Educational Initiatives)

(This is the concluding part on common misconceptions among students regarding measurement. The first part was carried last week under the heading ‘Measuring misconceptions’)