Seriation to developing pre-number concepts, Mathematics

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Seriation :  You have read about a preschooler's ability to order. Ordering a set of objects means to arrange them in a sequence according to some rule. This arrangement could be on the basis of size, shape, colour or any other attribute.

For example, you could order a set of red and green leaves on the basis of colour - one red, one green, one red

Seriation is a particular type of ordering in which the objects are arranged according to an increase (or decrease) in some attribute like length, shape, weight, and so on. For example, you could seriate a set of stones according to their weight - the heaviest one coming first, and then the next heavy one, and so on, ending with the lightest one.

While designing seriation tasks for children, we must keep their abilities in mind. For instance, seriating more than three objects may be difficult for preschoolers as the following example illustrates.

Example 1 : 4-year-old Bachi was given five sticks of different lengths, and asked to order the in according to length. To do so she placed the first stick next to herself. Then she picked up another and placed it with reference to the first one. This was alright so far. While placing the third stick, she referred to the previous two sticks, and placed it correctly. Now, while placing the fourth stick, she referred only to the third stick, instead of looking at the total arrangement. So, finally her arrangement looked like.

Bachi could seriate three objects. But, when it came to the fourth, she couldn't relate it to all the previous sticks. She couldn't see that it is longer than the second, but shorter than the third, and therefore, must come in between them. After the third stick, she perceived each subsequent one only in relation to the previous stick that had been put in the sequence.

Example 3 also brings out the need to be clear about the logical processes involved in any task given to a child. In particular, before we expect a child to perform seriation tasks, we should see if she is able to

i) order in two directions (e.g., apply the relations 'bigger than' and 'smaller than' at the same time),

ii) understand the logic of transitivity (i.e., if A is more than B and B is more than C, then A is more than C).

Let us now take a brief look at some ordering and seriation activities for children. We have listed them in terms of levels of increasing difficulty.

The simplest ordering activity is asking children to copy a pattern. For example, make a row of alternating chalk and pencils, and ask children to make a similar row using chalk and pencils from a heap.

At a higher level of difficulty, you could ask children to continue a pattern. For example, place a twig and two beads, repeat this unit a few times, 'and then ask children to continue it.

The question to be answered in ordering activities is "what comes next?" At the next level of difficulty is asking children to seriate a collection of objects on the basis of some attribute. You could begin by giving children three objects to seriate and then gradually increase the number. Initially you may need to prompt them by asking questions such as "Which is the smallest?", "Which is the longest?", and explain how to do the task. If children put objects in a series incorrectly, ask them questions like "Is A (pointing to the object) thinner than C (pointing to the object )?" or "This one looks bigger, shouldn't it come here?". This will help them to analyse the arrangement and develop the concepts involved.

When carrying out seriation activities, using words like 'last', 'first' and 'before' helps children develop these concepts. Such activities will also help them to see that attributes are relative. A button which may be the largest in one set, may be the smallest in another. Thus, there are no absolute dimensions.

Now why don't you try and think of some seriation activities? activity each where children seriate on the basis of size, texture and weight. What concepts do they acquire as they do these tasks?

So far we have considered activities to strengthen children's abilities to classify and seriate. Let us now discuss activities to help them grasp the concept of one to-one correspondence.


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