The usefulness of multiplication tables lies not in their practical application – though they can help one to avoid being bamboozled by supermarket offers – but in the beauty and symmetry revealed once they have been learned (I can’t do my times tables, and I don’t care, 17 February). Each table has its own character, but 9-times, which gave Peter Bradshaw so much difficulty, is especially lovely, the first digit ascending stepwise as the second descends, so that pairs of digits in the upper half are mirror images of those in the lower. Then there is the delight in finding that the sum of the digits in each product is 9 (except for 11 times 9, where 9 is reached by summing a second time). I am sorry that a generation of children were denied this joy, but delighted that it is to be restored to their successors. Facts are not understanding, but human intelligence is adept at teasing out the patterns that turn mere knowledge into appreciation, leading on to synthesis and the creation of new ideas.
J Robin Hughes
Sheffield
• Peter Bradshaw gives a tedious method of finding 7x9. He could have noted that the numbers 7 and 9 are immediately adjacent to 8. The answer is therefore 8 squared (64) minus 1 squared (1) giving 63. This is a simple example of a wider method known to the Babylonians over 4,000 years ago and can be very easily demonstrated with simple materials in a primary school. In our enlightened times, however, we obviously prefer the “character forming” slog of rote memorisation without any exploration of the fascinating and valuable mathematics inherent in these tables.
John Porter
Oxford
• Having been at elementary school in the 1940s I’m OK with my times tables, but still can’t recite the names of the rivers of Yorkshire in clockwise order, my dad’s acid test for anyone claiming to be educated.
Peter Wrigley.
Birstall, Yorkshire
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