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:

Scatergories and cocktails at Christmas

Scatergories and cocktails at Christmas

Exploding Kittens - the most serious game in the world

Exploding Kittens – the most serious game in the world

Seven Wonders - complicated but good.

Seven Wonders – complicated but good.

Some rather serious scrabble playing.

Some rather serious scrabble playing.

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!

 

 

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Photo bomb

 

 

 

 

Had a fantastic day today. We’ve had a manic time leading up to last weekend but this week has been nicely relaxed for me at least. Girls still studying and Martin working but Jonathan and I are properly chilling out.

Today we’ve managed to do pomander making to Christmas music.

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We had a lovely Christmas ham based lunch and then went on a blustery walk at Gurnard.

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Back home for hot chocolate, cookies and cake watching Elf.

Now the others are playing Settlers of Catan and I’m going to head off to nine lessons and carols at Carisbrooke church.

Merry Christmas for tomorrow everyone :-)

 

One of the best things about The Learning Zone is our annual cookie exchange, organised by one of our members. This year we had a whole afternoon of festive fun. The English and drama group put on an amusing play with magically growing hamsters – yes seriously. Then we exchanged cookies – some of which had the most amazing wrapping this year. Then we sang a mix of sea shanties and carols rather raucously which was great!

Here are a few cookie pics to make you which you had joined in!

Our basket of rather cheaply and simplistically packaged cookies, we made chewy chocolate-chip cookies, German lebkuchen and Dutch pepernoten :

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But got these amazing cookies in return:

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And just look at this house – I think some people were just showing off!

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We loved these boxes too:

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and there were so many other lovely and delicious cookies from so many other generous people, we feel really blessed to be part of such a great group.

 

Every time we come back from The Netherlands we say we’ll cycle more. This time we seem to be doing reasonably well at it. Yesterday I had a glorious cycle to Newport to buy some new crochet hooks. On the way there I heard a saxophonist playing in the woods which was an unexpected pleasure.

I’m glad we live at the Cowes end though as I get all the annoying obstacles out of the way early ( the hilly bit with no right of way and no visibilty at Medina Vally Centre, the stupidly close poles on the bridge that we definitely wouldn’t have managed to fit our kiddy trailer through, and the kicked out junction with no right of way at Stage Lane) and can just enjoy the rest of the ride home, the angle of the views are slightly better on the way back to cowes too!

Cycling home I realised that being on my bike on a car-free path – particularly in my favourite gear ratio (2:6 if you are interested) – makes me feel almost as contented as swimming does. If we had Dutch style infrastructure and attitudes to cyclists I would feel happy very often :-)

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My favourite day at this site was definitely when we went to visit the Maastricht caves . We even had to cycle (or in my case push) up a proper hill to get there and we arrived a little early for the English language tour so there was time for yet another beer!

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The tour guide was brilliant, we had a long hot walk to the caves as the usual entrance was closed during which he established that we were a group that were a mix of English and German speaking so he switched flawlessly between both languages throughout the cave tour.

The extra walk was well worth it as we got to see into the vault which is usually too far for the tour. This was where many Dutch pictures were hidden through the 2nd world war, as well as a hidden radio and a fair few people!

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The caves are really man-made tunnels and there are the most amazing charcoal drawings throughout the caves.

Some dinosaurs,

the tour guide was rather critical of the fact that there were a couple of dinosaurs that were incorrectly included as they couldn’t have been from this area.

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An illustration of 5 people who helped the Spanish in the 17th century and then had their heads chopped off and displayed at De Vijf Koppen (The Five Heads Bastion).

We were quite excited to see this as we had visited this bastion on our walking tour the day before!

 

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A map of the underground caves and tunnels, it really is incredible just how extensive they are.

 

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My favourite part was hearing about the Jewish man who used the tunnels to escape to safety during the second world war and had carved his name in a wall in the 1940s and then seeing underneath the same name with a date just a few years ago when he had revisited the caves.

As well as the charcoal drawings there were many sculptures in the soft rock.

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The tour guide gave us a choice of the more adventurous experience or the standard one – we opted for the adventurous one and got to experience a little of the more creepy nature of the caves as the tour guide went ahead of us with the lanterns leaving us in complete darkness to follow him using our fingers on the walls as our guide. It was slow, scary and very disorientating even though i knew we were safe my heart was pounding at the complete helplessness I felt, if the tour guide left us we would have had no way out. He told us about some monks who had become lost in the mines and when they were later found their fingertips had been completely worn away as they had tried to trace their way out by running their hands along the rough walls. Many people have lost their lives in the caves and even with the torch light I was unable to identify which caverns we had been in before.

Jonathan was the only child on the tour so got to have a go at cutting a bit of the stone, it was soft but the idea of doing it for hours on end in the cold humidity was very unpleasant. People stopped working in the mines at the age of about 35 as the damp conditions led to horrendous arthritis.

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The temperature is about 12 degrees all the time in the mines which on the hottest day of the holiday was was a welcome relief!

Back outside we had lovely dappled sunshine

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and after a trek back up the hill we needed another cool beer and then enjoyed the unusual experience of free-wheeling down a Dutch hill to head back to the van.

Maastricht was an easy 30 minute cycle from out camp site, so we headed there for a couple of days.

The first day after the obligatory visit to the, rather impressive, tourist information centre (VVV)

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we set out on a walking tour of the city.

First stop was the magnificent bookshop converted from an ancient Dominican church – Boekhandel Dominicanen

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We opted for the fortifications tour so we saw lots of, well, fortifications.

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We learned that “molen” means mill and saw some watermills.

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Jonathan wanted to take some photos of the deer in the town park.

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We ended up back at the very empty town square and had an ice cream, toasted sandwich and a beer before cycling back to the camp site.

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We love going on holiday to The Netherlands – this year we decided to go somewhere other than the Katjekelder park in Nord Brabant so we headed for a camp site just outside Maastricht, Camping De Oosterdriessen.

This was a great choice: It had a large areas to camp in separated by light hedges,

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A lake to swim in,

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And some good weather to sit outside and eat the tarts

 

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and drink the wine we bought in France.

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In my pre-GCSE group we have been doing some algebra and today we were dealing with substitution and simplifying. I love card sort activities and today we managed two of them one for each topic.

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Spot the error in the organised work below:

 

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And look who photo bombed:

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It’s been a while since I did a day in the life type post (or indeed any post) so for anyone who may be interested here is what one day in our life looks like now we just have one teenager being autonomously educated at home.

A fairly typical start to the day as I need to drag Jonathan out of bed (he’d had a late night with a friend over the night before out at local church clubs followed by chippy chips and playing on the computer) because we had an activity to get to. If we hadn’t been heading out I’d have just let him sleep – for me one of the many advantages of home education (and no it doesn’t mean they’ll never be able to get up for a job – I had the same approach with the older two and amazingly they get up for work when they need to).

It’s the day after the general election so in the car Jonathan and I discuss the result – purposive conversation – it’s been the mainstay of our home education for as long as I can remember.

We arrive at Yaverland Beach for a fossil hunt and one of the home-ed mums shows us some fossils and talks about the local geology.

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One of the things I love about home education is the mixed age activities we can do, we had children here from 1 to 16 and a mix of mums and dads too.

We had a gap between the fossil hunt and horse riding so as a treat Jonathan got to choose lunch. He opted for paninis at Blaze in Ryde – My sister and my mum had taken us there and we’d loved it and I’d promised him we’d get lunch there one day so this was the day. The car Journey is filled with election talk on the Jeremy Vine show and we end up discussing the Single Transferable Vote system – which we realised he has learned about from one of the guys from the Hello Internet Podcasts after Ruth asked what it was and he explained very clearly. I haven’t watched that one but the one on Scandinavia which Jonathan sent to me was fascinating.

Anyway the paninis were lovely and we both managed to get a bit of reading done while we were waiting for them, Jonathan wasn’t so impressed with the chips!

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Time to head back over to the other side of the island and go horse riding with some other members of our home ed group. Jonathan is pleased with his ride today as he got to canter which is his favourite bit!

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A not so quick trip to Aldi on the way home – Jonathan must be bored waiting in the car as I discovered these arty shots on my camera when I look at the memory card.

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Then he wanted to edit a video for youtube and do a bit of maths (homework for his GCSE group) and computer studies (slowly working through the IGCSE book).

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Then he managed to draw something, scan it to the computer and do something to it in Paint – Ruth helped him a bit to suggest how he could do it but they both sounded like they were talking gobbledegook to me!

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And that was pretty much it except for the obligatory time spent on Dota.

This is not a typical day – we don’t really have those – our weeks tend to follow a bit of a pattern based on when external activities occur but these are often subject to change.

Monday: Usually D and D day plus a bit of maths homework and some video making and computing but this week a visit to Seaview Wildlife Encounter as we had my mum and sister visiting. Jonathan mostly wanted to keep a wallaby – in fact as soon as we got home he was looking up how much space they needed and measuring up the garden!

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Tuesday was spent doing volunteer falconry and then Karate – with a hasty dash home to pick up gear and grab a bite to eat between the two (the pics are from a previous week).

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Wednesday was spent with a lazy morning – probably watching TV or youtube, then maths GCSE group, then off to the park with a couple of fellow GCSErs back home to spend some time writing song parodies or playing on the Wii with his friends followed by more recording, editing and gaming.

Thursday starts off slowly and gets progressively busier as the day goes on – some maths and computing in the morning, listening to podcasts, drawing for uploading to something on the computer and some time spent on his DS during the afternoon. heading off with a friend to a couple of after-school groups at the local church followed by friend coming home with him and playing on the computer.

Not a typical week but it gives a flavour of our life now there is just one of them at home – things are certainly different from when I wrote this blog post at the same time of year in 2011 and they were all home still.

 

One of the things I do is run a few Pre GCSE maths groups, this is a relatively new venture for me and I am loving it. Compared to the GCSE groups we are more relaxed, have more time to explore and discover, more time to play games and more time to cover the topics.

One of the things I really love is a good card sort activity – matching, dominoes etc. You can do the work on the subject you want to cover without worrying about writing things down and you can work collaboratively too.

So today we’ve been working on using protractors accurately, measuring and calculating angles. I really enjoyed this card sort activity from the brilliant Mr Barton’s maths website.

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