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Place ten pebbles (or any other such objects) in front of a child who can recite number names upto ten in the correct sequence. Ask him/her to count them aloud while touching the pebbles with his/her finger. You may need to show the child what you mean. But once he/she begins counting, do not interrupt. Watch carefully as the child counts, and record your observations according to the following questions.
a) Did the child count one or more pebbles more than once?
b) Did the child leave out why pebble?
c) Did the child say a number name with but touching a pebble?
d) Did the child go on saying number names even, after he/she had touched all the pebbles?
the basis of your observations, what conclusions can you draw about the child's ability to count ?
If the answers to all the questions in E1 are 'No', then it is most likely that the child can count upto ten. If the answer to any question is 'yes', then it means that the child does not know how to count. What the exercise above brings out is that the ability to recite number names only shows that the child has a good memory. On the other hand, being able to count shows that the child is moving towards building a concept of number.
∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + c Detailed derivation of ∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx = ∫(cosec 2 x
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