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What is Number Sense and Perceptual Numbers

Activity

Imagine that these ovals represent eggs. How many eggs have been drawn? You will quickly say “three”.

How would you explain to a child in class that there are three eggs?

Will start counting saying One, Two, Three?

If you do so, here are some questions that you need to answer for yourself.

Think about these questions:

  1. You said two while pointing to Egg B. Is it one egg or two eggs? If it is only one egg, why did you say two?
  2. What is the sense in which “two” is being used here?
  3. You said one while pointing to Egg A and two while pointing to Egg B.
    If one + two equals three does it mean that Egg A + Egg B equals Egg C?
  4. Is this not a case where 1 + 2 <>3?
    [Note: > denotes greater than and < denotes lesser than]
  5. Why did you use the words one, two and three? Why not a, b & c? What is the meaning of each of the words one, two & three?
  6. While you use the word three in counting, are you not already pre-supposing the meaning that you are in fact expected to clarify to the student?

All these questions should clarify a fundamental concept in Mathematics that Number Sense is different from Counting.

We normally believe that a child gets Number Sense through counting. The truth is that Counting presupposes Number Sense.

We intuitively understand the meaning of the words “One”, “Two” and “Three” as denoting quantity and the relation underlying them. That is why we voice them in that order.

So children should spend more time in internalising Number Sense before they start counting. Hence teachers should spend more time in helping students get an idea of what each number stands for, rather than just counting.

Number Sense is the ability to distinguish between

One and Many
Between many types of Many (different quantities)

It is the ability to realise that a box of chocolates contain less number of chocolates when one chocolate is removed from it. Even animals and birds seem to have this number sense for small quantities. Birds seem to known when one of their eggs in missing in the nest.

Most humans can recognize collections of objects up to 5 just by looking at them and not counting. With a little training they can do this up to 10. This is because Nature and our own body has sets of objects up to ten which a child is constantly exposed to. All humans have one head, two eyes, two ears, two hands, all animals have 4 legs, all birds have 2 legs, we have 5 fingers in each hand which we keep on seeing day in and day out, flowers have petals of different numbers etc etc.

If we see a group of three friends at a distance, we can “see” that there are three friends, without the need to count.

When counting the number of seeds in a pile, we automatically group them in threes or fours and skip count easily. The grouping is natural while the skip counting is “learnt”.

For this reason, number one to five are also called Perceptual Numbers, i.e. numbers that can be recognized without counting.

Number Sense in children should be developed by making them recognize groups of objects and their own fingers from one to five. With repeated practice children would be able to do this. After all different quantities make different patterns and the human mind is very adept at recognising patterns.

A human child has the ability to recognise dogs in all their varieties and from and at any angle. Why should they not be able to distinguish between a collection of four objects and three objects by sight? Why should we assume that they need the art of counting to be able to do this? After all a child will not see the second activity as a part of mathematics. It is adults who feel that “recognizing” a collection of three objects requires counting whereas “recognizing” a dog does not.

Contributed by S Sundaram

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