Pre-Number Concepts 3

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The activities in the previous chapter enable children to see objects as part of various collections and leads to the idea of sets. Let us now see the development of concepts related to sets.

Cardinality – By seeing collections of different sizes, the idea emerges that &ldquo;quantity&rdquo; can also be seen as a property of sets. A collection of &ldquo;four&rdquo; triangles, &ldquo;four&rdquo; pencils, &ldquo;four&rdquo; tokens can be seen to have a common property which can be called &ldquo;fourness&rdquo;.
 * 1) Cardinality – looking at the number (quantity) of things and not the individual sizes of things
 * 2) Ability to Perceive &amp; show (by fingers) numbers up to 5 by sight (without counting)
 * 3) Visual comparison of small sets or sets widely different in their cardinality (More, Less, Same as)
 * 4) Comparing with vocabulary - More Than, Less Than or Equal To
 * 5) Comparing with One-to-One Correspondence
 * 6) Seriation - Arranging sets in order – increasing or decreasing

Once cardinality can be seen as a property of a set, then various sets can be compared by their cardinality.

Numbers with Fingers – A child develops the ability (without counting, just by sight) to recognize numbers by the number of fingers shown or show a number with appropriate number of fingers. This is a very important skill which can develop into complex representations of numbers with fingers.

Visual Comparison – Collections which are significantly different in their cardinality can be compared just by sight. Even a small child can pick out a larger collection of sweets without counting. It leads to the idea of greater/ smaller.

More Than/ Less Than/ Equal To OR Bigger than/ Smaller than– Development of vocabulary to express results of comparing 2 sets.

One-To-One Correspondence– Small sets can be compared by sight. But larger sets need the idea of One-To-One correspondence for comparison. For example, assume that we have a collection of cups &amp; spoons. We can put one spoon each in a cup. If spoons are over and there are still empty cups, then it means that the collection of cups is more.On the other hand if all the cups are filled and there are more spoons left then the collection of spoons is more than that of cups.

This is a very powerful idea of comparing sets without finding out their individual quantities. In higher math, different kinds of infinities are compared using this idea.

Seriation - is arranging a collection of things in increasing or decreasing order of their quantities. It is the extension of comparison of 2 sets to multiple sets. Seriation is ordering a given set of collections either in the increasing (ascending) or decreasing (descending) order using the property of cardinality.

Seriation gives an insight as to the increasing cardinality of numbers. It provides the reason why numbers are arranged in the sequence 1,2,3,4.... etc. Every subsequent number is &ldquo;1 more&rdquo; than the previous number!

There is no logic in the way the alphabet (a, b, c etc) are arranged. But there is a clear logic in the way numbers (1,2,3...) are arranged.

Development of above concepts &amp; skills

Teachers need to plan activities (refer Chapter 4.5) for checking the understanding of all the above concepts &amp;abilities. They are not chronological in the manner in which they develop. They are all inter-connected and reinforce one another. Hence, they have to be done, repeated and assessed at frequent intervals.

If a child has difficulty in understanding a concept, teachers need to first check if the difficulty is due to language. They need to give the instructions for an activity in a language the child can understand. It is also better to use activity materials with which the child is familiar because of his home experiences.

The vocabulary used for learning these concepts; One, Many, More, Less, Share etc may also be unfamiliar to the children. However, they need to be remembered. Hence the teacher should deliberately use these words, in the appropriate context, many times and ask children to use them many times, so they would be remembered by frequent use.

The normal sequence for learning anything is Observing, Listening, Speaking, Reading and Writing. It applies to learning Math also. The child should observe an activity/process, listen to the teacher explaining that process and the related number names, identify (read) numbers associated with that process in any representation and then only write a number in numeral form.

Understanding language

All the above concepts &amp; activities need understanding of a lot of specific vocabulary. Teachers should ensure that all students understand all these commands, instructions &amp; words and can execute them.

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