We need better math games
(or: This music has a great beat. Why isn’t everyone getting up and dancing?)
The idea that math could ever be fun or interesting is, for many kids, something that was drained out of them years ago. Young children may still be open to it, but plenty of teenagers have more than a decade of hating math behind them, and that’s hard to undo.
“But not in my class!” I over-confidently thought: “I have a whole bunch of fun and interactive math activities lined up. Watch as I transform jaded math-phobic teenagers into excited and engaged learners!”
Spoiler alert: it turned out to be harder than I thought. I gave the kids math activities that, to my eyes, were simply wonderful. And they just weren’t that into them.
“I think these activities are great. Why aren’t the kids feeling the same way?”
If you enjoy math, then it can be hard to understand why other people don’t feel that way too. “Hey, look at how these different ideas come together! Isn’t that surprising, and wonderful?” “Look at this really intriguing math problem, doesn’t it just make you want to solve it?”
“Oh, you don’t? But look, it’s so cool, don’t you see? Huh, still no? Erm… ok, now what?”
Here’s an analogy which, I’m guessing, might be easier for math-loving folks to relate to. Imagine you’re at a party or a wedding reception, and high-energy music starts playing. Your dance-loving friend tries to pull you onto the dance floor, but you resist. “Doesn’t this music just make you want to get up and dance?” exclaims your friend. Well, no, actually it doesn’t, at least not often for me. Dancing may come naturally for some people, but not me. An old saying tells us: “Dance as though nobody is watching.” Well, people actually are watching, and I feel self-conscious. I’m no good at dancing. I’m just not a dancing person. Thanks, but I think I’ll sit this one out.
That’s how most people feel about math. If, like me, you’re a math teacher, then this problem confronts you every day. You can try to engage students with math problems and activities that you think are fun, but, alas, that fun is not something that they are feeling. And just like when your friend says to you, “Doesn’t this music just make you want to dance?”, well, it just doesn’t. What’s to be done?
Interactive online math tools to the rescue?
Luckily, these days several wonderful interactive online math platforms exist. Amazingly, they are free. Amongst the very best are Mathigon, Geogebra and Desmos. Desmos was originally a web-based graphing calculator, but it has expanded into offering a wide range of interactive math activities. You can browse a selection here: teacher.desmos.com
These activities invite active exploration. They are beautifully designed and fun. They transform math from being intangible into being hands-on. They allow kids to play around with math concepts, to try stuff out and see what happens. There’s even an integrated teacher dashboard that allows you at a glance to see how all the kids in your class are doing.
However, in my experience as a math teacher even these activities, which seem great to me, are not enough.
Kids don’t want problems or activities. They want games
Everybody loves to play a good game. And as for kids: playing games on their phones is all they want to do. Sometimes it seems impossible to get them to do anything else. Just look at how Wordle took the world by storm. I know some teenagers who hate school and who never read books, but who are absolutely hooked on Wordle.
Activities can be interesting, but games can be exciting. We all crave excitement, kids especially so. We need more and better math games.
What is the special ingredient that turns a mere activity into a game? There’s probably no single answer to that question, but I think this element is important: to feel like a game, there has to be something to battle against.
Games require some sort of battle. That’s ok, as long as losing does’t hurt
As a teacher, I’m painfully aware of how often math has been a source of anxiety and frustration for my students. I don’t want that to happen in my classes. So, I tend to be wary, perhaps too much, about applying time-pressure or instigating peer-competition. However, from talking with my students I’ve come to learn that kids actually enjoy time-pressure and competition, as long as there’s no downside risk.
As soon as there is a risk of a negative outcome, the fun disappears. For example, applying to colleges involves time-pressure and competition, but very few people find that to be fun.
The next time you see a kid glued to a game, try to take a peek at what they are battling against. It might be working to defeat another player, or racing against the clock, or fighting off attacks from mobs, or trying to beat a high-score, or struggling to guess a word before all six chances have been used up. The type of battle may vary, but there will be one. Without any such battle, it’s no longer a game.
Why math problems and activities are not enough
That, I think, is the reason why math problems and activities are not enough. There’s nothing to battle against. If a student happens to have been hooked in by the problem and is itching to solve it, then that’s great. If they feel that urge to solve, then that gives them their battle, and no additional gaming element is required.
However, that’s a big if. A lot of kids simply won’t feel that itch to solve the problem. That doesn’t mean they’ll never be able to feel it, or that they are at any fault. Probably, alas, the idea that math could ever be interesting was drained out from them years ago. Years of math-induced pain and frustration have built up a thick callus of resistance. Hopefully that damage can be undone, but even if it can then it will take a long time.
So, we give students math problems and activities that, to us, seem great. But many of the students are left cold, and as teachers we struggle to understand why. Just like the friend who can’t understand why we don’t want to join them on the dance floor, it can be hard for us to see why kids are not finding an activity engaging. But all too often, at least in my experience with math-jaded teenagers, they do not find the activity engaging. We need to give them something better.
Lots of math games already exist. Problem solved, right?
Ok, so kids don’t always like math problems or activities, but everybody likes games. So, all we need to do is to turn the math into a game. Gamification! That’s learning solved. Easy, right?
Obviously, things haven’t turned out to be that easy. But why not? Typing “math games” into the App Store search box yields hundreds of shiny-looking hits, and it’s clear that many of them have had a lot of thought, effort and creativity put into them. Why, then, are kids still struggling to learn math?
Why is it so hard to make math games that actually help kids learn?
Here’s the ideal:
1. Start with a confused and math-phobic kid.
2. Give them a math game to play with.
3. Watch their understanding of math grow in leaps and bounds, while they are having fun.
But that doesn’t seem to end up actually happening. What is going wrong? Here are some obstacles that immediately start showing up:
Problems that prevent math games from succeeding
1. The math is not really part of the game-play
- In too many existing math games, there’s a math component and a game component sandwiched next to each other, but they remain fundamentally distinct.
For example: an arithmetic problem gets presented onscreen, and if the child clicks on the correct answer then a little animal does a dance. But this is just normal math, with candy sprinkled on top. The candy, not the math, is the real attraction. The popular web-based quiz platform Kahoot suffers from a similar problem. Kids really enjoy Kahoot, and plenty of pre-made math Kahoot quizzes already exist online, ready to play. However, the fun game-like parts (the friendly competition, the animated graphics, and the ever-changing leaderboard) are quite distinct from the actual math. That usually consists just of standard problems, often pasted straight from a textbook.
Needed instead: the math must be at the core of the gameplay itself.
2. Kids don’t know how to start
- When confronted with a math problem, whether in a game or in a traditional classroom setting, many kids do not know how to start. They hunt around in their list of half-remembered meaningless-seeming rules, and try to find one that looks like it might fit. But often no rule seems to fit, or the rule that sprang to mind turns out to hit a wall. And then the kids are stuck.
For a game to be engaging, there always has to be some sort of next step immediately available, even if you don’t know whether that step will actually succeed. You might not know what the right move is, but at least you feel that you can move. In math class, and also in math games, kids can feel paralyzed. That’s not a good feeling at all.
Needed: To be accessible, any math game must have a very gentle on-ramp. It can become harder after that, but getting started needs to be as smooth and painless as possible.
3. Kids don’t feel in control
- Getting stuck is ok, if you have control over the situation and can get yourself unstuck whenever you want. However, kids rarely feel that they have that power: definitely not in math class, and usually not in math games either.
To borrow an idea from an advertising campaign: math games need “an easy button”, available when needed, but active only when it is wanted. Conversely, in order to stay challenged, kids also need to be able to make the game harder, as soon as they feel comfortable doing so.
Towards a good enough math game: an initial attempt
To summarise the above, here’s the goal: a math game that is actually fun to play, in which the math is central to the gaming aspect rather than being awkwardly bolted on, and which is extremely easy to start but can be made harder by the player as their comfort level increases.
During the past year of my work as a school math teacher, I have started trying to make such games. They are made in Desmos, because it’s a powerful web-based math platform that has nice class-management features already built-in. Below I describe one initial game attempt: straight-line graph space invaders. It’s doubtless very crude compared to what is potentially attainable, but from watching kids in my classes play the game, I think this sort of approach shows promise.
Here’s a link to the game:
The straight-line equation y = mx + b
Seen through adult eyes, it can be hard to understand how this seemingly simple representation of a line can cause so much bafflement and frustration to school-kids. But, oh, it certainly does. The pain of seeing them struggle with it is heightened by knowing that so much wonderful and powerful mathematics is, at its core, really just glorified y = mx + b. Matrices and linear algebra, regression and much else in statistics, derivatives as the slopes of lines tangent to curves. That one simple formula carries with it the keys to all those kingdoms and more.
How the space invaders game tries to incorporate the key features
In brief, here is how the game tries to incorporate the key features that were laid out above:
1. The element of battle
- You need to blast the space invader before it reaches you. You are battling against that time pressure (although, crucially, that pressure starts very gently). There are also elements of competition: a class-wide high-score is shown (using the “aggregate” function of Desmos’s Computation Layer) which you can try to beat, as is each player’s own personal best high-score. The battle is risk-free: if you lose, you can simply play again.
2. The math is the game play
- Solving the math problem and blasting the space invader are one and the same act. You blast the space invader by pointing your ship along the invader’s line, and you do that by typing in the y = mx + b equation with the correct slope and intercept.
3. A very easy on-ramp
- In its default initial state, the alien moves very slowly. Moreover, the slope and y-intercept of its line are literally shown onscreen. In this easy default state, the player could simply transcribe numbers from one part of the screen to another, without any understanding of the actual math. However, the player can move beyond that initial set-up, whenever they feel comfortable doing so.
4. Player-control over the difficulty, with incentives for ramping it up
- The player can choose how easy or hard to make the task. There is an incentive for choosing the harder conditions: you get to score more points for each successful blast. This can be done by making the alien move faster or, in the more mathematically interesting case, by hiding the onscreen display of the slope or intercept values, or both.
Some initial feedback from teens: the game is fun
This year I have been teaching 11th and 12th-graders, who are a few years older than the target audience for this game. Nonetheless, I’ve run it by them, and their feedback has been encouraging. They’ve told me that it’s fun to play, and that they wished they’d have had access to this sort of game when they were learning y = mx + b for the first time.
Some of my students have also told me that really like this more interactive way of learning math, and that it has been better for building up their understanding than the old approach of memorizing of techniques that they were used to. Traditional ways of teaching math have not led to stellar results, especially not in the US. It’s time to try different approaches, and math games strike me as a very promising direction to explore.
An essential ingredient, still missing: the game must work on a phone
In its current form, the game works fine on a laptop screen, but not yet on a phone. There isn’t enough room on a phone screen to display the play area and the text-entry area at the same time. That’s a big problem. It’s an especially bad problem for any game aimed at teenagers, because their phone is their world. If the game doesn’t work on a phone, then it might as well not exist.
Fixing this will probably require a small backend change in the Desmos mobile app. At present, the only type of onscreen keyboard that it offers is the standard graphing-calculator one, which includes options to type π, exponents, different types of parentheses, and a wide range of math functions. That’s great, if you need those tools, but they take up an unnecessarily large amount of phone-screen real estate if all that you need to type is some version of y = mx + b. An option to show a stripped-down version of the standard Desmos keyboard might make phone-compatibility a lot easier to achieve.
Goal: math at the heart of the game, and kids actually wanting to play
I hope, one day, that teachers of other subjects will get mad at me. “Hey,” they’ll say. “I keep on needing to confiscate the phones from kids in my class. They’re hiding their phones under their desks, thinking I don’t notice. And do you know what they’re trying to play? Your damn math games. They’re hooked on trying to beat each other’s high scores. Are you happy now?”
Yes, I’d be very happy indeed.
