Strengthening Perceptual Numbers

Importance of Perceptual Numbers

Perceptual Numbers, recognizing quantities one to five, by "perception or sight" without counting are the foundation on which math learning is built.

The idea of number itself is an abstract one. Before the invention of numerals, there was no "crystal clear" way by which someone could point at something and say "this is three". If we show "three fingers" the learner could confuse three as something to do with fingers.

The abstract nature of numbers is the reason why animals cannot understand numbers beyond their evolutionary needs.

All children develop a sense of "size" naturally. But all do not necessarily develop a good sense of "numerosity" or "numbers as quantity" even for smaller numbers.

Children come to school with varying abilities to "perceive" numbers. Children whose number sense is weak, would find math a very difficult discipline to master.

Hence one of the first tasks of a preschool teacher is to check & strengthen the perceptual number skill of all students before proceeding with math.

Activities for Strengthening Perceptual Numbers

Children should to be able to identify numbers 1 to 5 in various forms, starting from concrete to abstract. Here are the various representations. In chapter 7.1 we will deal in detail with the necessity of "representing" numbers through various means.

These representations are arranged in an increasing order of abstractness. They start from representing numbers using concrete everyday objects, then pictures representing everyday objects, and then to tally marks and then to numerals & words.

1. Sound Representation - Children first encounter numbers as "number sounds" embedded in instructions & conversations among family members. E.g Bring "two" plates, we have "three" children etc). If more than one language is spoken at home, children may come across more than one "sound" in which a number is referred to. (Three or Theen or Moondru).

2. Real Object Representation - 2 pencils, 5 boys, 8 flowers etc using objects that we use & refer to in daily life.

   1. Usually, the sound representation goes hand in hand with the real object representation. When a child hears the request "please bring two plates" she is associating the word "two" or "Irandu" with the concrete idea of a certain quantity of plates.

   2. Hence in the classroom, the teacher can give instructions like "pick up two pencils" or "bring four tokens". By observing the children over a period of time, she can identify children whose perceptual number sense needs strengthening.

   3. The teacher can also ensure that a particular student whose understanding of four may be weak, gets more practice involving sets of four objects.

3. Action Representation - by actions like jumping, clapping etc

4. Finger Representation - Indicating a quantity with fingers. Though it is a form of Real Object representation, it is important since fingers are available to all 24X7. Finger Representation is very important and is dealt with in detail separately in chapter 5.5.

   1. Teacher can ask children to show as many fingers as the number she either calls out holds out with her fingers.

   2. She can encourage them to show the same number with different combinations of the fingers.

   3. She can also ask children to show a number with either one hand or both hands. In showing four using one finger on the left hand and three on the right, the child is also learning subconsciously that one and three together make four!

5. Picture Representation - Identifying the number of objects or persons in a picture. It is only the human mind that can see a small picture of an elephant and relate it to the actual elephant it saw at a different time and place!

   1. The teacher can use cards with pictures of a collection of many things like fruits, flowers, animals etc. She can ask children to pick up any card which has the same number of things as the number word she speaks out.

6. Tally Mark Representation - Identifying a number by the number of Tally Marks as ×, +, o etc. The tally marks can represent whatever (a chocolate or a toy) that we want to represent.

   1. Numbers represented with tally marks can be done in many ways that reflect patterns and relations. Here is an example for 6.

   2. The like in the case of picture cards, the teacher can design activities using these tally Mark cards.