Strengthening Perceptual Numbers

< 3.4 Perceptual Numbers | Topic Index | 4.2 Number Sense >

Numerosity is More Difficult to Understand than Size

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 to be a very difficult discipline to master.

The above concepts are best taught through activities. We will deal in detail with the concept of "activity-based learning" in chapter 4.5.

Along with pre-number activities, the teacher needs to ensure that a firm understanding of numbers 1 to 5 & their visual images gets anchored in the minds of the students. These as we saw in chapter 3.4, are called Perceptual Numbers.

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.
 * 3) 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.
 * 4) 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.
 * 5) The teacher can also ensure that a particular student whose understanding of four may be weak, gets more practice involving sets of four objects.
 * 6) Action Representation - by actions like jumping, clapping etc
 * 7) 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.
 * 8) Teacher can ask children to show as many fingers as the number she either calls out holds out with her fingers.
 * 9) She can encourage them to show the same number with different combinations of the fingers.
 * 10) 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!
 * 11) 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!
 * 12) 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.
 * 13) Tally Mark Representation - Identifying a number by the number of Tally Marks as &times;, +, o etc. The tally marks can represent whatever (a chocolate or a toy) that we want to represent.
 * 14) Numbers represented with tally marks can be done in many ways that reflect patterns and relations. Here is an example for 6.
 * 15) The like in the case of picture cards, the teacher can design activities using these tally Mark cards.
 * 16) Numeral Representation - 1,2,3,4 etc. Numerals have different shapes which vary from language to language. When a child is learning 2 languages then numbers could be taught with numerals of both languages. Hence, we see that a child should master at least 5 other representations, before encountering numerals.
 * 17) At the beginning stages, the teacher should restrict to numerals up to 5.
 * 18) Word Representation - One, Two, Three etc. Number words are also written in various ways from language to language. When a child is learning 2 languages then numbers could be taught to write in both languages.
 * 19) The teacher should not spell these words but teach them as "sight" words. This is an accepted idea in language learning.

Please note that, at this stage, we are not talking of writing numerals & number words. The activities are limited to listening to, speaking about and sight reading of perceptual numbers.

< 3.4 Perceptual Numbers | Topic Index | 4.2 Number Sense >