**Same maths, different medium: Where video games are getting it wrong**

## Making good on the promise of game-based learning

Video games ought to be the perfect medium for rescuing the learning potential of mathematics. School maths continues to haunt students with symbolic representations that both uglify and mystify the subject beyond recognition. In principle, video games afford learners rich, visual representations of maths that appeal to our intuitions and allow us the freedom explore mathematical concepts. Many have mused thus:

- Papert envisioned of the thousands of forms of functions of computers that would place the student in control of their learning as they explored their digital environment — the child would be the programmer not the programmed.
- Keith Devlin recently devoted an entire book to the prospect, unpicking the affordances of video games as a medium for illuminating concepts in ways unachievable through static textbooks. Equally important is the context in which these representations are presented — mathematical thinking must be situated within the gameplay, with concepts blending into the environment.
- Jordan Shapiro writes that “games force players to interact with problems in ways that take relationships into account.” Surely then, games are the perfect arena for probing the patterns and structure that underpin mathematical concepts.
- Adventure games are an especially good match for mathematics. Pascal Luban explains that such games are built on a steady stream of puzzles, encouraging players to probe the inner working of their virtual world. Now insert
*maths problems*in place of puzzles (they are synonymous, after all).

With so much written about the virtuous intersection of video games and mathematics, it is disheartening to see so many game developers neglect the potential of their medium for instruction (and indeed construction):

I will call out three examples (among many):

- Operation math — billed as a ‘global learning adventure’, this glorified mental maths practice app would have you believe you have taken on the role of a spy, cracking over 100 missions around the world by putting your mental maths skills to use. The production value is stellar — the speed and sound of gameplay may even get you buzzing for a while. But let’s be clear: real spies don’t crack safes by executing their times tables. No
*safe*in the world would justify its name if it yielded to the bluntness of mental maths. The desperation to engage students in an engaging narrative results in a missed opportunity to inspire them with the richness of number. At worst, it warps their perception of real-world problem solving — as if mental maths is the NSA’s key recruitment criteria.

- Math Ninja — the name sparks visions of Neo emerging from his training in The Matrix to declare ‘I know kung fu’. Instead, the ‘math’ is divorced from the ‘ninja’. A procession of mental maths tasks serves only to arm your character (yes, a ninja) with pellets to fire at his tomato-shaped enemies. It has nothing on games like
*Countdown*and*Prime Climb*in either a) fostering both fluency and understanding of numbers or b) developing the player’s confidence and agility with number operations. A renaming may be in order.

- Mathmateer —
*build your very own rockets and take them to the stars*is the promise. Disjointed maths problems are your helping hand. Mathmateer spans a range of maths topics, from*counting*to*telling the time*, that have no discernable link to the mechanics of your rocket. Rather than embracing the overlap between maths and physics, the game slaps together an arbitrary space theme with even more arbitrary mathematics.

These games fall victim a sloppy juxtaposition of abstract mathematics and the game environment. They reinforce the most wretched, static representations of mathematics — the very same you will find in print and that turn so many students away from the subject. The mathematics remains rooted in the narrowness of procedures and timed performance. The engagement is suspect, appealing to shallow gameplay that is divorced from the actual mathematics. Luban advises that “goal puzzles should enrich the adventure instead of being an excuse for it.” The developers did not get his note.

Many games are motivated by the formal requirements of school mathematics, and forcefully emulate the look and feel of the standard maths curriculum. Game-based learning will only bear fruit when deliberate pedagogy, predicated on the dynamic, visual representations afforded by digital, seamlessly combines with interactive gameplay.

Learning programs such as *Motion Math*, *Dreambox*, *Maths-Whizz* (disclaimer: I am employed by Whizz), *ST Math* and *Zorbit’s Math* all make serious effort to bring maths concepts to life using interactive animations. All flirt with game-based learning. Wuzzit Trouble represents gaming from start to finish and, with Devlin’s help, subtly embeds elements of problem solving, number sense and linear algebra. How readily the approach scales to other areas of mathematics remains to be seen.

Balancing pedagogy and gameplay is no straightforward task. Guidance is available — perhaps too much. James Gee lists no fewer than 36 principles for learning through games. But theory alone does not suffice. Super Math World carried more pedagogical intent than any game I have encountered, fostering number sense within an immersive gaming environment whose dynamics governed by number properties. The pedagogy is sound, the learning goals clear. The gameplay, sadly, is clunky, falling way short of the smooth experiences players now demand. Citing a lack of funding, the creators of Super Math World recently announced a scaling back. A reminder that game-based learning relies on execution as well as intention.

Where does that leave us? The one principle for game-based learning that I would impress on maths app developers is this:

*Integrate mathematical representations within your gaming environment*.

More specifically: avoid the sloppy juxtaposition by ensuring mathematical tasks arise as a natural consequence of gameplay. Embed maths problems into the environment. Ensure the problems are a coherent driver of gameplay rather than a distraction. And only introduce symbols in their proper context of modelling one of these problems.

I have undoubtedly missed out some exemplars of game-based learning in maths. Please point them out to me; I am always keen to discover and play with maths apps that strive for the right blend of pedagogy and gaming.