A simple test for whether the math is really part of the game
What happens if we remove the mathematics from a math game? Not permanently, just long enough to see what remains.
It’s a genuinely interesting question, not a loaded one. Some of the most popular math products in the world have done something remarkable: they have made children want to do more mathematics than they might ever choose to do on their own. That is worth sitting with before anything else.
But wanting to play and wanting to do mathematics aren’t always the same want. Sometimes they point in the same direction. Sometimes one is just borrowing the other’s energy for a while.
Here’s a simple way to tell which is which.
The mathematics removal test
The test is simple: remove the mathematics. Does essentially the same game still exist?
Imagine a game where a player battles an opponent. Before each attack, they answer a math question. Now remove that question. The battle still happens, the opponent, the outcome, the sense of winning or losing, all of it survives. Swap the math question for a spelling word or a trivia fact, and the game barely changes shape.
The mathematics is important to the experience. But it’s interchangeable within it.
Now imagine a different kind of game. The moves available to a player are determined by number relationships. Understanding factors, probability, equivalence or structure changes what a player can see and what they can do. Mathematical choices create the risks, the openings and the consequences.
Remove the mathematics from that game and nothing meaningful remains, no moves, no strategy, no game.
The mathematics isn’t content placed inside the system. The mathematics is the system.
Three different relationships between mathematics and games
There are many good ways to use games in education. It helps to separate three broad approaches.
Mathematics around the game. Students earn points, badges or leaderboard positions for completing questions that could otherwise sit on a worksheet. This is usually called gamification. Motivation matters, feedback matters, a sense of progress can help students persist. But the mathematics and the game mechanics stay largely separate, the student completes the mathematics, then receives a reward.
Mathematics as the gate to the game. Here, a correct answer unlocks the fun part, the attack lands, the door opens, the turn continues. Mathematics has a more active role, it allows the game to continue rather than simply earning points beside it. But the relationship is still sequential, first the mathematics, then the game. If the questions could be swapped for another subject without changing the core experience, the mathematics still isn’t what’s generating the play.
Mathematics as the game system. Here, mathematical relationships determine what actions are possible and which choices are effective. The player isn’t answering a question before making a move, the mathematical decision is the move. Understanding the mathematics changes a player’s agency, what they can see, anticipate, defend against or build toward.
Much of what we currently call game-based mathematics sits in the first two categories, and for understandable reasons, they work. They have earned real, hard-won engagement from millions of children who could easily be doing something else with their time.
The third space feels different: less crowded, harder to build in, and still surprisingly underexplored. Imagine what becomes possible there.
The alignment of motivation
This distinction matters because each model creates a different relationship between motivation and learning.
When mathematics is the gate to a game, a student’s immediate goal may be to get through the mathematics so the enjoyable experience can continue. The game provides the motivation. The mathematics can become something to complete on the way back to the experience the student actually came for. Students may still learn, recall may improve, accuracy may improve, valuable practice may happen, but the game and the mathematics are still pulling on different parts of the experience.
When mathematics is the game system, something changes. Deeper mathematical understanding gives the player more power within the experience itself. Seeing more relationships means seeing more moves, greater fluency creates more options, stronger mathematical judgement helps a player anticipate, defend, build and respond. Better mathematics makes you a better player. The motivation to get better at the game and the motivation to get better at mathematics start pointing in the same direction.
That’s the crucial distinction: in one model, mathematics purchases access to the fun. In the other, mathematics creates the possibilities within it.
What becomes possible?
A question-based game can be genuinely effective for retrieval and repetition. But when mathematical structure creates the gameplay, a different kind of learning becomes available.
The player isn’t only retrieving knowledge. They’re choosing when and how to use it, comparing possibilities, predicting consequences, testing ideas and adapting when things don’t go as expected. They’re learning that mathematical knowledge isn’t simply something to recall. It is something to use.
A student might know that 7 × 8 is 56. That matters. But a richer kind of fluency appears when the student recognises when 56 is useful, how it connects to other possibilities, what choosing it might make available and whether a different choice would be stronger. The knowledge has moved from recall into judgement, and that’s difficult to build through a sequence of isolated questions, even beautifully designed ones.
The game doesn’t need to hide the mathematics
There’s sometimes an assumption that children will only engage with mathematics if we conceal it. Wrap the learning in characters and rewards, build an entertaining world around it, hope students tolerate the mathematics because the experience surrounding it is fun.
That can help. But it also risks quietly communicating something unintended: the mathematics is the part you endure to reach the fun.
What if the issue isn’t that children can see the mathematics? What if it’s that they’ve too rarely experienced mathematics as something playable in its own right? Mathematics already contains many of the qualities that make games compelling, patterns, constraints, trade-offs, surprises, multiple paths, risk and consequence, moments of insight. The task isn’t always to hide these things beneath a game layer. It’s to design experiences that reveal them.
A design question for the sector
Before asking whether a math game is engaging, it’s worth asking where the mathematics is actually happening. Is it present in the questions? Is it used to unlock rewards? Or does it shape the player’s decisions?
Try the removal test. Would the same characters, levels, battles and rewards carry spelling questions tomorrow without changing anything that really matters? If so, that may be an engaging delivery system for mathematical practice, a legitimate and useful thing to have built. It’s just a different achievement from making mathematical structure itself playable.
And this distinction matters when we think about learning. Students may be visibly motivated, they may ask to use a product again and again, and that matters too. But engagement alone doesn’t tell us what they’re becoming better at. Are they getting faster at isolated questions, building stronger recall, persisting for longer? Or are they making richer mathematical decisions and seeing structures and relationships they couldn’t see before? A game may support several of these outcomes at once, worth examining them separately rather than assuming engagement means all of them are happening.
One approach encourages students to answer more questions. The other can encourage them to think harder about which mathematical idea to use, and why.
Designing from the mathematics outward
Many educational games begin with a familiar entertainment structure and then look for places where mathematical questions can be inserted. There’s another way in.
Start with the mathematics itself. Ask what decisions this mathematical idea makes possible, where the natural tensions and trade-offs are, what one player could anticipate about another, what changes when one student sees a relationship another one misses, what choices could have visible consequences, and what would make a player want to test a better strategy next time.
It’s a harder design process. It’s much easier to attach questions to a battle than to build a compelling battle out of mathematical structure. But the result can do something a bolted-on question never quite manages, the student stops switching between learning and playing. The learning happens through the play.
What happens when we remove mathematics?
So, what happens if we remove mathematics from a math game?
Sometimes, almost everything survives. The characters continue their journey, the rewards and progression carry on, the battles still work, the game simply needs a new set of questions. That’s a game that delivers mathematics, and it can still be a genuinely useful thing to build.
But sometimes, removing the mathematics causes the moves to disappear, the strategy to disappear, the tension to disappear, and the game stops making sense on its own terms.
In those cases, mathematics hasn’t been delivered by the game. It has become playable.
That’s a far more ambitious design goal. It may also be one of the most interesting open spaces in game-based learning, one we have only begun to explore.
