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sums will set you freehow to teach your child numbers arithmetic mathematics‘equality’ or ‘same as’ - balance |
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The idea of ‘equality’ is not simple and is very widely misunderstood. There ain’t no such thing as equality. No two things in the real world are the ‘same’, or ‘equal’. The idea is irrational and unsound. When we talk of equality, we should really talk of not caring about the real differences, or we can talk about balancing two different items. The two people on the seesaw, or the coins in the Mint scales below, will be in balance. They are not the same or equal. Jack on one side of the seesaw is not Jill at the other end of the seesaw. The coins in the two trays are different coins. If you wish dig in further, start with the error called ‘equality’.
1+1 (one plus one) does not = (equal) 2 (two). Each of the characters above were typed in at different times, with different keystrokes and appear on your screen in different places. Paying attention, you will note that 1+1 doesn’t even look like 2. It is vital for anyone who wishes to understand the real world, or arithmetic, or mathematics, or even to be able to think clearly, not to become confused by the convenience of balances. No two ‘things’ can ever be the ‘same’. The idea of equality is extraordinarily useful, but can very easily become a mind trap and a confusion to rationality and clarity of thought. Do not let the young learner fall into this stultifying/stupifying mind trap. For example, regularly draw their attention to facts such as one pigeon is not another pigeon, one plate is not the ‘same as’ another plate, the eaten carrot is not the carrot on the plate, that this block is not that block - it is made out of different wood, from a different part of the tree, at a different time, with different movements of hands or machinery. All equals means is that “at this moment, in this situation, I don’t care about the real differences. I don’t care which pigeon I eat, or which carrot is on the plate. Someone else may worry or agonise over the difference, but right this moment I just don’t care”. Not even this ‘one’ is the ‘same’ or ‘equal’ to this ‘one’, nor this ‘1’ is ‘equal’ to this ‘1’. When you write the numbers on paper, the ‘ones’ are made with different movements, using different graphite from the pencil, at different times, on different parts of the paper. You may think this is just being pedantic, or picky, but it is not. Learning to make such distinctions is imperative for following and understanding arithmetic, and the real world, particularly in building healthy social relationships.
It is surprisingly difficult to obtain good photos of seesaws and balances. It looks like the jobsworths are trying to turn the whole population into a bunch of wooses and to remove all fun! Next, seesaws will probably be provided with cabins lined with cottonwool and seat belts, but you must wear a crash helmet. Even the Spanish seesaw (see image above) has a fun eliminator beneath each end to stop the poor little darlings going into orbit, or learning to use their legs as shock absorbers. Meanwhile, all scales (balances) are being eliminated in favour of digital contraptions where you cannot see the workings. Perhaps you can find a real seesaw in a museum somewhere to show the precious little darlings what it was like in the bad old days. We found the balance above in a museum!
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| sums will set you free includes the series of documents about economics and money at abelard.org. | |||
| moneybookers information | e-gold information | fiat money and inflation | |
| calculating moving averages | the arithmetic of fractional banking | ||
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number arithmetic mathematics - ‘equality’ or
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© abelard, 2009, 31 july the web address for this page is https://www.abelard.org/sums/teaching_number_arithmetic_equality.php |
