How to Make Decisions About Math CurriculaWhen There Are So Many to Choose From

You’re sitting up late at night, scrolling through curriculum reviews, blog posts, and Facebook threads that all tell you something different about how to teach mathematics to your child. Your devotion to giving your child the best experience consumes you because you may have seen your child suffer. Maybe it’s the anxiety of falling behind and not understanding. Maybe it’s the frustration of not being challenged and craving more. Either way, what you want is the same thing: a child who is happy, curious, and who genuinely understands. Because you know that understanding is what opens doors.

But as you research, you realise you have no idea where to begin. The options multiply. The advice contradicts itself. And you start to distrust your own knowledge to make this crucial decision in your child’s life. The weight is real, because you’re the one who made this call. You took your child out of a system that wasn’t working. If this doesn’t work either, that’s on you.

So you do what makes sense, you look for help. A Facebook group. A homeschool co-op. A parent who’s been at this longer. But what you get back is a list. Perhaps ten curriculum names or twelve links. But no one actually explains why. No one asks what your child actually needs. And you’re back to square one.

My experience across two decades, in classrooms, lecture halls, and curriculum meetings, showed me the same thing over and over: learning mathematics as a set of rules fails. Not sometimes. Universally. Rules can get a child through a test. But they don’t build understanding. And without understanding, the rules dissolve, leaving behind anxiety, confusion, and the quiet belief that mathematics is something you’re either born with or you’re not. Adults carry that belief for the rest of their lives. Many of you reading this may carry it now.

For a long time, I was part of the system that produced this. I believed what most educators believe, that if you give children enough variety, enough resources, enough different ways to see a concept, understanding will emerge. A key part of my role as a university lecturer and consultant was to analyse the classroom materials we use and evaluate how effectively they help children see the mathematics. And for years, I thought they were working.

Then I started noticing something I couldn’t ignore. The children weren’t seeing what I was seeing. When I looked at a resource, I could see the mathematical structure in it, the patterns, the relationships, the connections between ideas. But I had twenty years of accumulated knowledge behind my eyes. I was projecting that knowledge onto the materials. The structure I saw wasn’t in the resource. It was in me. The children were looking at the same materials and seeing something far more limited — disconnected activities, isolated procedures, surfaces without depth.

That realisation changed everything. I understood that more resources wouldn’t solve the problem. More variety just meant more surfaces and if none of them made the underlying structure visible, the children were simply looking at more shadows on the wall.

I was on a journey to close that gap. Then something changed. I encountered the work of Dr Andrew Waywood, and for the first time I saw the actual structure underneath. Not teaching strategies or better resources, but the grammar of how numbers relate to each other. The deep patterns that connect counting to place value to fractions to algebra. It was made visible, teachable and explorable for the first time.

Once I could see it, it was as bright as day, and I knew that if I could make it visible to children — through something they could touch, talk about, and explore — then everything I’d watched go wrong could be rebuilt from the ground up. So I did what I’ve always done. I drew it.

Here’s something worth sitting with for a moment. Mathematics has a grammar, just like language does.

When your child learned to read, they didn’t memorise every word as a whole shape. They learned phonics — the structure that connects sounds to letters. Once that structure was visible and teachable, reading changed for millions of children. Before phonics, we were asking children to learn to read without ever showing them how the code worked. Many couldn’t. It wasn’t because they weren’t capable. It was because the structure was hidden.

Mathematics has the same problem. There are deep patterns that connect everything. From the first time your child counts objects all the way through to algebra. Patterns a child can feel and explore long before they can name them. A child who genuinely understands why ten ones become one ten, and can feel that relationship in their hands, is already doing algebraic thinking. They just don’t know it yet.

But until now, no one had made that structure visible and teachable in the way phonics made reading visible and teachable. Andrew spent twenty years identifying the actual grammar of how numbers work. I spent fifteen years turning it into something a child could explore at a kitchen table, with their hands, through conversation and story.

The way it works is simpler than it sounds. Your child talks about what they see. They build it with their hands — on the beads, on the page, with the model in front of them. And they write it in numbers and symbols. All three happen together, not one after another. And all three are saying the same thing in different ways.

When what your child says matches what they build matches what they write, the understanding is real. And when they don’t match, that mismatch isn’t a mistake. It’s where the deepest learning happens, because the conversation that follows is the child working out why, and finding their way to coherence on their own terms. We choose to use comics to write our curriculum because a comic is a picture story or mini problem that invites a child into talking, doing, and writing arithmetic ideas.

I want to tell you what this looks like in practice, because the first time I saw it happen with a room full of children, it changed what I believed was possible.

Imagine that same scene again, but this time it’s just you and your child. You have the comic in your hands and you’re both conversing. You’re not in a classroom of thirty, you don’t have to follow a schedule, and best of all you don’t have to work to a bell which interrupts the thinking and learning. It’s just the two of you, sitting together and following a character’s thinking through a mathematical journey.

Your child reads. The character is working something out — trying things, getting stuck, trying again. Your child picks up the beads and builds what the character is building. You ask, “What did you notice?” And the conversation that follows is the mathematics.

Your child might work on one comic for two weeks. Not because it’s long but because the thinking is deep. Then you might choose to leave mathematics alone for a while. Come back to it when they ask. When they wonder. That might be a week, a month, or more.

Because the learning through this curriculum is solid, real, and memorable. Your child can pick up from where they left off at any time and take it up with ease.

Because once your child genuinely understands something — once they truly own it — it doesn’t need to be drilled every day. Extended, yes. Taken further, yes. But not repeated. Repetition without understanding is what makes a subject mundane. It is why the child who is struggling never moves forward — you cannot repeat your way to understanding you never had. And it is why the child who is advanced grows frustrated, because they already own it, and being asked to do it again feels like being held back from where they want to go.

You came to this article looking for help choosing a mathematics curriculum. What I hope you’re leaving with is something more useful than a recommendation — a way of seeing.

You now know what genuine mathematical learning looks like. Not worksheets completed. Not speed drills passed. A child who talks about what they see, builds it with their hands, writes it in symbols, and discovers that all three are saying the same thing. A child whose confusion is treated as the beginning of understanding, not evidence of failure.

You also know what it doesn’t look like. And if you’re honest with yourself, you may have already recognised it in some of what’s sitting on your shelf right now. Resources that keep your child busy without ever revealing the structure underneath. Curricula that move forward whether your child understands or not — the same pattern you took them out of school to escape.

We already know that curricula worldwide are failing our children. Mathematics scores continue to fall, even after content is simplified, even after new programs are introduced, even after billions are spent on resources that promise to close the gap. More of the same is not the answer. It never was. The scores aren’t falling because mathematics is getting harder. They’re falling because the approach never had a grammar — and without a grammar, no amount of simplification, repetition, or new packaging will make the structure visible to a child who has never been shown how to see it.

Here’s something I’ve come to understand, and it took me a long time to trust it even though I always sensed it was true: it doesn’t take as long to learn mathematics as the system has led you to believe. Place value does not need seven years of schooling. Fractions do not need eight weeks of isolated drilling — I watched classrooms dedicate exactly that, only to see every child flounder. The learning felt slow because the structure was hidden. When the grammar is visible and connected, children don’t need to relearn concepts year after year because the understanding was real the first time. Each idea builds on the last. What took years of circling back now takes weeks of genuine exploration.

I saw this in all its glory when we wrote our curriculum. Not as a theory. As a reality — child after child, classroom after classroom. Learning that was fast because it was deep. Understanding that lasted because it was built on a grammar, not a set of rules.

Every year a child spends learning mathematics without that grammar is a year the belief quietly grows that mathematics is not for them. That belief is not true. But it is very difficult to undo once it takes root.

Here is what that chance looks like: you and your child, sitting together with a comic and a string of beads. Your child reads. They build. They talk. You listen. You ask, “What did you notice?” And in that conversation, mathematics stops being something your child endures — and becomes something they explore.

That’s what we built Linear Abacus to make possible. A complete mathematical grammar — made visible through comics, explorable through conversation, and designed from the beginning for a parent and child working together at a kitchen table.