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.

* * *

*How do you do maths in your house?*

*What approach to maths works best for your children?*

I’d love to hear from you. 🙂

* * *

*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!

### Resources

#### Books

Let’s Play Math Denise Gaskins. A wonderful book all homeschoolers should read. See my review here.

What’s Math Got to Do with It? (UK title The Elephant in the Classroom) Jo Boaler

#### Living maths activities we’ve done04

How to make a multiplication tower

#### 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

Living maths curriculum 2013-14

How to help your child fall in love with maths (even if they hate it)

How my autodidactic 9 year old is learning maths without a curriculum

How we do maths without a curriculum

Why we love Edward Zaccaro more than Khan Academy – About my 9 and 10 year olds’ favourite maths books

Maths – Why Faster Isn’t Smarter

#### Teaching trigonometry

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

#### Geometry

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.

#### Times tables

Fluency Without Fear Jo Boaler, Fluency Without Fear

It’s interesting Lucinda.Sure this method of learning can change the way of education

Thank you, Jewel. Let’s hope so! How are you? I hope everything’s good with you. 🙂

I have way too many thoughts to get out coherently at the moment. I loved this post and my mind is full.

But my main thought – I wish we lived round the corner from you and not on the other side of the world.

And another one – upside-down table, rolling on a ball, pet on lap all while doing maths – yes, yes and yes.

Yet another – questioning maths rules. Oh yes. “But Mum, don’t you think that there could be a situation, somewhere in this infinite universe, where that isn’t true? I don’t think we should assume it’s always true.” This was about all angles in a quadrilateral adding to 360.

Last one for now – a super MOOC on Udacity called Intro to Physics. The presenter is really cool and he explains trig principles in relation to finding the circumference of the earth. This is easily one of the best MOOCs we’ve come across.

Okay, that’s enough for now. I need to head over to your other blog :o)

I loved your daughter’s question… and then when I saw it was about quadrilateral angles I laughed even more. 😂 Aren’t they wonderful?!

Just checked out the physics MOOC … it looks gorgeous! I’d watch it just for the beautiful shots of Italy. It’s exactly what I’ve been looking for for Jasper, too – thank you!

Oh and yes – me too re living round the corner! I shall come over there one day and we can talk nineteen to the dozen at each other (or is that just me?). In the meantime, hurray for technology. 🙂

This post makes me happy. It gives me hope that the way I’ve wanted to teach math with my kiddos is the way I not only could teach math, but the way I probably should teach it, too. <3

Sounds like everything’s lining up for you, Ginny. 🙂

Love this! It looks like my house with all the wiggle worms 🙂 I’m rereading Leta Play Math right now. So good!

Thank you, Caitlin! I

loveLet’s Play Math. Yesterday a friend who’s preparing to become a school teacher asked me to help her prepare for her maths test. She’s nervous because she thinks she can’t do school maths (although she could do applied business maths perfectly well in her previous career). As I happily worked with my friend, I realised quite how much people like Denise Gaskins and Jo Boaler have helped redefine my relationship with maths. 🙂I miss seeing notifications in my email box letting me know that you’ve posted a new blog post. You inspire me and reading about your approach to homeschooling is always like a breath of fresh air.

I always love hearing from you, Marla. How are you? Are your older children doing any travelling this summer? And how is your book going?

Thank you for your encouragement, you’re so always so generous about my writing. I’d love to post here more often, but I seem to write quite slowly and Laugh, Love, Learn is still taking up lots of my time. You inspire me to come back here, though. 🙂