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CONSTRUCTING TABLES VERSUS ROTE LEARNING : Ask any adult how she would help a child to acquire simple multiplication facts. There is a very strong possibility that she would say, "By getting her to learn the tabled." And what method would she use for this? Getting the child to recite it again and again, that is, lots of drill.
But is it necessary for children to recite and learn tables by rote? Teachers say that this is needed for quick multiplication and immediate recall of multiplication facts. However, constant recitation alone does not usually translate into quick recall of multiplication facts, as the user needs to start from the beginning of the table each time.
Rather than emphasising drill, we need to make an effort to help children construct tables so that they understand how the tables work. This is what Maya, a teacher in an experimental school, believes and practises. In the following example we have given her method in detail.
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If the distances from origin of the centres of 3 circles x 2 +y 2 +2alphaix= a 2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
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