Bye bye chunking?(85 Posts)
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Wow if I hadn't read about this in the Times education supplement, I wouldn't have believed it but it seems that chunking is being abandoned - officially - link here: www.tes.co.uk/article.aspx?storycode=6316142
Although I will concede that understanding division is multiple subtractions was good - I also know that many children were told they couldn't divide by old fashioned methods (long division - I guess now called short division) - and my children were certainly told their work was wrong.
Was the problem here that a method was adopted which parents were excluded from and which did not allow tried and true old fashioned methods to occur alongside them as well?
I love a bit of chunking - taught it this week to my more able Year 3s. And for the record the 7 in 72 is 70 not 7 and there lies the problem with maths. Children need to understand the value of numbers and the concepts of calculation not follow procedures.
My pet hate is saying multiplying by 10 is 'sticking' a 0 on the end!! Arghhhhhh!!!
Lougle, I don't need to make up these examples, they are all around us. Once you open your eyes to them, you see them everywhere. For example, this morning on the Today programme they announced the discovery of a rodent creature millions of years old and they said that it weighed 'half a pound'. The point here is that the scientists who did the work would have done the calculations in metric and some joker at the BBC has converted this to an imperial unit. Why can't they leave it in metric so that our children can relate it to something they understand and have learnt at school, thus reinforcing their learning, instead of confusing them by using units they don't understand?
In fact, one of the worst offenders in this respect is the BBC. They mix and match units all the time. Children need to see a proper system of units being used in the correct manner if they are to learn about maths and science.
Now I don't claim to be an expert in anything. I don't actually believe in the concept of an 'expert' because no matter how good you are, there is always an awful lot more to learn. But I do have a certain amount of experience in this field. I have taught mathematics to thousands of children in several age groups over thirty years and I can assure you that many, many of them are completely confused by measurement because of this imperial/metric business. Not only that, adults are confused too. My accountant and his brother run their own business and as they are fully qualified chartered accountants, they are pretty intelligent guys. They both say, however, that they are confused my the measurement systems in this country! It's not just the kids that are having problems.
Again, Lougle, you are putting words into my mouth. I have never said that children should never learn the 12 and 14 times tables. What I say on this subject is that all children should learn the tables up to 10 x 10 and if they are able, it is good for them to learn the square numbers up to 20 x 20 because of Pythagoras' Theorem. If they really want to go on and learn their 12 and 14 times tables (or any other for that matter) that's fine by me. Well done them!
I sometimes I feel I am pushing a boulder uphill here and as my mother in law used to say, 'Someone convinced against their will is of the same opinion still'.
For that reason, I am going to stop commenting on this subject for a while now, but I can tell you (with the backing of experience behind me) that those parents who insist on using imperial units for all the situations we have discussed will have to do a lot of extra work with their children on the conversions and the understanding of what measurement using two systems is all about if they are not to fall behind others who use only metric. Not something in my experience that many parents are willing to do, I find. In fact, many parents are so confused by all this that they are not willing to even give this a try.
If you are and you do, I wish you the best of luck.
See you in another thread.
" But there is a point somewhere in between - usually between about 14 and 18 years old - when they won't give you the answer. When you ask them why not, those that will tell you say it is because they don't know what units to use"
I know I'm 5'8" or 1.72m or 172cm - I was taught. Furthermore, if people have trouble with having two scales on a tape measure, then they simply need to be taught to read it carefully.
How long do you spend thinking up these examples? It really isn't the terrible thing you imagine to have to learn the 12 times table and the 14 times table. Children can always choose to partition it up, so that they are in fact calculating (10 x a) + (2 x a), etc.
Haberdashery, you will never hear me say, 'Add a Nought' to multiply by ten! So please don't intimate that this is what I said.
According to that rule, 3.14 x 10 = 3.140 !
Haberdashery and Lougle, you are putting words into my mouth. I have never expressed the opinions you give. I think if you re-read what I have said you will find what I am saying is that metrication not only makes maths easier, it also makes it easier to understand. Imperial units make things over complicated, stop children seeing that we live in a metric world, greatly reduce the opportunities to practise maths in the home and result in many giving up and saying they can't do maths.
My own children were brought up in the seventies when the emphasis on imperial units in schools was much less than it is now (believe it or not) and they both ended up with excellent maths qualifications because we used to do lots of simple arithmetical exercises in the car and at home.
There is another problem with imperial units that I have not mentioned in this thread and it is that scales on weighing machines (analogue) etc are much more difficult to read because two scales are placed side by side. On measuring tapes it is even worse because you will see that inches are always placed at the top and centimetres underneath. This means that the units most people use for measurement are at the bottom of the tape when it is much easier to use if the scale you want is on the top. It also reduces the size of the figures on the scale. If you use a metric only tape measure, you will find it much easier to use, as over six billion people in the rest of the world do.
We seem to have a passion in this country for making access to maths much more difficult than in other countries and because we are British we are proud of it. It's quite ridiculous really.
Here's another example. When you ask young children how tall they are, if they have measured themselves at school they will give it to you in metres or metres and centimetres. If you ask adults, they will normally give it to you in feet and inches. But there is a point somewhere in between - usually between about 14 and 18 years old - when they won't give you the answer. When you ask them why not, those that will tell you say it is because they don't know what units to use. What good is that? If you go to other countries and ask people of all ages how tall they are, they always give it in metres, 'I'm 1.79 m', for example. (US excepted, of course).
Another example: Have you noticed how television and monitor screens are always given in inches when every part of the screen and all the electronics etc have been designed and manufactured in metric units?
I think if you want an easy method to use which doesn't require you to understand what you're doing then metric units are massively easier. Put a zero on the end to multiply by ten or whatever. Like lougle said earlier in the thread "there seems to have been a definite shift away from 'what works' to 'why it works'". Personally, I think this is entirely positive. I would far rather see children being given the tools to understand arithmetical operations than given a method which works every time but which they don't necessarily understand. If you don't mind whether people understand it or not, then you might as well use a calculator for everything!
I think this is where we conflict. You think that metrication makes maths easier or somehow more straight forward. I think that if you have a sound grasp of a method and what you are doing when you use it, the numbers you use are irrelevant. That means that metrication isn't necessary.
And I thought if you had a gas oven you had no choice but to use a gas mark?
So why do people use Fahrenheit?
I thought it was only Americans?
It doesn't sound at all complex to me! It sounds like common sense, given a basic understanding of decimals and fractions.
I'm sure someone who was able to do that would also be able to handle the traditional layout and method but I don't think anyone who was at a point where the above was confusing or complex would really benefit from it that much. I'd far rather see them using whatever strategies they had available to try and understand what they are actually doing than blindly applying a method (which I think is what often used to happen when the traditional methods were the only ones taught).
I would suggest then, that if you can handle the complexities of what you have described, you should be able to divide in the traditional long/short division layout. What do you think?
>> supposing when dividing by 8 the remainder was 7?
This one would obviously be very easy because you'd be able to take 1/8 away from 8/8 in order to get 7/8.
As for the others, I can't see what would be wrong with doing 7 or 13 into 100 or 1000 or any multiple of those and then moving the decimal place if you only want a few decimal places. If you are getting into non-terminating decimals and want a lot of decimal places, I'd imagine that you would have sufficient understanding of what you are doing to either use a calculator or another method apart from chunking.
Haberdashery, okay, perhaps I chose an easy example. What about dividing by 7 or 13 etc? Or supposing when dividing by 8 the remainder was 7?
If you understand decimals and fractions, surely you will know that 1/8 is 0.125? And if you don't, you are likely to know that a half is 0.5 or a quarter is 0.25 and can just halve them until you get it right? As long as you understand what you are doing, there won't be a problem.
Coming back to chunking as per the original posting, I have the question, 'What comes after chunking?' and no-one I have read has answered that yet. The point here is what do you do about decimals. Suppose, for example you want to do the sum 785/8, giving the answer to 3 decimal places. You will get to the point where you have the answer 98 remainder 1. What do you do then?
PastSellByDate, I don't think we are disagreeing about very much at all. I am not against studying old number systems. On the contrary, I very much welcome it as it helps children appreciate how powerful our place value system is. Try multiplying MMDCCXLII by CXXIV without converting to our number system first, which is what the Romans had to do.
In a historical context, of course we can take a look at imperial units as we can most other things, but that is not what is happening at present. We are in a crazy situation as I have described earlier in that we actually live in a metric world, but mostly the children see imperial units and they are expected to convert between one and the other. I am aware of Mr Goves new emphasis on conversion and even more familiarisation with imperial units and that is what I find so horrifying. Andrew Percy and his ilk just don't get it, to use a modern political phrase. What a coincidence that he also mentioned the car as an example, but did he tell us about the 10000 metric measurements that go into making a car? Not likely! All he said is that children see miles and miles/hour, which is exactly my point ...Why?
He also mentions pints for beer, but does he mention that the glasses that hold the beer and designed and manufactured in metric units, and the barrels that hold the beer, and the equipment that pumps the beer, and the equipment used to produce the beer in the first place and so and so on? Not likely!
And as to road signs, well the changeover to metric is long, long overdue and even the Government knows this. I have written to them several times to ask why this has not been done and every time they give a different answer ranging from the cost to the fact that they are waiting for at least 50% of drivers to have learnt metric units at school. We passed that stage years ago.
As to the cost, the Government estimates £800 million to change the signs; the UK Metric Association estimates slightly less based on the Irish experience, but even if we are generous and allow for £1 billion, that only works out at less than £3 per person per year if we spread the cost over five years. In Government terms that's absolutely peanuts and this is a once only cost - it will not have to be repeated year on year like most Government expenditure. By comparison, the O2 (formerly the Millennium Dome) cost £800 million and the tunnel they were thinking of building around Stone Henge a few years ago (now abandoned) was to cost £500 million.
In my opinion, people like Andrew Percy are doing untold damage to our children's maths education and because of his status as an MP, people listen to him.
Coming to your point about time, the first agreed definition of a metre was based on the distance from the North Pole to the Equator. The only reason for linking it to time via the caesium atom oscillations was to fix it more accurately and that is what modern scientists need to do to calibrate their instruments accurately, of course. I don't think I have ever said that time is based on 10. What I said is that the only metric unit for time measurement is the second (subdivided when necessary into milliseconds etc). We certainly use 12, 24 and 60 in everyday time, but that's a matter of convenience and not something that damages our children's maths.
Some people seem to think that because I advocate complete metrication in all aspects of everyday measurement, I think children should only be multiplying and dividing by 10. That's just nonsense, of course. What I am saying is that multiplying and dividing by powers of ten using metric units helps children to understand left and right shifting so that they can then go on to multiply by many other numbers. For example, a book weighs 456 grams, how much would 300 similar books weigh? Here we multiply by 100 by left shifting two places giving 45600 grams and then we multiply by 3, giving 136800 grams. If we wish to have this in kilograms, all we have to do is right shift three places to divide by 1000, giving 136.8 Kg. If we want this in tonnes, we divide by 1000 again (right shift of 3 places), giving 0.1368 t.
Finally, let me put it this way. Supposing we had been using metric units for hundreds of years and someone came along and said, 'Hey guys, I've just invented a new measuring system. We start with a unit of one inch which I randomly chose as the average width of some guys' thumbs and if we put twelve of these together we get a foot, which doesn't bear much resemblance to a real foot, but don't worry about that. Next, we fit three of these feet together and call that a yard. Are you with me so far? Next we put 22 yards together and that makes a chain, and ten of these make a furlong. Finally eight furlongs make a mile, and just to make it interesting we will put tenths of a mile on our car odometers that don't bear any resemblance to those furlongs I was just telling you about. Area, of course, will be the acre (lovely name, don't you think) and that will be the area of a rectangle one furlong long and one chain wide, giving 4840 square yards in an acre.
Now let me tell you about weight. There will be something called the ounce...'
Do you think it would catch on?
Can I just say that I wasn't asking for imperial to be taught for maths - I was saying that it should move across to 'history' perhaps as part of a Victorian history unit. I find it a huge mistake that children aren't exposed to history of mathematics as part of the primary curriculum introductions to Egyptians, Romans and Greeks.
The Egyptian numbering system, which heavily relies on counting by fives, turned out to be a breakthrough for DD1, who is particularly visual in her learning. She was suddenly able to subtract because she could cross out upside down U symbols or hand symbols - and she got that before she could master doing the same with digits.
Roman numerals. Greek Golden Mean or Pi (sorry can't make symbol) are all fun. Archimedes displacing mass with water to work out density (linke to TED Ed video here: ed.ted.com/videos?q=how+taking+a+bath+lead+to+Archimedes%E2%80%99+Principle - are great examples of logic and problem solving (ye olde lateral thinking) and a lot of fun.
Again Alan, I think you need to update yourself on the latest Gove plans - because he is signalling that knowledge of the imperial system will be a requirement in the primary curriculum www.telegraph.co.uk/education/educationopinion/9790670/Modern-schools-must-teach-imperial-measurements.html.
And just to be persnickety Alan - time is not base 10 but based on multiples of 12 (24 hrs in a day/ 60 seconds in a minute). And time fundamentally underlies the history of the metre (brief history video here: www.youtube.com/watch?v=dvVCNhWJvvo).
Can I also add that I work in gas marks because even the brand new cooker delivered to us this week is labelled in gas marks. You tend to work with what you're given. It would be lovely to have celsius on the knob as well - but I suppose space was the issue - and yes I basically know gas mark 4 = 250C because I use it so much - but have to look up the rest.
I got a C in gcse maths, a scrape at my grammar school.
I'm 37. At work I use percentages, which I can do in my head. Division which I can't. I looked at the you tube video linked above, if I had been taught that at school instead of long division I reckon I would have been a far more confident mathematician.
I was rubbish at maths at school. It just wasn't relevant to my life and I was poorly taught. I taught myself number bonds in my twenties. Learnt my tables too. My maths improved. There was only ever one technique taught in my day.
Alan I agree wholeheartedly with everything you have said.
Alan, multiplying both numbers by 10 is what we would teach in order to do division by decimals using short division, however, I don't think that had been explicitly taught by the time the pupils did the test. However, that is another method that they need to remember, whereas if they understand what division is, they should be able to figure out the method I outlined intuitively without needing to be told what to do in that particular situation. The problem a lot of maths students have is seeing a question like the one I gave and thinking 'I've forgotten how to do that method' and so not attempting it, or applying the method incorrectly and not spotting a nonsensical answer, rather than figuring out the answer for themselves based on what they know about numbers and the operations.
It's why employers bemoan that young people can't work out percentages etc when that same young person passed a GCSE where percentages were correctly worked out. They learn the abstract method for the test, then immediately forget it.
Noblegiraffe, my take on this question is to multiply both numbers by ten so the sum becomes 260/8 which is easier. Now this takes time to teach and for the children to understand why it works. All the more reason then to stop doing all these silly metric/imperial conversions and release time to explore this sort of idea. This is exactly the sort of thing I am talking about.
Have to rush now, just remembered I have to collect wife - she's great, but woe betide me if I'm late!
To the supporters of imperial units, please let me put it this way. If you are arguing to keep both sets of units and do the conversions, you are obviously keen for your children to do well, in mathematics as well as other subjects, so let's take that as our starting point.
Every time you use a gas mark instead of Celsius temperature, you are closing the door on the opportunity for children to see how the temperature of cooking a cake compares with the temperature outside or the temperature of boiling water, for instance.
Every time you use feet and inches instead of metres, you are closing the door on the opportunity for children to see how much taller (or perhaps shorter) you are than they and to see how many times taller you are. For instance dad is 1.82 m, child is 1.43 m. Dad is 0.39 m or 39 cm taller. Dad is 1.82/1.43 = 1.27 times as tall as child. Try doing that when the parent is five foot seven and the child is 1.43 m. Yes, I know you can do it using those conversions you keep talking about, but people don't!
Every time you use pints instead of litres and millimetres, you are closing the door on the opportunity for children to learn about left shift and right shift of numbers when multiplying by 10, 100 etc. So 2.6 litres = 2.6 x 1000 = 2600 ml. Try doing that with pints, quarts, gallons etc. This is an extremely important idea in the understanding of maths today.
Every time you use acres instead of hectares, you are closing the door on the opportunity for children to understand that a hectare is 100m x 100m = 10000 square metres, so 4.6 hectares is 46 000 square metres. You just can't do that when an acre is the area of a rectangle a furlong long and a chain wide!
There are so many opportunities to help your children practise maths with metric that are not there with imperial. When I was at school we had to add, subtract and multiply (and the bright ones even had to divide) hundredweights, quarters, stones, pounds and ounces. At least it had some relevance in those days. But what a waste of time nowadays.
Re chunking versus short division: rote learning of algorithms is all very well when it comes to answering the sorts of questions that come up in maths tests, but when it comes to mental maths and real life where you don't always need an exact answer, an understanding of what division actually means is also important.
I'm thinking of an exam paper my pupils sit in either Y7 or 8, I can't remember. It has a question on it that most pupils get wrong or don't even attempt. It's something like 'a lorry can carry 26 tonnes maximum. A log weighs 0.8 tonnes, how many logs can the lorry carry?'
Those that go for short division and attempt 26/0.8 usually come unstuck. Those that do repeated addition waste lots of time. The successful ones say '10 logs weigh 8 tonnes, so 30 weigh 24 tonnes, then you can fit on another couple' tend to get it right, but there aren't many of them.
Elibean, thanks for your support. Does this mean they don't even use 'livre' to mean 500g any more?
I totally agree with AlanYoung re metric v imperial.
I may feel nostalgic for shillings (and slide rules ) but please, schools, do not inflict this confusion on the next generation!
And my mother is French. She only uses 'livre' when in the UK, referring to an Imperial pound. In France, she only uses kilos.
With regard to the temperatures (I thought you said 'gas masks' at first - must get my glasses changed!), have you noticed how the temperatures are mostly given in Celcius (sometimes with accompanying Fahrenheit) during normal times, but when it gets hot newspapers (typically the Mail and Exress) give it in Fahrenheit. Suddenly it is 95 degrees, just at the time when children are learning that water boils at 100 degrees. If it gets much warmer, surely we will all evaporate! How children are ever supposed to succeed in maths and science in this country is a mystery to me.