Development of Number Sense 1

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We saw that teachers in pre-school need to find out the skill level of "perceptual numbers" among their students. They also need to build on these rudimentary levels to achieve a robust sense of numbers. To help in designing suitable learning activities for this purpose, we will now look at the stages by which a feel for numbers develops in the human mind.

Though the stages are given in a sequence, the actual process takes place with a lot of overlaps and recurrences. The outcomes also depend on the child's innate strengths & weaknesses in dealing with abstraction and the effectiveness of the activities.

Many of the stages start at home. They should be continued and reinforced at school as well.

Stage 1 (More at Home & Less at School)


 * 1) When children play with daily use items, they perceive properties like colour, shape, texture etc which they can perceive directly and the related names can be taught to them.
 * 2) By seeing many different items of the same colour, they develop an idea of colour (or shape or texture) which is independent of these items. By seeing a number of unrelated red things like a pencil, fruit, door colour etc, they form an idea of "red" colour independent of these things.
 * 3) In this process the adjective "red" as in red pencil, red fruit becomes a noun "red" which they can visualise independently.
 * 4) This can be seen as the process by which a quality (red) related to concrete objects (pencil, fruit etc) becomes an abstract idea (abstract noun) in the mind.

Stage 2 (More School &amp; Less Home)


 * 1) While sorting various items by more than one criterion e.g colour and/or shape, they realise that the same item (long blue pencil) could belong to either a set of blue pencils or long pencils or a set of long blue objects (pencil, walking stick).
 * 2) They come across collections of different items with the same quantity as in a set of five pencils, five fingers in the palm, the corners of a (pentagonal) star etc. This gives rise to the idea that the number of things in a set, say 5, can itself be seen as a property of the set.
 * So, a set of pencils can be called a set of red pencils or long pencils or a set of 5 things or just a set of 5.
 * 1) They see the fingers of a palm, a pentagonal star or a set of pencils can be said to share the property of having the same quantity which is known as 5 or Five.
 * 2) Over a period of time, they acquire the ability to think of "five" as an independent idea which can be applied to a number of things.
 * 3) At this point we can say that the child has acquired a sense of "five-ness". Sense of numbers 1 to 4 is also learnt in a similar fashion.
 * 4) Numbers 1 to 5 are also relatable easily with the parts of their body ( 1 - head/ mouth/ nose, 2 - eyes/ ears/ hands/ legs, 3 - wheels of an autorickshaw/ three middle fingers, 4 - legs of animals/ crawling baby, 5 - fingers in the palm). These parts of the body are with them 24X7 and they experience them continuously.
 * 5) They acquire a sense of these quantities and the word sounds with which they are associated. In homes where more than one language is spoken, children learn to associate words in both the languages with the number.

Stage 3 (School)

In brief, starting stage of number sense is the ability to see objects & events in terms of sets and the ability to compare sets & understand the cardinality of a set.
 * 1) They also realise that these numbers can be compared (3 chocolates is more than 2, my brother who is 6 years old is older than me)
 * 2) They realise that these quantities, as well as the associated words can be arranged in a logical sequence, either in increasing or decreasing order. At this stage, teachers can introduce them to the sequence &amp; logic of counting from 1 to 5.

Chapter 4.4 gives this sequence of stages in graphic form. This is a process could take varying amounts of time for various children depending on their prior experiences.

We can describe the process in brief as below.



Teachers can also request parents to strengthen the sense of numbers in their children, at home, by using number names as part of their conversation and instructions. They can also encourage children to show these numbers either with their fingers or by pointing out to groups of things (legs of a table, plates on the table) in the house.

We will deal in the next few chapters with a series of learning activities for developing various other aspects leading to number sense in the pre-school stage.

At the pre-school stage these activities can collectively be called "pre-number" activities i.e foundational activities necessary for developing elementary number sense. These focus mainly on listening to, identifying & reading (as patterns) and speaking about numbers. They need not include writing of numbers.

Before taking up these pre-number activities we will first deal in the next chapter with activities that strengthen the understanding of perceptual numbers 1 to 5. This is also a pre-number stage since we are dealing only with understanding, listening &amp; speaking of these numbers. We deal with it separately because of its criticality in building number sense.

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