I’ve been drawing since I was a child. Pencil sketches, oil paintings, illustrations made for the pleasure of making them. When I drew Galileo at nine years old, I wasn’t thinking about mathematics. I was following curiosity onto the page.
So when it came time to show what genuine mathematical exploration looks like — what it actually feels like to wrestle with a relationship, get it wrong, try again, and finally break through — I did what I’ve always done. I drew it.
What emerged was something that hadn’t existed before in mathematics education: a comic that doesn’t illustrate mathematics from the outside, but lives inside it. Where the character’s thinking — including the wrong turns — is the curriculum.
The Linear Abacus Manual alongside the comic explorations — designed to be used together
Why Comics? Why This Kind of Comic?
There is a reason children love comics, and it has nothing to do with pictures making things easier. A well-made comic is cognitively demanding. You navigate the page. You infer what happens between panels. You hold multiple threads simultaneously. You move back when something earlier clicks into new meaning.
These aren’t simplifications of thinking. They’re forms of thinking.
Our comics ask children to read both horizontally — moving through the panels of a story — and vertically, returning to earlier moments in the book as later ones recontextualise them. A child who reads page 230 may suddenly understand something differently about page 218. The mathematics isn’t delivered in a sequence. It accumulates. It deepens. It becomes something the child has genuinely inhabited, not merely received.
Tina Smith described teaching her children algebra through storytelling — breaking word problems into narratives, asking her children to visualise and draw before working with the mathematics. “This is a problem, this is a story,” she would say. “Break it up. Visualise it. Draw the picture. Now work the maths out.” This is exactly the instinct our comics are built on: story first, structure second, symbols third — all in conversation with each other.
Inside the explorations — each page follows a character thinking, getting it wrong, and breaking through
A Closer Look: What the Pages Actually Show
Let me walk you through what a child and parent encounter when they open one of our explorations — not in abstract terms, but in the actual sequence of experience.
Inside the Exploration: Multiplying Fractions
The story comes first
Before a single calculation appears, the reader meets a situation: Jack has ¾ of an apple. He gives Jill ⅓ of what he has. How much of the original apple does Jill get? The character thinks aloud, translating the words into a mathematical question: ¾ × ⅓ = ?
The tool makes it visible
The character moves to the Linear Abacus. Four beads represent the whole apple. Three of them represent Jack’s share. Now: how do you find ⅓ of those three beads? The child beside their parent can do the same with their own abacus — feeling the relationship in their hands while following the character’s thinking on the page.
The character searches systematically, and keeps going
The exploration moves to a harder problem: ¾ × ⅘. The character needs to find ⅘ of ¾ — but to do that on the abacus, the 3 beads representing ¾ need to be divisible into 5 equal parts. They aren’t. Not yet.
So the character searches for an equivalent fraction. They double the beads in each quarter — now 8 total, 6 representing ¾. Still can’t divide 6 into 5 parts evenly. They triple — 12 total, 9 representing ¾. No. Four times — 16 total, 12 representing ¾. Still no.
Each attempt is shown in full on the page. The frustration is visible. But this isn’t random trial and error — the character is doing something mathematically precise: hunting for a multiple of 3 that is also divisible by 5. They just don’t know that’s what they’re doing yet. The abacus is forcing the question into the open.
The breakthrough arrives — earned, not given
Five times: 5 × 4 = 20 beads total, meaning 15 beads represent ¾. And 15 divides into 5 equal parts — 3 beads each. The structure finally yields. “PERSISTENCE PAYS OFF!”
But notice what the character has also discovered along the way: a string of equivalent fractions — ¾ = 68 = 912 = 1216 = 1520. They weren’t looking for these. The search produced them. The comic makes this visible with the line: “It’s pretty cool that I’m finding all these equivalent fractions along the way!”
The grammar becomes visible
The final pages don’t just show the answer — they show both the strategic method and the standard algorithm side by side, with the insight: “Both approaches show the same grammatical relationships.” The child isn’t being told which method is correct. They’re being shown that both methods express the same underlying structure.
The Framework Behind Everything
Talk Do Write · Not a Sequence. A Living Triangle.
↕ all three happen at once, each illuminating the others ↕
Most mathematics approaches treat these as stages — first concrete, then representational, then abstract. Our framework treats them as simultaneous. The talking shapes what the doing reveals. The doing changes what gets written. The writing opens new questions for the conversation.
This is grounded in Dr. Andrew Waywood’s discovery that mathematical concepts are fully grasped only when a child can simultaneously build a model, interpret a word problem, and perform a calculation — moving fluidly between all three, not arriving at the last one after completing the first two.
The comics make this possible. The character models all three at once — narrating their thinking, manipulating the abacus, and moving toward symbolic notation — so that the child reading alongside them can do the same.
Microwriting: The Conversation Guide
A New Concept · Developed by Linear Abacus
What to say. When to stay silent. How to follow the child’s thinking.
Accompanying each comic exploration is what we call a Microwriting guide — short, precise prompts that help parents and teachers facilitate the conversation without leading it.
Not “here’s the answer.” Not “now explain fractions.” But: “What did you notice when the character tried tripling?” Or: “Can you show me on your abacus what happened just before the breakthrough?” Or simply: “What do you think comes next?”
Microwriting gives the parent something the worksheet never could: a way into the conversation. A place to stand. A set of questions that reveal structure without giving it away — that honour the child’s thinking rather than replacing it.
This is what homeschooling parents do naturally in every other subject. Microwriting makes it systematic for mathematics.
What Parents and Teachers Actually Report
When I first introduced these explorations in classrooms, the teacher responses surprised even me. Not because the children improved — I expected that. But because of what teachers said about themselves.
Cindy, a Grade 1/2 teacher, described it this way: “Through using the Linear Abacus and participating in professional learning, I began to see the ‘why’ behind the concepts. For the first time, I felt like I was genuinely teaching mathematics, not just delivering it. That shift transformed my confidence. My enjoyment of maths grew alongside my students’, and they became more engaged, curious, and willing to explore different strategies because they could see connections.”
From homeschooling families, the shift was just as pronounced. Carolina described the change in her children: “Our son had been quite behind and often lacked confidence. Since starting with Linear Abacus, we’ve seen huge improvement — not only in skills, but in attitude. He’s gone from feeling overwhelmed to actually enjoying maths and wanting to learn more. Our daughter used to find maths stressful, but now she loves it.”
“I like the Linear Abacus because it makes me learn easily. I can even measure myself using it!”— Rubani, student
What Rubani describes — learning easily, finding new uses, exploring beyond the lesson — is what happens when the grammar becomes visible. When the tool grows with the child. When the conversation doesn’t end when the comic does.
The Parent as the Hero of This Story
I want to be clear about something. The comics, the abacus, the Microwriting guides, the grammar — none of these replace you. They exist to support you.
You are the one who sits beside your child. You are the one who notices when they’re stuck and stays with them rather than reaching for the answer. You are the one whose curiosity — genuine or performed — gives your child permission to be curious too. You are the one who makes the kitchen table a place where thinking is valued.
Jamie Heston put it exactly right: “You’re not pouring knowledge into an empty vessel. You’re working alongside them. You’re facilitating.”
The framework we’ve built exists so that you can facilitate mathematical exploration the way you already facilitate everything else — through conversation, through presence, through following the child’s thinking wherever it leads.
You don’t need to be a mathematician. You need to be the person in the room who finds the question genuinely interesting. That’s everything.
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You don’t need to be a maths expert.
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