One of the most common questions I get about unschooling is how will the children learn maths. It's funny how nervous maths makes us. There seems to be a collective anxiety around the subject. Certainly it was the one thing guaranteed to make me wobble when we took the children out of school. My insecurities led to me acquiring quite a collection of exercise books designed to make maths fun, and which have sat untouched on the bookshelf for a long time.
For a while, right at the beginning of our home journey, D spent some time on these textbooks each day. They weren't a lot of fun, and he was annoyed that he was expected to use the methods shown in the book when he wanted to practise mental arithmetic and try things his own way. To him, it felt restrictive and boring. To me, the process seemed incoherent with the rest of his and his siblings' learning. It didn't make sense that this one subject would be impossible to engage with in a more natural and enjoyable way. As someone who gets a lot of satisfaction out of statistics and spreadsheets, I know that numbers are not joyless at all. So, with that knowledge, we let go of the textbooks and everyone got on with exploring numbers in their own way.
I think it's helpful to differentiate between two kinds (or maybe levels) of maths. There's the kind that most of us use every day and, depending on the day, can involve things like adding, subtracting, multiplying, dividing, percentages and fractions. Usually, these happen in the context of solving a problem, making a decision, or just learning about something. If we think about how we adults engage with numbers on a daily basis, we can see that it is as much about feeling confident with numbers and problem solving as anything else. Working out who owes what in a restaurant, the best place to change your pounds to dollars or which bank offers a better mortgage deal are all good examples of putting logic and reasoning together with our number skills.
Then, there's the more advanced maths that comes along later, many years after a child has already built up a relationship with numbers and is engaging with them every day. It's the kind of maths that most of us won't get the chance to meet often in life, like trigonometry, square roots and algebra.
So, back to the question. How do they learn maths? I would answer that it is almost impossible not to learn everyday maths. Maths is everywhere in life. It's true that on an average day you're unlikely to need to work out an equation or the angles of a triangle (I haven't needed either since taking my maths O-level at the age of 16), but, you will need to work with numbers, and there are plenty of reasons why children would want to get to grips with that as soon as possible.
In an interview with Natural Child Project in 1980, educator John Holt, who was an early advocate of unschooling explained his thoughts on maths learning. "The best way to meet numbers is in real life, as everything else...You know, there are numbers in building; there are numbers in construction; there are numbers in business; there are numbers in photography; there are numbers in music; there are fractions in cooking. So wherever numbers are in real life, then let's go and meet them and work with them." That interview took place nearly 40 years ago, but I think his thoughts are just as relevant today.
As I began this post, I took some time to pay attention to C's interactions with numbers. She is six and has never done any formal maths learning, but she has a pretty good grasp of the basics. Yesterday involved a lot of counting - she was organising her impressive collection of toy animals and wanted to see how many she has. Then there was more counting when we played some games of pairs and we were seeing who the winner was (C, of course, my memory isn't a patch on hers). Later on, she did some measuring when we made cupcakes and, in the evening, she had a go at multiplication. She had created a cinema in the sitting room and we were the customers. I offered to pay for everyone, so she worked out how much that was. Finally, at bedtime, we had a long conversation about what she could buy with her pocket money and how much she would have left if she bought certain things. She likes to work this all out for herself and gets annoyed if I ruin things by coming up with the answer before she's had a go. She is absolutely motivated to figure it all out and only gives up if she knows it really is beyond her. Of course, to C, none of this is about maths. This is about toy animals, pretend cinemas, cupcakes and working out how best to use her pocket money. This is stuff that really matters.
Money is a wonderful place for children to gain confidence with numbers. All children want to master money. They see the part it plays in our lives and how it limits us, opens doors, creates stress and buys lovely things. Of course they want to master it! Being open with family finances and inviting them to get involved is a powerful way to facilitate confidence with numbers and a healthy attitude to money. I started a spreadsheet recently where we record all our daily money transactions. This was really an exercise for me as I was working out our budget. But I keep the sheet open on my computer so anyone can see it and it helps us all be conscious about the choices we're making.
Here are just a few more ways that numbers come up in our daily lives:
Business plans D and E are keen to set up a business of some kind and we talk through a lot of ideas. The main motivation of these businesses is to make money, so they delve into the costs and prices they could charge. They think a lot about how much it would take to get started, the investment needed and so on.
Gaming Gaming is packed with numbers. D was patiently walking me through one of his games the other day. It was highly strategic and the aim was to expand your empire. One of the ways to advance was to set up plantations and trade with other countries. This involved checking for different commodity prices and working out which was worth the investment. This all had to be done quickly or someone else could get the better of you. Gaming isn't my forte and, interestingly, as D was explaining how the game worked I had a flashback to being around 12 years old and sitting in a maths class that was over my head. I got that slightly panicky 'Why isn't this going into my brain?' feeling. No wonder maths still makes me nervous.
Money dealings Percentages come up constantly in daily life. For example, D wanted to create a game and sell it via an online platform. A particular platform he likes takes a percentage of the earnings, so he needed to figure out if this was a good deal or not. Discounts are also often expressed in percentages and since everyone is keen to make their pocket money go as far as possible, these skills have been mastered quickly. Percentages also come up in conversations about buying property and working with banks. Loans, mortgages etc, these can all be interesting territory for a child who is keen to understand how it all works.
Geography E loves geography and likes to know statistics about different countries and cities, from population to average GDP to the size of the countries themselves. We do a lot of invented quizzes about biggest and smallest cities, mountains, islands etc. The numbers in this context are often in the millions and it's great to see how confidently he handles them.
These are just a few examples of how our children are naturally interacting with numbers and building their knowledge and confidence. We also get competitive with our Fitbits to see who has walked the most steps; we play Monopoly and other board games that use money; we buy things on eBay; we talk about how many years ago things happened in history; D does 3D game design; E is becoming a dab hand at spreadsheets as a way to put his ideas and concepts in order; we plan trips and look at prices and timetables; we measure lots of things, such as ingredients, cord for macrame or wood for a DIY project...and so on.
In all of these examples, the numbers themselves are not the point. And getting things right for the sake of getting them right (or pleasing someone else) is definitely not the point. Solving the problem, acquiring the knowledge, finding the best deal, making more money—that's the point. There is nothing so meaningful as real life.
When they are ready and want to, they can engage further in maths as a subject and I imagine they'll find it interesting. For now, just becoming accomplished and confident with numbers as they come up in real life seems to me to be the most logical way to live.