# Game-based math learning can open up new educational possibilities

One question we get asked from time to time from people who have enjoyed playing our launch app *Wuzzit Trouble* is whether that puzzle is part of our new BrainQuake app. The answer is a “Yes, but …”

*Wuzzit Trouble* was a standalone mobile game that presented players with 75 puzzles based on a digital gears mechanic. Based on very positive critical reviews and two independent, peer-reviewed, comparison-group university studies that showed the game led to substantial learning gains (see the Research page on our website), we applied for, and were awarded, a 2.5 year, $1.1M federal grant from the US Department of Education, which enabled us to expand our original product to something far more substantial.

As a first step, we modified the original *Wuzzit Trouble* game to operate with an adaptive engine that drew on a large database of puzzles to match the difficulty of the puzzles presented with the player’s current ability to solve them. (So in the new app, players encounter many more “Gears” puzzles, and different players will encounter different sequences of “Gears” puzzles that are at the upper limit of their ability based on their performence so far.)

Following successful classroom trials of the “Gears” puzzle with an adaptive engine, we embarked on the design and construction of two additional puzzles covering more areas of mathematics, that drew on the same adaptive engine, and we developed a real-time, comprehensive formative assessment that provides feedback through our proprietary, multi-dimensional *BrainQuake Score*.

The entire system is presented to the player (student) by way of a “World Map”, a familiar game-interface where progress and navigation are handled by moving along a geographical path through various regions. (See image above.)

The three puzzles, *Gears*, *Tiles*, and *Tanks*, are built on integer arithmetic and algebra, on linear growth and algebra, and on proportional reasoning and fractions, respectively. *Gears* is the greatly expanded version of the *Wuzzit Trouble* puzzle. But (and this is the “but” or our “Yes, but …” response) we did more that put in an adaptive engine and change the visual design. We also added some additional features that, in addition to being fun variants of the puzzle, provide valuable new learning experiences.

For example, take a look at the following video clip of the screen display when I was playing through the *BrainQuake* app.

From a game perspective, having drive-cogs that disintegrate after one or more uses is a fun additional feature. But it is far more than that. When one or more drive cogs has a limit on the number of times it can be used, it forces additional attention on order of operations, and requires a more algorithmic approach at solution.

Even with *Wuzzit Trouble*, we already required attention to these features in order for a player to gain maximum points by capturing all bonus items (and avoiding dangerous items). But the new breaking-cogs feature ups the ante by requiring attention to order of operations is order to complete the puzzle at all!

The breakable cogs do not appear very frequently; they are intended to be a game variation. But from a learning perspective, we can (and do) deploy them at appropriate levels in order to ensure the player (student) has to pay attention on some particular mathematical notion.

For example, players early in their mathematical education frequently rely on additive thinking, repeating a single cog rotation several times; but faced with a cog that will break after one use, they will be forced to use the multi-rotate feature, i.e., multiplicative thinking.

This particular example provides just one example of the myriad of occasions where video games open up learning possibilities that traditional educational media do not. It would of course be possible — in theory — to present students with, say, an equation to be solved and stipulate that as they manipulate the equation they can multiply by 5 at most once. But such a restriction would seem bizarre, and students would naturally regard it as ad hoc and pointless. In the *Gears* puzzle, it is perfectly plausible that the occasional cog has developed cracks and is likely to fail. Indeed, mechanical parts do develop metal fatigue that renders them likely to crack and break apart.

But pedagogy aside, most players who have experienced the new *BrainQuake* app have simply found the breaking cog feature in *Gears* to be a delightful twist to a puzzle that had already drawn accolades when it first appeared as *Wuzzit Trouble*.

– Keith