# MISCONCEPTIONS: MATHS : Applications In Daily Life

Hey there! today we’re going to start a new series named ‘MISCONCEPTIONS’. As we all know that, there are lot of mistakes that we do while studying, like reading wrong side of chapter, working over outsourced activities, and all those misconceptions. So, are you one of them?

## (1) Why was the question asked in ASSET test?

This question checks whether children understand that volume is conserved when a liquid is poured from one container to another, without any spillage or overflow.

## (2) What did students answer?

41% of students chose B, correctly and 31% chose A, the most common wrong answer.
Possible reason for choosing A : Since the height of the water in the pan is much lower than in the jug, students probably feel that there is less water in the pan.
Possible reason for choosing C : Very few students chose this option and are probably making a random guess.
Possible reason for choosing D : These students may be feeling that they actually have to measure the quantity of water before concluding anything.

## (3) Learnings

The student response data show that ‘conservation of volume’ is not understood clearly. Students feel that there is more water in a taller/ narrower container as the height of water in it is more i.e. they take the height of water to mean volume. They may also feel that a smaller and fuller container has more water than a larger one with the same amount of water, taking “fullness” to be a measure of more or less quantity. Understanding ‘Conservation of Volume’ typically involves understanding that the volume depends on both the height and the width of the vessel. According to developmental psychologists, most children learn to appreciate this on their own by the age of 5-6 years, but if they still haven’t grasped this, they can be helped to understand this, using strategies as shared in the next section.

## (4) How do we handle this?

The solution to this problem lies in letting the children experiment with volume with a number of differently shaped containers, filling and emptying containers, and reaching the correct conclusions on their own. The teacher could take a number of containers of different sizes, and a few identical cups to measure out, and carry out the following activities.
• She could ask the students to measure and pour one cup of water into each of the containers. Ask them to mark the level of water in each. Ask them if they have poured the same amount of water in each and ask them to come up with reasons as to why the water levels are different.
• Show the class different containers of the same volume like mineral water bottles, soft drink bottles, oil cans, etc and stress that though all of them are of different shapes, the volume of all of them is same. She may ask the students to verify the same by asking them to fill these containers by using small cups and observing how many cups of water each holds.
• The teacher could empty the contents of say a wide vessel, and a tall thin vessel measuring out with a cup and show that each contains the same number of cups of water, though the water levels are different.
• To check whether the students are comparing volume in terms of height alone she could pour say 6 cups of water in a wide vessel and 4 cups into a tall thin vessel, in front of the class and ask them which contains more water and discuss their reasons. She can check whether the students are able to ignore the lower water level in the wide vessel and still say that it contains more water as 6 cups are poured into it.