I Do and I Understand - GB

[Music] [Music] hand down oh dismiss I am a teacher at a junior mixed School in Blackpool and this is my class consisting of 399 and 10 yearolds at the beginning of a math lesson the first thing I've trained the children to do is to get a card from this rack on the wall the assignment card is it sometimes called a simply presents of child with a problem a real problem not just a Thum wrapped around with Words which we've often taken to be a problem in the past by pouring the water into the measuring J shape and area you will need a stap board on another B now F each box with sand using a cubic inch a problem has reality and it has interest for the child it belongs to his world because it belongs to his world he'll be interested in finding the solution to find how many PE there are on this St how many do you think they are about 600 about 500 we have to measure the circumference of each ball what is the distance around the ball we can't use a ruler for that we have to use the stre I think this is a preferable method of teaching mathematics because it does demand that you the teacher get around the class and talk to these children and discuss with them their problems and you can help them without telling them the answer or without giving two much away you can I think gain the child's interest and help it very much more than you can simply by paper and pencil yes you could weigh the empty ble on the scale and then weigh it when it's full of water and then double it and take it away and then you've got the way to the quart of water that won't be right you see because not all the we the same but if you consider really what research can tell us about how children think how children learn we must accept that they learn at this level purely through concrete situations through things which they can do and handle and touch and not through a world of abstract symbolism and things devoid of Reality by 16 that makes 4 miles do you think we should check it with the AA book yes the whole basis of what we are trying to do here is that by what we now call the concrete approach if the the child actually does something handles something he is more likely to retain it because it is an actual experience than he is by using his memory alone or just by virtue of having been taught we say that teaching by telling is often harmful and that memory alone is useless when you actually do something it sort of sticks of course everybody knows that for a certain type of problem you want a right answer but the point is that you've got to be able to go on getting the right answer if you simply do it by rot by parrot learning you're unlikely to remember it in a fortnight's time but if you really grasp to the underlying principle you'll not only be able to do the same problem but also something a little bit different in a fortnite's time I think we must be aware always that memory although a useful tool is not the whole story it's best put perhaps in the terms of a Chinese proverb I hear and I forget I see and I remember I do and I understand and it it's this understanding that we're after and that we can best make it possible for children to gain real understanding of the problem by allowing them to do to be actively involved in [Music] something good yes youve balanced it and that's called balancing the equation well if we double the dimensions the cube get eight times bigger yes cubes get very big quickly should you make a graph to show it multiply the three dimensions of each box and write down your answer we've done that what do you notice well what do you notice don't have to F each box stand all you have to do is multiply the dimensions that's fine good uh please we found out that one of these blocks weighs 10 and 1/4 oz but we want to find out how many of the how many of them weighs uh one stone please say not all of these blocks weigh 10/ qu ounces this one weighs 9 and 3/4 o and this one weighs 10 oz now in this sort of problem we're not really bothered about a/ qu of an ounce one way or the other but we've got to settle for something now what are we going to settle for 10 yes and I think 10 oz is sufficient isn't it yes and I think if you use 10 oz you will be able to find that out very easily and it's much better than messing about with all these quarter o what are the parameters well it could stick a pin through if it if it wouldn't bur well it will so we'll have to use the Cals what other route do you know that will take you from black to bonness well what other route is there to you can cut from L and the A6 I'll and go on the [Music] n6 we got the globe card this time I wish we had the train card can't swap it no py black that now we to measure from London to Winnipeg and Blackpool to Oakland and then we'll measure from Blackpool to Oakland first the hold black [Music] have you got you're right on thatle so if I gave you a diameter you could find me the circumference would you what would you do Jane well you multiply by three and a little bit that would be all right would it yes it certainly would good all right now supposing I gave you a circumference in the past we tended to think haven't with it if a classroom was quiet then there was concentration and this isn't true at all concentration only comes through interest to real involvement in what you're doing if the children are presented with situations with problems which are a real interest to them they get so deeply involved in them that there's no unnecessary noise they're working something out they're talking to each other the same as adults talk over the problem this is what we want surely we don't want children sitting up straight in their desks completely on their own language plays an essential part in mathematics children must discuss with each other what they're doing for by this means they learn and in this way children's vocabulary grows and in turn helps their written expression their written description of the kind of things they've been doing they learn more in fact from each other and from the material and the problems presented than they could ever do sitting quietly listening to a teacher the important thing about this is that children are like us all they do like this little bit of personal and individual attention but they much prefer that the teacher should come and talk to the three of them than stand out in front of the class like a sergeant major with a piece of chalk in his hand and talk to the whole class because I don't think that they feel then that it is personal to them the more personal a teacher can get with his teaching the more it is appreciated by the child and the more response you will get from the child too if he thinks that you are talking to it personally but if they're involved in group activities then it is possible to get Rob to see them and talk to them encourage them and perhaps pose an additional question which will help their thinking onto the next stage now have a look at these three plasticine shapes right Derek which do you think is the biggest of the three the cylinder the cylinder all right now aleec which do you think is the heaviest of the three the CU now chrisy which is the biggest uh the cube the cube and which you think is the heaviest the cube the cube again all right well we'll see shall we Cube now what's that half what's that 2 and a half Chris what's that 2 and a half all right you surprised now something changes here edua when I move this new shape now watch it carefully now what changes the area the area right now ion something else is changing what is it that that what's that to then the height the height which height the slant height or the vertical height the vertical the vertical height that's right so if I want to find the area of this new shape which is a parallel what must I multiply [Applause] together the base by the vertical height the base by the vertical height this is the basic difference isn't it before we were concerned with getting the answer right at now the thinking teacher is concerned with how much of this did the child understand how far had he got in his thinking it's a completely different approach from the old approach of accuracy and getting the answer right and get getting it ticked after a while I'm sure old children find this method much preferable they enjoy their maths they look forward to it because after all it is something which they can enjoy they are doing something in some cases I'm quite certain the children think they are having quite a game but a very purposeful game and from our point of view we must see that this is [Music] so I suppose the reason that the whole of math teaching is in such a mess at present is that the syllabus hasn't changed in effect for 300 years in fact some RIT brand Winkle coming back after being asleep for a thousand years would be able to do most of the oleev syllabus in particular the primary school syllabus was last fundamentally looked at over a century ago when the main object was to train people to do sums on a high stool at a large desk to be Victorian Clarks and until about 5 years ago no one had ever thought of altering this dismal State of [Music] Affairs what we're looking for is an improvement in the whole approach and an attitude to the learning of mathematics this we cannot yet assess but we can say that there is interest that tremendous progress is being made that children are now doing things at 9 and 10 which were formly done at 13 and 14 I think we can widely General eyes and say that we have underestimated children's ability in a very wide way we we haven't realized how much they're capable of this we can be sure of anything else is prediction but we would confidently predict that by approaching mathematics in this way children will get a joy and a pleasure in it which the majority of children have never had [Music] before time pack up come on bring the operators in play time help come [Applause]