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PostPosted: Tue Aug 02, 2011 8:30 pm 
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When I was at secondary school in the late 70s someone pinned an newspaper article on the school notice board. Basically, some study showed that a significant proportion of 16 year olds were leaving school with a weak grasp of English and Maths. In the intervening decades various other studies have come to the same conclusion.

Why am I mentioning this now? Well, today the media have been making a big deal about a study that showed that 1 in 4 of London's children was leaving primary school with a weak grasp of English and Maths. Cue various 'experts' going on about how a significant proportion of 16 year olds were leaving school with a weak grasp of English and Maths. One radio broadcaster was going on about how one of his teachers made him rewrite his homework if there was only one spelling mistake. This, he said, motivated him to try harder. But the kids of today ......... :roll:

My point is this. If standards were declining back in the 70s and every few years since studies have regularly made the same assertion then does that mean today's 16 year old is educationally substandard compared to me as a 16 year old back in the 70s?

And doesn't this contradict the studies that show that today's teenager, thanks to the Internet, foriegn travel, heathier diets, improved teaching standards, TV etc is more worldly and knowlegeable than previous generations?

You ask a 40 something white middleclass professional about his schooling then off course he/she will talk about strict teachers, lots of homework, respect for teachers etc. That is why, today, he is a middleclass professional. If you look at the life history of some 40 something unskilled worker you will probably find that 30 years ago he left school with a weak grasp of English and Maths.

If anything, these 40 something 'experts' are living proof that they aren't cleverer than the current young generation.


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PostPosted: Tue Aug 02, 2011 9:19 pm 
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Every generation laments the standards of those that come after it. They also lament the poor standards of today's music, that the winters have less snow and the summers aren't as balmy, that films aren't what they were and so on. It's just that you are nostalgic for your own youth, and won't accept that things haven't been in decline since your happy days.


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PostPosted: Wed Aug 03, 2011 12:56 am 
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I think teenagers and children today would stand more of a chance of grasping maths - sorry, numeracy, if they didn't need a whole sheet of paper to work out one multiplication or division sum - chunking, number lines etc - what was wrong with good old fashioned long multiplication or division, as long as you knew your times tables the rest was easy. I'm afraid I'm a rebel and I am teaching my children the 'right' way to do it, they might lose points for the working out but at least they will get the answer right.

As for teenagers grasp on English - sorry, literacy, u no u don't knead to spell coz u got spell checker, write? :wink:


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PostPosted: Wed Aug 03, 2011 9:11 am 
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Kiwimum wrote:
I think teenagers and children today would stand more of a chance of grasping maths - sorry, numeracy, if they didn't need a whole sheet of paper to work out one multiplication or division sum - chunking, number lines etc - what was wrong with good old fashioned long multiplication or division


You don't need a blind knowledge of how to multiply on paper: you either need to do it in your head (perhaps as an estimate to cross-check a calculator) or you do it on a calculator. Very few people indeed could explain how long multiplication (and, particularly, long division) actually works: it was a rote process learnt because learning it by rote was the least worst option. Now there's no point in teaching a rote method to do multiplication, because it's just as much a black box with no checking for errors as using a calculator. So you either teach a method that actually shows what's happening (the distinction between maths and numeracy), or if you're going to use a black box, you may as well use a less error prone calculator rather than an error-prone rote method.

Long multiplication of reals using involves some rule of thumb about counting the numbers to the right of the decimal point, adding the results together and then putting the decimal point in the answer there. Explain how that works. Now, explain how to locate the decimal point in long division, and why that works.

We had someone on this very forum a few months ago puzzled as to why division by 0.1 made the answer bigger. Chunking explains that. Long division doesn't, and is astoundingly error prone, which is why, outside of school exercises, no-one ever did it, even prior to calculators: they used slide rules, including ones the size of a door with a magnifying lens on the scale, ready reckoners, Brunsviga mechanical calculators and log tables.

Ah, log tables. A lot of people in their late forties and older will have been taught logarithms as a means to multiply and divide large numbers. You know: look up the two numbers in the book, add or subtract the results (remember the mean differences!) and then look up the result on another page to get the rough answer. If you were flash you'd have a table of logarithmic sines and so on in order to cut out the middle-man while doing trigonometry.

Now then: explain how it works. Extra credit for the business about putting the minus sign on top of the integer part, not to the left.

_That's_ why logarithms have moved from pre-O Level to A Level: instead of being a black-box tool to perform a task that there's no other way of doing, they arise (as natural logs, rather than base ten, too) as part of calculus and not before. You're going to need a calculator anyway (as you can't buy log tables any more) so using logs as a means to do arithmetic as a black box is entirely pointless.

Long multiplication and division were rubbish as means to actually do work. That's why so many alternative methods were used to avoid using them. If they were so easy, why did people use slide rules? Why were ready reckoners on the counter in every shop? Why did Brunsviga (http://www.columbia.edu/cu/computinghis ... sviga.html) make so much money? Why was the Busicom 141-PF (http://www.vintagecalculators.com/html/ ... 41-pf.html) something companies would mortgage their souls to buy?


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PostPosted: Wed Aug 03, 2011 10:19 am 
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I like chunking, more children understand the actual processes behind the algorithm and it makes it easier to do mental maths.
The numeracy strategy is all about understanding and use of maths, not just how to do sums. For once a 'strategy' I actually approved of ( with both my teacher and scientist heads on)


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PostPosted: Wed Aug 03, 2011 11:19 am 
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Well call me old-fashioned but I'm still sticking with the skills I was taught as a child and have stood me in good stead thus far - and I get the idea behind multipling or dividing 2 numbers despite the fact I never learnt chunking, perhaps because I just need to use these skills in day-to-day situations (I don't always have a calculator to hand!) and not because I want to explain mathematical theory.

As for logarithms, I learnt these in school and have yet to find a use for them in my life, I don't think this is what is being referred to as a weak grasp of maths if 16 year-olds are unable to get their head around these. Perhaps it is referring to the shop assistant who can't add two things together without a till or the apprectice bricklayer who can't work out the area of a square.


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PostPosted: Wed Aug 03, 2011 11:43 am 
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" I just need to use these skills in day-to-day situations (I don't always have a calculator to hand!) and not because I want to explain mathematical theory."

But given the topic of this forum, a substantial proportion of the our children will want to do A Level Maths. And for that, they will need to understand what these things mean. And they'll understand what logarithms are, and why they're useful: even though you don't know it, you're using the discrete logarithm problem every time you log on to a website.

But even if you put aside the crazy, radical idea that teaching children how things work is better than teaching them blind rote methods, the currently en vogue methods are excellent anyway. The grid method of multiplication, for example, is just a different way of laying out a standard long multiplication, and is less error prone. Chunking is a fantastically better method for doing division than traditional long division, and if you race a chunking user to work out 96709 divided by 97 you'll find out why. It's also really only a different way of writing down long division, except it doesn't try to get the result one digit at a time, instead giving you several chunks to add together: if you think about how long division works (I know, crazy) and how chunking works you'll see they're almost the same, except the latter is both faster and less error prone.

You were probably also taught to drive slowing down on the gears. You'll fail your driving test for that now. That's because we understand vehicle dynamics a bit better, and the technology has changed, so we both know why it's not as safe and why it's harder on the car.


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PostPosted: Wed Aug 03, 2011 12:01 pm 
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tokyonambu wrote:
" But given the topic of this forum, a substantial proportion of the our children will want to do A Level Maths. And for that, they will need to understand what these things mean.

I'm not sure the question posted at the top of this thread refers to our children on this forum but rather to the 1 in 4 children in London leaving primary school with a weak grasp of maths and english as quoted by the OP.
My children are much brighter than I ever was... and I seem to be getting dimmer by the minute!!


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PostPosted: Wed Aug 03, 2011 12:25 pm 
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I suppose to answer the question we need to know what the lowest 25% of the population could and couldn't do in the 1970s, and the same now.

However I do know that carrots tasted much better when I was a child.


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PostPosted: Wed Aug 03, 2011 12:30 pm 
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mmmmm, and apples!

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