Solving the Ultimate Math Problem

3 min readApr 11, 2020
The Gears puzzle. A learner-friendly interface to mathematics that breaks the Symbol Barrier. Photo by BrainQuake.

On the BrainQuake website, we call it “the Ultimate Math Problem.” In my 2011 book about math education video-game design I called it “the Symbol Barrier.” That name is mine, but I got the idea from a landmark 1993 book called Street Mathematics and School Mathematics, which described the results of a study three education researchers conducted in the busy street-markets of Recife, Brazil.

You can find a description of the study in my book, and in a ten-minute video I produced to explain how the street mathematics phenomenon was the inspiration for our launch app Wuzzit Trouble, released in September 2013. For now, let me cut straight to the chase: when ordinary people are faced with performing some kind of mental mathematical task in their daily lives or work on a regular basis, they rapidly become proficient at it, performing at a 98% accuracy level. Yet when presented with the very same kinds of problems expressed in the traditional symbols of mathematics and asked to solve them using paper-and-pencil, their accuracy drops to an astonishingly low 37%.

It’s not that they cannot do the mathematics. Indeed, they can do it in their heads, in busy, noisy environments. Rather, the problem they have learning traditional math is one of language and abstraction. When I read about that finding some time in the late 1990s, my research interests as a professional mathematician shifted immediately to incorporate a focus on mathematics learning. A few years later, my educational work led to me being hired as a math consultant to an educational video game company, which brought me into contact with a small group of highly talented individuals that in time led to the creation of BrainQuake.

Tiles puzzle. The tiles are learner-friendly representations of linear functions. Photos by BrainQuake.

Our goal was to design and build — and subject to rigorous, independent efficacy studies — quality video games that provide learning experiences that break the symbol barrier, by using familiar video-game objects such as gears, sliders, tiles, and the like as representations of mathematical concepts alternative to the traditional symbols. This makes it possible for learners to engage with mathematics without the need to first master the symbols, as was the case with the child stallholders in the Recife street market.

Once someone has learned how to do the mathematical thinking, they can then turn to mastering the symbolic approach as a separate challenge. In other words, BrainQuake recognized that learning mathematics involves two challenges, one of thinking a certain way, the other mastering a new language, and designed video games that separate those two challenges into two parts. [In a subsequent blog, I’ll talk about how we address the second problem —subsequent mastery of the symbols.]

Tanks puzzle. We use different shaped valves with different numbering systems to yield deeper understanding. Photos by BrainQuake.

The educational power of this approach becomes clear when you see how, by presenting mathematical problems with a different representation — a different math interface, if you will — upper elementary and middle-school students are able to solve problems typically left to high school or beyond.

The images of the Gears, Tiles and Tanks puzzles shown here demonstrate that dramatically. And make no mistake about it, the computing device the game runs on does not solve the problems; the player does. Indeed, they solve the problems using the same logical steps as they would if they were working in the traditional format. The only difference is the language used to represent the problem and to take those solution steps. Breaking the Symbol Barrier works. What’s more, there is independent research to prove it, which I’ll talk about in future posts.

– Keith