Maths Part 1: Give Them Time to Make Sense of It

Right, maths. (Rolls up sleeves).

Of all the subjects I've taught and observed children learn over the years, maths is the one I've found myself doing the most research around, because it never feels straightforward.

Some children seem to just 'get it' while others take their time to understand. Some seem to picture numbers and patterns, others need to see objects and pictures or doodle on a piece of paper to make sense of things. Everyone's so different when it comes to maths (more on that later).

So how we approach it with our children is never quite as simple as just finding a good curriculum, book or online programme and following it along in a nice, orderly fashion (no matter how nice that sounds).

It's different to literacy. Once a child learns to read, they've unlocked a huge amount of other learning. There'll always be more to understand but, once they can decode letters, the skill is set for life.

But maths isn't just one skill, it's lots of different skills that build on each other. You need to be able to use them together, adapt them to different problems and spot the patterns and relationships between them. 🤯

You can see why some children get shaky around maths - especially if you, as the home ed parent, feel shaky yourself.

Here are five things I have to keep in mind when supporting my own children with maths, shaped by what I've seen work (and not work), and lots of reading and observation along the way.

In my next post coming in a couple of weeks, I'll share the resources I've found helpful, inspiring and really worth knowing about.

1) Familiarity First: Let Children Meet Ideas Before They Learn Them

Children need some familiarity with an idea before they're expected to learn it properly.

Imagine learning fractions without ever having shared out a cake or divided something into equal pieces. Or learning to tell the analogue time without seeing an analogue clock (time can be notoriously difficult for children to get their heads around). They would seem like alien concepts.

With maths, it really helps if children have come across an idea before. When you already know a bit about what you're learning, it doesn't feel so scary because you have something to connect new ideas to.

This is why maths in everyday life (cooking, using money etc.) as well as conversations, puzzles and games are so important. They get children familiar with numbers, shapes, measurements, patterns etc. without any pressure.

When my own children have some familiarity with an idea already - in any subject or topic - they're more confident when they come across it again. I notice a sense of, "Oh yes, I've heard about this before!"

The other benefit is that, over time, lots and lots of these experiences give children something to picture when the maths becomes more abstract. They won't always have their fingers, counters, blocks or cakes in front of them, so being able to hold a picture of what's happening in their head becomes really useful.

Tricky sounding questions like 'What's half of a third?" don't sound so scary when you can draw it our or picture it in your head.

2) Maths is Problem Solving - So Let's Provide the Problems

At its core, maths is problem solving.

If we want to teach children to think mathematically, we have to be careful how much information we're giving them in advance. We want them to work it out for themselves.

If we teach them all the methods for solving various problems, they might get the answers right, but do they actually understand what they've just done?

Or are they just following a list of rules and shortcuts to help them answer a question (like 'just move the decimal point' or 'just add a zero.' 🙈), but have no clue why they're doing it?

Problem solving and puzzles allow them to work things out for themselves and play around with ideas without the pressure of getting something 'right.'

For me, there are a few different parts to this, and they all need to develop alongside each other.

1) The basic skills: Counting, place value, multiplication, mental arithmetic, number bonds, shapes, scaling numbers up and down. These provide the groundwork for problem solving and require lots of time and repetition. This is where games of all types come in (dice, card, pen & paper, verbal, board games) and everyday scenarios, so they're practising these skills in a fun and meaningful way. The more they understand these skills, the easier - and more fun - problem solving becomes. This part is definitely not something to rush.

2) Problem solving. As their skills are developing (it takes years), you can start on the problems and puzzles alongside them. Let them explore, try different things and make mistakes (it's best to use pen and paper or whiteboards rather than neat notebooks). They'll be working on their core skills at the same time, but in a meaningful context - this is what we want! With enough time and space to play around and explore, they'll start to find quicker and more efficient ways of tackling problems. (I'll share more resources for problem solving in my next post).

3) More formal maths: Formal lessons, workbooks and tests have their place, but they're not the whole point of maths learning. Long division or column subtraction help with efficiency and accuracy, but if they haven't had time to explore and play around first, these methods can feel like random rules to remember, rather than useful tools for solving problems. As the problems get more complicated or the maths needs to be used in a different way, things can get very tricky if they don't really understand what's going on underneath.

There’s often a rush from the foundations to formal methods, and the middle bit gets squeezed out (at school, it was often something the children who finished their work first got to tackle). But the problem solving part is the really important part, and sort of the whole point of maths!

Yes there are sometimes things that require explicit teaching. The point is that those things make much more sense when they're connected to understanding. There's no need to rush ahead when it isn't necessary to do so.

3) Listen to Their Reasoning: How Are They Solving It?

Look beyond whether your child got the answer right and pay attention to how they worked something out.

The way they work something out in their head might be completely different to the way you do it - which can lead to a fair bit of head-scratching and frustration on both sides!

But hearing or watching how they do it can tell you a lot. They might have found a really clever way of getting to the answer that you wouldn't have thought of. Or they might have made a simple mistake but actually have a good understanding of the maths. Sometimes they'll say something that shows you there's still a crucial part they're missing.

When my children are solving a problem, I try not to help too quickly, but rather observe from the sidelines or ask them later how they did it. It's not easy to hold back but there's nothing worse than jumping in with a correction, or offers of help, when someone's in the middle of working something out, or is about to notice their own error.

All of this gives you clues about where they might need a bit of help or more of a challenge. Sometimes they need more practise, more games, a different explanation or maybe - the one I notice the most often - they just need a bit more time and exploration before things will click.

For example, if they're struggling with subtraction, which part exactly? Are they struggling to visualise it, understand the concept, or do they just get stuck when they have to cross the zeroes? (I've always loved maths and mental arithmetic, but my brain still hates subtracting past zeroes!)

Or perhaps they understand multiplication but just take a while to work out the answer. They don't have to recall their times tables in one second flat. The understanding is more important, and speed comes with practice.

4) Maths is Personal: Children Don't All Think the Same Way

Everyone's different in how they visualise and approach maths.

Ask two different children how they add two numbers together in their head, and you'll get two different answers. The point where maths ideas click into place for children, and how they understand what they're seeing, are usually completely different.

So when books or lessons talk about how to 'solve' a maths problem and only show one or two methods or explanations, it might make sense to one child and leave another completely confused. (Have you ever seen maths explained in a different way and suddenly thought, "Why didn't anyone explain it like this at school?")

It's why using different resources and objects, and showing them the same idea in lots of different ways is so important. It gives them different ways into the maths, rather than expecting them to remember a method that makes no sense to them.

With home education, we usually have more time meaning we can wait for things to make sense at the right time for our children.

For example, I play Monopoly a lot with my kids, and the learning I've seen through this one game - without any instruction from me - has been really eye opening. At first, I'd help with counting spaces, adding dice and working out change. Over time, they started doing more of it themselves. They'd watch me do it on my turn, have a go with smaller numbers and gradually work their way up to bigger ones.

They eventually learnt these gradual skills (for example, moving from making £8 to finding change from £500), but the time it took for each of them, and the way they both approached it, were completely different.

5) Keep Maths Simple: Not All Maths Resources Are Created Equal

Sometimes the problem is just a rubbish maths book. 😂

We've been given various maths activity books over the years (usually by well-meaning relatives!) only to discover that their explanations are way too complicated. They can take a fundamental idea, like place value, and make it sound incredibly complex.

Sometimes a rough sketch on paper or a few blocks are far more effective than a long-winded explanation or complicated diagram that makes no sense to your child.

However, workbooks can be great for practising skills or as an extra puzzle or challenge - some kids really love them - but I'd avoid using them to 'teach' a new idea. If a child's first experience of fractions or place value is a workbook rather than using objects or drawing things out, they're likely to struggle to visualise what it all actually means.

Plus shiny workbooks don't exactly look like places where children can play around, explore and make mistakes (especially those children with perfectionist tendencies!). Scrap paper is much better for this.

If you do choose a book, have a quick look through it yourself first. Does it make sense to you? Could you explain the idea simply to someone else? And do the questions actually help your child understand the maths, or is there so much going on that the maths gets a bit lost?

A final thought

I think maths can be an area where we accidentally put children off.

It doesn't need to be complicated, but it does need time, understanding and plenty of opportunities to play with ideas.

I've found myself becoming much less concerned about whether my children have covered something and much more interested in whether they actually understand it. That understanding can take a long time to develop, but one of the great things about home education is that we don't have to rush it.