Ross MackellUK-qualified primary teacher · 10 min read

You sit down to help with maths homework. You show your child how you'd do it. And they look at you and say: "That's not how my teacher does it."

If that's happened in your house, you're not doing anything wrong. Maths really is taught differently in primary schools now, and there's a good reason for it.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll explain what changed, why your child draws pictures and uses blocks, what all the new words mean, and whether you should teach them your old method. By the end, homework time should feel a lot less confusing.

What changed in primary maths, and why

In September 2014, a new national curriculum for maths came into force in England. It asked more of children at a younger age, and it put a big focus on three things: fluency, reasoning and problem solving.

Around the same time, the government funded a network of Maths Hubs and a teacher exchange with Shanghai. Lots of schools moved to what's called teaching for mastery. If you want the official version, the NCETM's five big ideas sum it up. Here's the parent version.

• The old way: learn the steps, practise the steps, move on. Lots of us were great at following steps.
• The problem: children could follow the steps but didn't understand why they worked. Change the question slightly, and everything fell apart.
• The new way: understand first, then learn the method. The whole class moves through topics together, and children don't move on until they really get it.

Here's the important bit for parents: the written methods your child ends up with are pretty much the same ones you learned. Column addition, column subtraction, short multiplication, long division. The difference is the journey to get there.

Concrete, pictorial, abstract: why your child uses blocks and drawings

If your child comes home talking about blocks, counters and drawings, this is why. Most schools teach in three stages, known as concrete, pictorial, abstract (or CPA for short). Let's use 23 + 15.

1. Concrete: real objects

Base ten blocks, counters, even pasta. 23 is two sticks of ten and three single cubes. Add one ten and five ones and you can count what you've got: three tens and eight ones. That's 38.

2. Pictorial: drawings

Same idea, but on paper. Draw a line for each ten and a dot for each one. This is where your child proves they understand without needing the blocks in front of them.

3. Abstract: just numbers

Now it's written as a column sum.

By now your child knows the 3 in 38 means three tens, not three. That's the whole point of the first two stages.

The research backs this up. The Education Endowment Foundation's guidance on manipulatives recommends using objects and pictures to build understanding, as long as children are moved on to written methods. And the NCETM explains the thinking in more depth in its piece on representation and structure.

The new maths words, in plain English

Half the battle with homework is the vocabulary. Here are the words that come up most.

You don't need to use these words yourself. But knowing what they mean stops that moment of "I have no idea what you're talking about."

The bar model: a worked example

The bar model is the one that confuses parents most. It's also one of the most powerful things your child learns. Here's a typical Year 5 question.

1. Draw Amy's bar: one box.
2. Draw Sam's bar underneath: three boxes the same size as Amy's. Three times as many, so three boxes.
3. Count the boxes: four altogether. Put a bracket round them all and write 48.
4. Four equal boxes make 48, so one box is 48 ÷ 4 = 12.
5. Amy has one box: 12 stickers. Sam has three: 36. Check: 12 + 36 = 48.

Notice there's no guessing. The picture tells your child exactly which calculation to do. That's why schools love it, and it works all the way up to secondary school.

But look at step 4. The bar model only tells your child what to calculate. They still need to be able to work out 48 ÷ 4. If division is shaky, the bar model can't save them. (If that's your child, my bus stop method guide walks through short division step by step.)

Should I teach my child my old method?

This is the question I get asked most by parents. Here's my honest answer as a teacher.

• Don't contradict the teacher. Two methods at once often confuses a child more than either one on its own.
• Ask first, show second. Say "Can you show me how your teacher does it?" and let your child explain. You'll learn their method, and explaining it helps them remember.
• Your method isn't wrong. If your child already understands place value and is in Year 5 or 6, the formal written methods are probably the same as yours anyway.
• If you're both stuck, draw it out. Tens and ones, or a bar model. You can't go wrong with a picture.

The goal isn't for your child to do it your way or the teacher's way. It's for them to understand it well enough to explain it to you.

Does the new way actually work?

I'll be straight with you, because I think parents deserve the honest version.

Understanding first is a good idea. Objects and pictures really do help children see what numbers mean, and Ofsted's review of maths research agrees that children need both understanding and fluent recall of facts and methods. But the evidence on the full "Shanghai-style" approach in English schools is more mixed than the headlines suggest. A government-funded evaluation found the teacher exchange didn't boost Key Stage 2 results in the way many hoped.

Here's what I see in the classroom. The children who struggle in Year 5 and 6 are rarely struggling with "reasoning". They're struggling because one or two of the basic written methods were never fully secure. Subtraction with exchanging. Times tables. Short division. Then every reasoning question built on top of those methods falls apart.

That's why I always say: arithmetic first. Get the core methods solid and the reasoning questions suddenly make sense. The government's own maths guidance for Key Stages 1 and 2 makes the same point: some skills have to be secure before a child is ready to move on.

3 things to do at home

1. Ask "how do you know?" after every answer. It's the reasoning muscle schools are building, and it costs you nothing.
2. Keep something to count with on the table during homework: Lego, pasta, coins. Concrete first, always.
3. Practise the facts. Number bonds and times tables still matter just as much. Understanding doesn't replace knowing your facts; it sits on top of them. My guide on how to learn times tables fast has a simple plan.

Frequently asked questions

Why is maths taught differently now?

Because England introduced a new national curriculum in 2014, and most primary schools adopted a mastery approach. Children learn why a method works, using objects and drawings, before they learn the written method.

What does concrete, pictorial, abstract mean?

It's the three-stage way most schools teach a new idea. Concrete means real objects like blocks or counters. Pictorial means drawings of those objects. Abstract means just numbers and symbols, like a written column sum.

What is exchanging in maths?

Exchanging is the school word for what many parents call borrowing or carrying. It means swapping one ten for ten ones (or one hundred for ten tens) so a calculation can be done in columns.

What is a bar model?

A bar model is a drawing of rectangles that shows how the numbers in a word problem relate to each other. It helps children see which calculation to do, so they don't have to guess.

Should I teach my child the old way of doing maths?

Ask your child to show you their school method first and support that. Two methods at once can confuse a child. By Years 5 and 6, the formal written methods are usually the same ones parents learned.