Maths
The pupils were not doing mathematics at all: they were doing arithmetic. Even in the first year we were doing plane geometry, and elementary algebra. By Olevel we were also familiar with basic trigonometry, log and exponential functions, and some conics. We had not started calculus, but we were a long, long way beyond long division.
The long division test was a stunt, as silly as asking a first year university physicist to use a sliderule. What's a sliderule? An obsolete instrument for mechanising calculation, the key word being obsolete.
johno
The long division test was a stunt, as silly as asking a first year university physicist to use a sliderule. What's a sliderule? An obsolete instrument for mechanising calculation, the key word being obsolete.
johno
sums
Yes I suppose it was a bit of a stunt but I don't agree with your comparison. Long division isn't superceded by calculators as understanding the basics of arithmetic IS mathematics. Mathematicians need to understand logarithmic scales and the rules by which 'addition' of log distances can be used to multiply numbers. Slide rules were a tool for scientists and engineers which used tyhis maths to achieve ease of calculation. Using long division and multiplication techniques in DT or science today would I agree be silly, but arithmetic in a mathematics lesson is mathematics. I also note that long multiplication didn't feature. Was that because they could do this, despite it being equally useless by the same argument.
Doc W

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you souldt be arguing about maths and accient tools cos theres a magic thing called technology, you can add subtract and do all sort of magic things, you dont need to use your mind that much anymore just bust out your fone with a calculator on it! also music and a video camera and just a normal camera, all in a phone!
I love Emily
Re: sums
I'm sorry Mr Jefford. My post was meant for those with an attention span Below is a quick quote to help you see that I agree with you(ish) concentrate now!
I'm not suggesting that you NEED to use your mind just that it's sometimes a good thing to do anyway.
Doc W wrote: Using long division and multiplication techniques in DT or science today would I agree be silly.
I'm not suggesting that you NEED to use your mind just that it's sometimes a good thing to do anyway.
Doc W

 Posts: 33
 Joined: Mon Apr 24, 2006 9:47 am
 Location: Pitstone
utility vs education
I suppose what I'm trying to get across here is the dual nature of our mission in education. Part of the reason for school is to train you to do useful things  like use a calculator. Another thing we are trying to do is to get you to appreciate humankinds intellectual achievements and understand them better. The method by which we do long division is the result of a lot of intellectual endeavour and, some people think, a beautiful thing in it's own right. If you disagree with this it's just because mathematics isn't your thing.Noone is suggesting that you use it to calculate stuff in the real world.
A good analogy is your study of classics. As I remember you quite enjoyed this lesson. It's interesting partly because it helps us understand where english words come from but mostly it was just intellectual fun. Like using log tables (and long division) it's a bit relevent but its worth shouldn't be judged only on this basis.
Of course I'd make the same argument for Physics  useful and beautiful, like Physics teachers!
A good analogy is your study of classics. As I remember you quite enjoyed this lesson. It's interesting partly because it helps us understand where english words come from but mostly it was just intellectual fun. Like using log tables (and long division) it's a bit relevent but its worth shouldn't be judged only on this basis.
Of course I'd make the same argument for Physics  useful and beautiful, like Physics teachers!
Last edited by Doc W on Mon Apr 24, 2006 7:49 pm, edited 1 time in total.
Doc W
A problem with the way that things like long division is taught is that you never learn to see the wonderful clarity of modern notation. It is worth learning Roman numerals and trying to multiply even small numbers using them (at least as useful as playing sudoku) to realise the value of the modern system.
There was a time before the symbols for addition, subtraction, multiplication, and division, had been invented. Just expressing a simple calculation was a tedious task in those days. When Arabic numbers were first introduced some superstitious people thought that they were literally magical because they allowed you to calculate in ways that were impossible before, when most people had to make do with fivebar gate symbols for counting.
What depresses me about the reliance on pocket calculators is the scope they provide for new kinds of errors, different from the ones that used to be made by people calculating by hand. In my experience, the commonest error perpetrated even by honours undergraduates is to provide an answer with 12 significant figures, and the decimal place out by an order of magnitude or two. At least if you have had practise doing calculations by hand you learn to think about a sensible number of significant figures, and to do a rough calculation to be sure your answer is in the right order of magnitude.
The great consolation is that even though now it is easier to get into a university (of sorts) than it was to get into a grammar school in the '50s, the people destined for success are the ones who retain, against the odds, the humility to learn from their teachers.
johno
There was a time before the symbols for addition, subtraction, multiplication, and division, had been invented. Just expressing a simple calculation was a tedious task in those days. When Arabic numbers were first introduced some superstitious people thought that they were literally magical because they allowed you to calculate in ways that were impossible before, when most people had to make do with fivebar gate symbols for counting.
What depresses me about the reliance on pocket calculators is the scope they provide for new kinds of errors, different from the ones that used to be made by people calculating by hand. In my experience, the commonest error perpetrated even by honours undergraduates is to provide an answer with 12 significant figures, and the decimal place out by an order of magnitude or two. At least if you have had practise doing calculations by hand you learn to think about a sensible number of significant figures, and to do a rough calculation to be sure your answer is in the right order of magnitude.
The great consolation is that even though now it is easier to get into a university (of sorts) than it was to get into a grammar school in the '50s, the people destined for success are the ones who retain, against the odds, the humility to learn from their teachers.
johno
order of magnitude
The point about order of magnitude and SFs is well made. Calculators are fab devices but not (as Seb suggests) magic. Garbage in  garbage out. You need an appreciation of arithmetic to discern what's garbage and what isn't.
Doc W
On a nostalgic point it has always stuck in my mind since childhood at the speed people were able to do mental arithmetic.
In my father's shop they used to write each transaction on a till roll. At the end of the day he would of course have to add that long list up to get the day's takings. (IN £:s:d )
I still maintain today that he could do that a lot quicker than you could do it by entering the list into a calculator excluding maybe a really skilled comptometer.
Back to the discussion though. I am sure the pupils of today are more adept in mental arithmetic than they realise.
I am sure they could quickly work out how many weeks pocket money they need to buy that pair of trainers for example or can they afford to buy their friends a can of coke.
In my father's shop they used to write each transaction on a till roll. At the end of the day he would of course have to add that long list up to get the day's takings. (IN £:s:d )
I still maintain today that he could do that a lot quicker than you could do it by entering the list into a calculator excluding maybe a really skilled comptometer.
Back to the discussion though. I am sure the pupils of today are more adept in mental arithmetic than they realise.
I am sure they could quickly work out how many weeks pocket money they need to buy that pair of trainers for example or can they afford to buy their friends a can of coke.

 Posts: 33
 Joined: Mon Apr 24, 2006 9:47 am
 Location: Pitstone
sums
I don't think you are saying don't do maths at all. long division by hand is a cumbersome process. We only seem to differ in that I think that being able to do it is worthwhile even if there are easier ways and you don't seem to agree.
Doc W
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