Because I tutor maths and have got mine through a few GCSE exams I sometimes get asked about exams and maths so I thought I would layout what our maths journey looked like.
Two out of my three children did no formal maths before starting their GCSE studies aged between 11 and 13. In the interests of complete honesty I will declare that Ruth did do some worksheets that I found lurking about that involved packets of M&Ms and I taught Jonathan to add up in columns aged about 10; we were going round Lidl and I had a money off voucher to use but not much extra money so needed to add up. Rebekah was strange and liked doing worksheets or, better still, activities on the computer where her work would get a score and come with a printable certificate, so she sometimes did some formal maths.
Our general philosophy about education is that we (the adults and kids in the family) tend to learn things either at “point of need” or “point of interest”. Jonathan learned about adding in columns when I needed him to keep a fairly accurate idea of how much money we were spending from a complex list of numbers, until this point he had had no need to do this. It took him about 1 minute to get the concept. So what maths had they done to that point? They had done counting when they were small; we counted steps the same way as we would name colours of cars. Maths came up as we cooked: counting, approximating, doubling, halving, imperial measures, metric measures, times etc. etc. without making it a forced or contrived activity; as we cooked together these thing just came up as we talked and baked. Going to the shops, halving and quartering toast, playing with Lego – and I really mean just playing with it, not turning it into a maths activity, just playing with it automatically built the skills of estimating and realising that that you need four of this size to make one of that size. I remember my girls spending car journeys from Fife to Edinburgh to go to church chanting counting in twos and fives and tens – I never got them to do this- I have no idea why they were doing this but they did.
The other thing we did was play games, not made up “maths” games but real games. Obviously we played things like snakes and ladders,ludo and some strange game about snails by Orchard Games when they were little. Then endless games of Yahtzee as they got a bit older along with some Rummikub (and on very very few occasions because actually we all hate it – Monopoly). Card games at all levels from basic versions of Pontoon and Crib to the more complex games of Canasta we now enjoy. We discovered real games like Carcassonne, Settlers of Catan, Ticket to Ride etc. possibly not using so much arithmetic but the amount of probability that is informally calculated when we play Settlers is enormous.
For us game playing and cooking are a very real part of our lives so inevitably our learning has come during theses activities, not in a contrived way but in a natural way, yahtzee started with counting the numbers on the dice but quickly developed into doubling and Ruth, who liked to think about such things, would ask probing questions about the scores and what the best way of arranging answers etc. would be – the others never did.
Some current game playing pics to break up the waffling about maths:
I like maths so and again inevitably it gets talked about, when the girls added something up to work out costs or something we would discuss which methods they had used for it and they would be different, Ruth’s were always more creative – we called this Sum Talk at uni and it was one of my favourite things.
So how was our transition from informal, need to know, maths to formal GCSE? In all honesty, mixed. Rebekah wanted to do it and I couldn’t face the prospect of doing it with her and then a year or so later starting with Ruth so we did it together. Firstly I am not good at maintaining a self imposed structure so I asked a couple of friends to join us following the syllabus so I would have some external pressure to keep me focused – lets face it there is always going to be something more interesting to do than a GCSE syllabus maths session, there is no way I would have been able to keep to a timescale to help them through the GCSE. I have recently done the Gretchen Rubin Habits Quiz – it turns out I am an Obliger and respond well to having some external pressure so obviously this was the right approach for me to take. So we structured ourselves to do a class a week for about 18 months. These were supposed to be two hour classes, but sometimes they went on for as long as 5 hours – with runs round the garden and biscuits to keep everyone going. I had two different types of people in my group two “I have an instinctive feel for maths but no structure” types and two “I like to learn the method and stick with it” types, which was interesting. We had to back-fill a lot as we didn’t have 9 years of previous experience to draw on. This was usually done pretty quickly but all added to the time required to manage to get through the syllabus.
It was definitely doable for us to go from no formal maths to GCSE but it did take a fair amount of back-filling of the formal aspects of things and my kids all seemed to have a very good informal grasp of numbers and how they worked before we started and some weeks we spent hours and hours going over things. This was my girls’ first proper experience of sticking with a syllabus and it wasn’t always easy for any of us – we had to make sure the work was done in a timescale and we stuck to it – none of us really liked doing this but it got easier over time and we’ve even managed some other exams now with only the external pressure of the exam date to keep us going. Don’t let me leave you feeling that this was easy for us, despite everyone wanting to do all the exams we have done there have definitely been tears and the odd tantrum during the process. We also had the massive benefit of being able to do the modular exams, which sadly are no more, which really helped with spreading out the stress and were great for my group who had never experienced formal testing so the tiny exams were not very scary.
I hate doing GCSE exams; to me it takes away from the real process of education but they have been done by the kids as a means to an end, a hoop jumping activity. I think Ruth is finding A-level study to have more point to it and to be far more interesting but the idea of exams to test a huge amount of remembering still seems a strange thing to do in our current society.
Do I think it would have been easier for my children to do the GCSE maths if they had had more formal understanding of maths before we started? The short answer is yes, however I wouldn’t have wanted to have encroached onto our earlier time together with formal “work”. I would also say that despite not having done formal maths their informal maths skills were great; they didn’t know multiplication tables but they knew how to work them out, they knew that 1/8 was half of 1/4 and so 2/8 was equivalent of 1/4 so moving on to formal fractions was fairly easy as they knew about them informally. Without having those informal skills working through the syllabus would have taken much much longer.
I run GCSE maths groups despite the fact that I think that people can do it themselves at home with a book and some of the great web resources that are out there. A group can be helpful for a number of reasons: it can help you stay on track, it can help to have someone who isn’t mum or dad imposing the work (when she was little Rebekah always responded better to someone else other than me asking her to do something), as a home educating parent it is sometimes just nice for someone else to be doing the work of finding the resources and teaching the subject (I’ve certainly been grateful to people who have done Biology and English groups so it was something I didn’t have to think about as much).
You may wonder then why I teach a pre-GCSE maths group. From my perspective it is largely about time; in a 2 hour GCSE class we don’t have time to back-fill so if a group knows some of the skills beforehand we can spend more of the time on the syllabus. From the perspective of the students or the parents it can be about confidence, or about building up to working in a more formal group or concerns about their own maths skills. I have absolutely loved teaching the pre-GCSE group for the last year, I don’t have the pressure of sticking rigidly to a syllabus so can teach the things I/they think are important and have time to do it in ways that can really try to build understanding and we have time to play games and investigate things. In my GCSE group I don’t have much time so we can’t spend lessons playing battleships to teach co-ordinates or board games for algebra substitution but in my pre-GCSE group they can do this. This week we had some very competitive algebra game playing!