My daughter Sophie hasn’t done any formal maths since she was about 9 or 10 years old. But she does know a lot about this subject. She’s been learning maths in a different way.
Several years ago, I said to Sophie, “I’m thinking about making a podcast about unschool maths. Do you have anything to say about this topic?”
“Oh yes!” she replied. “You’re talking to the girl who hated maths and then turned around and now absolutely loves it. I have LOTS to say about unschool maths!”
The following post is an edited version of my podcast interview with Sophie. She was 14 at the time.
Sue: Why do you think a lot of children say that maths is boring?
Sophie: Even before they get a chance to play around with maths, they’ve made up their mind they hate it because the world says it’s boring and unenjoyable.
Sue: The world? Do you mean the people around them? I’ve heard a lot of parents say, “I never enjoyed maths at school. I don’t like maths.” Do you think it’s easy to pass that attitude on to children? Could they pick that up before they have a chance to see for themselves?
Sophie: Yes, children are mainly influenced by their parents. Their parents’ attitude about maths affects the child’s.
Sue: So if a parent doesn’t like maths and has found it difficult, it might be good not to say anything about that until the child has tried it for themselves?
Sophie: Yes.
Sue: Do you think that many adults and children get to the point where they say maths is boring because of the way it’s taught?
Sophie: Yes. The way maths is usually taught is boring and most children won’t enjoy learning that way.
Sue: So even online courses which look like fun because they use games and other interactive activities won’t necessarily encourage a child to enjoy maths?
Sophie: No, those sites are really just workbooks wearing makeup.
Sue: So how would you show that maths is worth learning?
Sophie: If a child says she doesn’t like maths, then approach it through something else. Show how maths is useful starting from something the child enjoys. I have a friend who makes miniatures. Learning about scale would be useful when making them.
Sue: Find something they can personally use?
Sophie: Yes, and show them that maths is the building blocks of everything.
Sue: And once you’ve got those building blocks, they can be used in lots of ways? What do you use maths for?
Sophie: My photography, my website designing, running, cooking.
Sue: How do you use maths in website design?
Sophie: I resize images by working out how many pixels I want them to be, what the megabyte limit is, how much I have to compress the images. I use maths to position things in the HTML….
Sue: What about running?
Sophie: We use maths when we’re working out how far we’ve gone, how fast we’ve been running, the average speed…
Sue: Measuring and multiplying so we know how many laps we need to run to get to 5 K?
Sophie: Exactly.
Sue: We do a lot of mental maths, don’t we? We don’t run with notebooks in our hands or calculators in our pockets. We’re working out these things on the go.
How about cooking? When people talk about real-life maths they always give the example of cooking. But real-life maths is much more than that, isn’t it? We spent a few weeks keeping our eyes open, didn’t we? We watched out for all the real-life maths that we were experiencing but don’t usually notice. Maths is all around us, but we had to stop and think about it to see how many experiences we were having every day. And there were a lot of them, weren’t there?
Sophie: Maths comes into everything: Music. Furniture – angles. Temperature for the weather.
Sue: Gemma-Rose learnt about percentages by reading her Kindle book.
So do you think you can learn a lot of maths just by living it?
Sophie: Yes, you can.
Sue: You can pick it up as you go along because you need it?
Sophie: Yes, just like spelling. We learnt about that as we went along.
Sue: So there’s no real reason why we have to learn these things in a formal way, is there?
When we’re talking about learning maths from real life experiences, we’re talking about learning maths because we need it. That’s the motivation for learning. A child needs it so she’ll learn it. But there’s another way of learning maths: Learning maths for its own sake. It’s such an interesting subject we want to know more whether we need it or not.
Do you think maths is interesting enough that you want to know more even though you might not need it?
Sophie: Yes!
Sue: Your older siblings didn’t want to learn anything they didn’t see a need for. But we’ve approached maths in a totally different way, haven’t we?
Do you remember how we read those maths books by Bill Handley? They sound like traditional maths books, but they’re not. The author shares new ways of doing traditional-type problems. We weren’t interested in the books because they helped you learn such things as the times tables. We like them because Handley introduced us to new ways of thinking about numbers. We became interested in playing around with them, didn’t we?
Sophie: He showed us different ways of doing maths. And how to do things faster. How to manipulate numbers in different ways. Yes, we weren’t interested because of the educational value. We were just having fun.
Sue: Why bother learning a new way to do maths? Isn’t the old way good enough? Why try to do things more quickly? Do you think it gives you confidence?
Sophie: It’s like doing a new stitch in knitting. It’s interesting. A challenge. Like playing a game. It’s enjoyable.
Sue: I’ve strewed a lot of maths. Can you remember any resources that you particularly liked?
Sophie: I liked the Numberphile Fibonacci videos. They’re good.
Sue: I look for resources that are produced by people who are passionate about maths.
Sophie: Yes, it’s better when people make resources because they love maths rather than because they want to show parents how to educate their kids. That love of maths spills over into their videos and whatever else they make. Their enthusiasm is contagious.
Sue: We could live without knowing anything about Fibonacci numbers. I’d forgotten what they are. I can’t remember ever using them. They’re not essential maths, are they? But they are interesting.
Sophie: Yes, we composed a piece of music using the Fibonacci number sequence. It was lots of fun. And we watched a video where they made a tartan based on the Fibonacci sequence.
Sue: What about Pi? Gemma-Rose isn’t proficient in the basics such as times tables, but she knows all about Pi. So do you think you can learn maths out of sequence?
Sophie: Yes.
Sue: So we shouldn’t say, “Pi isn’t in the maths syllabus until a certain year? You can’t learn about it until then. You’ve got to learn the basics first.”
Sophie: No, I think you should introduce the interesting stuff before the basic stuff. Kindle a child’s love of maths before making them do the basics. Don’t say, “You can do the fun stuff once you’ve learnt all this.”
Sue: When you talk about ‘fun stuff’, you’re not talking about computer games, are you?
Sophie: No, I’m talking about such things as Pi and Fibonacci, the way we’ve been learning about them.
Sue: Most people when they think of fun maths think of a parent trying to find fun ways to present basic concepts. Maybe a game to learn times tables.
Sophie: I mean learning about the more advanced, more interesting maths.
Sue: I think it’s all about showing children the big picture.
Sophie: Showing how all the basic stuff can be built into something bigger like Pi will kindle their love. If they like it, they might want to learn the basics themselves.
Sue: Show where maths can lead to? Then children might want to work their way back?
Sophie: Even if a child doesn’t understand everything about the big picture, they can still learn something. Some of the Numberphile videos are a bit advanced. I don’t understand everything. But I pick up bits and pieces. I still learn something from the videos.
Sue: Perhaps we can talk about Pi to show how we work.
We might find a video, watch it, and pick up some information. Down the track, we could find another resource about Pi. And then another. Each time we come back to Pi, we expand our knowledge a bit more.
Sophie: Yes, we can learn by returning to something. Keep coming back instead of doing it once and then ticking it off as done. Every time you come back, you’ll notice something you didn’t notice before. You’ll get a better knowledge of how it works.
Sue: Big picture maths, working backwards from the big picture, is a bit like how we learn English. We read books, observing all the skills in action, and we get inspired. And then we want to go back to the basics so we can write our own novel. Whereas if we started at the bottom with English – spelling, the grammar rules, punctuation – by the time we’ve got those skills in place we might have lost interest. We have to have some vision to keep us going. Something to inspire us.
Sophie: Even with English we don’t have to learn spelling etc. before we can start. We can just jump in. We learn as we go. The same with maths. We don’t need to have all the skills. We pick them up as we go along.
Sue: What happens if we expose a child to lots of interesting maths and they still don’t want to know? Is that okay?
Sophie: Yes, you’ve given the child a chance. You’ve shown them what maths is. Maths might just not be their thing. Not everyone wants to be a mathematician.
Sue: At least I’ve tried?
Sophie: Yes, and along the way, they’ll have picked up things. They will know all they need.
Sue: So kids can learn maths from real life experiences even if they’re not interested in learning maths just for its own sake? If they can’t see a use and aren’t enjoying it, let it go?
Sophie: Yes, they can always learn it later in life anyway. If they find they have a need for something like trigonometry, they can google it! They don’t have to learn it now.
Sue: The older kids had to learn maths ‘just in case.’ But kids can learn enough maths for what they need right now and if their need changes, children are capable of expanding their knowledge. Because they need it, they’re more inclined to learn it?
Sophie: Yes, you want to learn it rather than being told you’ve got to learn it.
Sue: Being told you have to learn something doesn’t really work, does it? You hold on to the knowledge until the topic has been ticked off in the records book or the worksheets have been completed or the exam is over or whatever, but then you forget it. You didn’t want to learn it in the first place. You have no need for it so you let it go.
If you’d like to hear more about our unschool maths story, you could listen to podcast episode 23, Unschool Maths: Why and How which includes Sophie’s interview. The edited written version doesn’t convey Sophie’s enthusiasm and excitement as well as the audio version. Sophie’s passion for maths is contagious. Perhaps her words will encourage you to unschool maths if you don’t already do this!
Images: In the first photo, Sophie is taking a photo of sister Imogen who is sitting on a bridge in the botanic gardens. Of course, Sophie is using maths as she adjusts her camera settings. Photography is one of her maths big pictures!
The second photo shows my youngest daughter Gemma-Rose who has just run over the bridge and past Sophie and Imogen. She’s probably mentally calculating distances and times. Running is Gemma-Rose’s maths big picture!
