Sunday, 25 November 2012

Getting it wrong!

I have a maths iPad app that Joseph plays from time to time. This week I found him playing on it and finding it a bit too easy, so he started to deliberately give the wrong answers. He enjoyed seeing what happened when he did this for a while, and then moved on to another activity where he guessed the right answer rather than counting to find out what it was; he was never more than 1 or 2 away so he was estimating rather than guessing really. For a split second I felt frustrated that he wasn't playing 'properly' and then I realised that he was doing something far more important; making the game his own, testing how it responded and finding alternative ways of discovering the correct answer. The minute it became more challenging he became more determined to work out the problem and give the correct answer.

I learned a few things from watching Joseph play the maths game. Firstly, he wasn't afraid to get it wrong and try out different things just to see what happened. This feels like a positive approach to learning - feeling happy to try different things out rather than feeling afraid to give an answer because it might be the wrong one. I suspect that if too much value is placed being 'right' and giving the 'correct' answer, a child may become afraid to get things wrong and stifle their ability to test their own theories. They may even stop having theories, and prefer to wait for someone to give them the 'right' answer. A few days ago Joseph was looking in an atlas at a map of the world. He is fascinated by the way the earth looks from above, and the distinctions between land, sea, ice and desert. he found the UK and then said "...and this is London" pointing to Spain! I said "Thats actually another country called Spain" and Joseph replied "Yes Mummy but I don't know countries like you do, so I'm going to pretend its London!" He then pinpointed various London landmarks all over Europe. He didn't need the 'right' answer, he was testing out knowledge he already has and applying it to his growing understanding of maps, distance and location. His activity was a valuable one, and at this point in his life the confidence to apply his knowledge in this way is no doubt far more important than knowing where Spain is on a map of the world!

As I've navigated the world as an adult it has become increasingly clear how few situations can be solved with 'right' versus 'wrong' thinking or ideas. Life is full of grey areas, ambiguity and subjectivity and as I watched Joseph play I reflected on how problem solving in 'real world' situations is so often based on testing theories, estimating and using a gut feeling, rather than referring to external 'facts'. Parenthood has been a brilliant example of this for me; I have yet to find a 'right' way, other than the way that is right for this family. I hope to nurture a learning environment where the boys can become well equipped for problem solving in everyday situations, and navigating the grey areas of life. Allowing them to learn in an environment where there are not too many 'right' or 'wrong' answers feels like a good way to do this, which is why Michael Gove's plans for an exam system based on rote learning seems so utterly misguided to me. So much that I took on board as 'fact' in school is actually simply a theory, and there are things I needed to get wrong in order to find out what was right. There doesn't have to be an answer for everything....wondering is wonderful, and children are brilliant at it!

Joseph and I were walking the other day and he noticed a rainbow in the road. I told him how oil and water had mixed to produce this and he thought for a while as he walked and then said, "No Mummy, I think a piece of rainbow broke off and fell down from the sky!" Thank goodness he doesn't take my word for everything and is prepared to apply his own theory!

Long may it last!


Tuesday, 6 November 2012

A little boy who loves numbers

I recently wrote about Joseph's growing knowledge of letters and sounds, although in actual fact his real interest seems to lay in numbers at the moment. I think this is because he is interested in the size and speed of everything and is constantly comparing objects, buildings, toys and just about anything else he can, in terms of which is the tallest, fastest and strongest! Because he realises that numbers are used to represent such things as speed and height he speaks about them quite a lot, and uses numbers to describe other things too, such as how strong a thing is, how much he loves a person or how friendly he feels towards them! Whenever I do something Joseph doesn't like he tells me "Mummy you are Zero my best friend now!"

Joseph is exploring numbers in a range of ways. He likes to write them in the condensation on windows and forms the shapes of numbers using his fingers. The other he day he asked me which '7' was best when he realised that the top of the 7 he was making with his fingers could point either way depending on how he did it. Making a number 5 using your fingers is quite a challenge, but Joseph has worked out a way he is happy with! He has created a game he will often play as we are driving along in the car; he asks me to guess what number he is making with his fingers and then when I guess the right one his hands pop out and he shows me. A number 6 and number 3 are photographed below!

I find this really interesting because it feels in a way like he is taking concepts from the outside world and literally making them a part of himself. Only a small percentage of the time Joseph spends thinking about numbers involves looking at them on a page or writing them down on paper, he is far more interested in using them actively; talking about them, playing with them in his head, using them for purposes that are useful to him, using them to help him understand other concepts that interest him such as time, height and speed and making them a part of his everyday world and language.

When we sit in the car Joseph is interested in speed limit signs and likes to read out the numbers. It's interesting that he isn't learning numbers in order; we were recently walking past a house and he told me "That house is number forty-four" and sure enough it was. Today he told me that Charlie has the number eighty-eight on his shirt, which he does. He's learning to recognise numbers in the way that makes most sense to him and once he gets over ten, recognising them seems easiest when they are paired up together...22, 33, 44 etc. Big numbers are what really interest him and he once had great fun writing a 4 on a piece of paper and asking me what it said, then adding more 4's one by one, asking what each number said until he had a whole row of 4's and we had reached the biggest number I knew how to say!! Sometimes if he sees a number such as 27 he'll call it 'twenty-seven-hundred', such is his interest in the really big numbers! Very often at bedtime he'll tell me he loves me 'eighty-thousand-seventy-eighty-eight-thousand'....or something similar!

In his head, Joseph is busily working out the order that these numbers fall into, and how 'big' they are relative to one another. During another recent walk Joseph asked whether seventy-six was bigger than fifty-four and then asked me to count to seventy-six while he listened to see where they are relative to one another. Yesterday he saw some Christmas lights and wanted to know how many 'sleeps' until Christmas. When I told him its about 50 he asked me to count to fifty and then complained "Oh! That's a lot isn't it!" Today I told him that Daddy's birthday is our next celebration and he asked how many sleeps, counted them under his breath and said "That's not too long is it!"

Adding, subtracting and dividing numbers happens very naturally all the time. Once again we were sat in the car recently having a dispute about how high the heating fans should be turned up. Joseph, who sits beside me in the front, likes to put them on number 4 because he is four years-old! I asked "and what if I asked you for it to be three less than that?" not because I was testing him, but because I wanted him to turn it down. He said without a thought, "It would be on one". While chatting about the fact that my God-Daughter would be coming to play a couple of weeks ago I reminded Joseph that he needed to be gentle with her because she is only 2 years-old. He said "She needs to have two more birthdays and then she'll be four!" Being one of three boys Joseph has lots of opportunity to divide...not that this always pleases him!

In response to the news that we are home-educating, several people have made comments like "How's your Maths?" or "I hope you're good at Algebra!" I didn't really struggle too much with the kind of maths we did in school, not that I remember the vast majority of it now! Instinctively I feel that if Joseph is left to play around with and explore numbers in the way he has been, using maths to solve real-world problems will become a natural extension of this. Whether or not he needs maths lessons to achieve this remains to be seen, for now I am absolutely confident that he is developing all the mathematical understanding he needs from going about his daily life, doing the things he enjoys.

Oliver recently told me that one of the biggest factors for him in deciding to home-educate our children was the fact he believed that if they wanted GCSE's (or whatever the equivalent is by the time our children reach that age) then they could learn all the relevant information in a short space of time and do not need 12 years of schooling in order to prepare them. He saw no need for them to spend all these years in school, when they could be outside of the system, doing things they enjoy and still gain qualifications if they want to. I have since found an article which backs up this belief in relation to maths. A group of teenagers in a school where no formal instruction was given decided they wanted to learn maths and learned the entire curriculum in 8 weeks!

Sounds unbelievable I know! Read here.

It's amazing what can be learned when a child is given time to develop the skills and space to develop the motivation. Our education system seems to work on the premise that a child will learn nothing unless they are made to. I think we underestimate just how much a motivated, inspired child can achieve!