I once wrote a post called How to help your child fall in love with maths (even if they hate it) in which I talked about how my children learn maths without a curriculum.
That was three years ago now. I’m pleased to say our approach is still going strong and that Cordie (12) and Jasper (11) love maths more than ever.
Today I thought I’d reflect on what aspects of our maths approach have been most successful, then in my next post I’ll share in more detail what each of my kids are doing for maths right now and what our maths plans are for their senior school years.
1. Let them ask questions
When I learned maths at school my goal was only ever to get the right answers. I would watch the teacher do an example, memorise the procedure and obediently do my sums. It never once occurred to me to ask why a particular maths method worked. (Or perhaps I just learned to suppress that curiosity very early on.)
When it came to exams, I crammed a bunch of procedures into my head, passed with A grades, then promptly forgot everything. For the next 20 years I had nightmares about going into a maths exam unprepared and not being able to answer a single question.
In contrast, my kids have always been allowed – encouraged – to ask questions. To be honest, by this point there’s no stopping them. In maths, as in life, they don’t accept anything unless they know why. Yes, sometimes regret this. 😉
Over the years I’ve learned to anticipate their questions by encouraging them to work things out for themselves in the first place.
A few examples
So when Cordie wanted to know how the long division algorithm worked, we went in search of answers (thank you, Denise’s Cookie Factory Guide to Long Division).
In geometry, most textbooks just present formulae for the area of shapes. But I knew that my children would want to know why these worked, so we figured them out for ourselves (see below for more details).
And when we recently came upon trigonometry, Cordie not only wanted to know what this branch of maths was used for but also what all those strange words actually meant. Which was possibly the first time it had occurred to me that sin, cos and tan were anything other than magic buttons on a calculator that when pressed while reciting the appropriate incantation – ‘SohCahToa!’ – spewed out the correct answer.
Of course when your kids ask questions, you need to . . .
2. Be willing to go off on tangents
The best thing about not following a curriculum is that you’re never tempted steamroll over your child’s curiosity in an effort to finish a bunch of material by the end of term.
So there’s always time for games…
And you have time to investigate questions, like ‘What’s the area of a non right-angled triangle?’ Which leads to several weeks of playing with shapes as you figure out the relationships between rectangles, parallelograms, triangles, trapeziums and even circles. Which means your kids never panic about forgetting a formula, because they know everything follows from cutting up a rectangle.
Having time to follow rabbit trails means you have time to explore questions like, ‘What’s trigonometry used for?’ Which leads you to research the history of trigonometry, from right back when ancient astronomers used it to calculate the positions of the stars, to how triangulation is used today in everything from MRI scanners to animation software.
And when your daughter who’s passionate about linguistics asks where the words sine, cosine and tangent come from, you can spend a pleasant half hour discovering how ‘sine’, like the word used to describe our facial cavities (sinuses) comes from the Sanskrit word for ‘bowstring’.
Of course, your child may not be as interested as mine in the etymology of maths terms, but by following whatever it is they are interested in, you’ll deepen their understanding of what they’re learning and make it more memorable.
3. Do buddy maths
Since the early days of homeschooling right up until now when they’re 11 and 12, I’ve done maths alongside my children.
In this way I’ve been able to share my passion for maths, clear up any confusion as soon as it occurs, and head off boredom by moving on as soon as I can see a concept’s been mastered. (Plus of course I’m there to help navigate rabbit trails and answer ‘why’ questions.)
4. Don’t drill them on maths facts (unless they ask you to)
This is a controversial one, and I won’t pretend I’ve never casually suggested to my kids how useful it might be for them to rote-learn their multiplication tables, but they were having none of it.
Jasper couldn’t see the point of memorising something he can quickly work out every time, and (like a lot of bright people) Cordie gets stressed by time pressure.
So I decided I may as well trust mathematicians like Jo Boaler who says that not drilling kids on maths facts is a sure way to increase both their maths confidence and their number sense.
“Drilling without understanding is harmful … I’m not saying that math facts aren’t important. I’m saying that math facts are best learned when we understand them and use them in different situations.”
Guess what? It worked! After years of having fun with numbers, neither of my children has a problem with doing rapid mental calculations – for numbers both below and above 12.
5. Do maths anywhere that works for your child
In an ideal world I’d teach my kids sitting down nicely at the table as they write neatly using pencil and paper. I’m easily distracted and repetitive movement in my peripheral vision drives me crazy.
However… as the adult I’ve had to adapt myself to accommodate how my kids learn best – on any given day.
So if my son wakes up with the wiggles and wants to do maths while he leaps around on a giant ball, I take deep breaths, read problems aloud, and hold up a whiteboard for him.
I used to worry that Jasper would never be able to be still enough to write out his answers, but I’ve noticed that when his mind is sufficiently engaged he’s quick to grab a whiteboard to draw a diagram or scribble some notes to help him figure out a problem. As maths gets more complex (and interesting) I anticipate him naturally doing this more and more.
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How do you do maths in your house?
What approach to maths works best for your children?
I’d love to hear from you. 🙂
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PS Bonus maths story – For a behind-the-scenes story about what maths is really like in our house, hop over to my blog about life in a family that embraces its quirkiness, Laugh, Love, Learn.
PPS Remember my maths nightmares? I haven’t had a single one since I started learning maths this way alongside my children!
Living maths activities we’ve done04
How to teach maths without a curriculum
Let’s Play Math – My review of the book that has acted as our guidebook through our years of learning maths without a curriculum
When every day is maths playtime – Our living maths approach when my children were 8 and 9 years old
Why we love Edward Zaccaro more than Khan Academy – About my 9 and 10 year olds’ favourite maths books
Teaching trigonometry Resourceaholic. When you introduce your child to trig, I highly recommend printing off a set of logarithmic ratios in table form before you reach for the calculator, and that you start out with the kind of approach outlined in this article.
Applications of trigonometry Dave’s short trig course
Origin of the terms Sine, Cosine, Tangent The Math Forum
How to use trigonometry to measure the height of a tree The Math Dude
Animated explanations for area of basic shapes I can’t find the one we used, but this is very similar. We cut the various shapes out of coloured card.
Fluency Without Fear Jo Boaler, Fluency Without Fear