I found this as I was tidying up my posts and deleting some that never got finished.I wrote it a couple of months ago but thought it was still worth posting.
As unschoolers we don't do school at home,in fact school in any way at all ;-)
We don't break things down into individual lessons,we don't assess how much Emily knows about any subject, we just live our lives and accept that learning does happen,it is less quantifiable,and is not recorded but it goes on every moment of every day.
A couple of things have happened over the last week or so that I thought would be worth recording here.
When Emily left school she hated anything to do with maths.Her teacher in year one did say she had an aptitude for maths but by year 3 when we took her out any spark of enjoyment around numbers had been well and truly extinguished.
We took the view that math is all around us in every day activities.Over the first few months she was at home we just went about daily life.Cooking, where she measured and weighed if she wanted to. We talked about things being quartered or halved etc just normal conversation about whatever we were doing.She would ask how long until Dad was home or how long to go until her favourite programme came on and she would ask about the time, how many minutes in 1/4 hr,1/2 hr and things like that,gradually and because she wanted to and it was important to her she fully understood telling the time.She can add and subtract very quickly in her head whenever she has a need to know about time:-)
There has been a similar pattern with using cash.Initially lot's of questions about how much is this, add this or this take away this. Now she is doing the sums herself and if she gets the wrong answer she will sometimes try again to get the answer herself or she may just ask us,we continue to give her the answer without any hesitation or attempt to get her to work through it.I am very often surprised with the speed of her calculations.
Last week in the car we were passing through town on our way to an appointment,we were listening to music, when out of the blue she asked me what 15x15 was.I told her the answer was 225, she just looked and said "Oh cos I thought it was 185" Where it came from I have no idea,I did ask why she wanted to know and she said "I just wondered".So on a car journey she had just decided to do some mental arithmetic for no reason other than her own curiosity and came very close to the answer.I was tempted to ask how she had come to her answer and help her work it out to get the right answer, but decided that knowing Emily as I do it was better not to,if she wanted to know how to work it out she would of asked me:-) She wasn't at all bothered she had got it wrong, it wasn't important, it was just something she had decided to try and the conversation moved on.It was a really great reminder to me that we never know what our children are working out,thinking through or making sense of.In that short silence in the car, multiplication happened to be the thing that she was thinking about.
One night she had been unable to sleep and she came downstairs,it was 10.30 and I was finishing writing a blog post,she was fidgety and didn't want to do anything in particular but wanted to wait around for me to go up.She ended up pulling a chair in front of the fridge .In the early days of home ed we bought some magnetic numbers and put them on the fridge Alan would set a sum before he went off to work,it was never a "have to do" activity but it was there and she would answer it at some point during the day when she saw it, if she wanted to.Then it just tailed off as she stopped wanting to do them,the numbers are still there.Her friends that come often play around with them but Emily has shown no interest in them for many many months.On that night she started to play around with them and made a 20 figure number up across the fridge door.Then she asked me what the divide sign was.We had a brief discussion about it and she asked me a couple of sums,10 divided by 5 was one and I talked her through it then she asked what 10 divided by 8 was, I was set to get out some pasta to show her but that had been enough for her she didn't want to take it further.I will offer to go through some more sums with her at some stage but she got what she wanted from that short exchange.
I firmly believe that if children have an interest they pursue it and if she had an interest in numbers she would follow that interest to the point she was satisfied.I see it as my job to spot that interest and to offer new and interesting ways to explore it.
I had no interest in math and spent tooooo many hours in a classroom having to do algebra etc,pass tests when needed,only to have forgotten everything about it and have never had a need to use it anyway!!
Emily has been and will go on, building a basic knowledge of maths in real life situations.If as time goes on it is something that interests her more then she will delve deeper and ask more questions,if she chooses at a later date to go on and do an exam and it is something she wants to do I have no doubt in my mind that she will be able to do it.The choice will be hers.