Logical Leaps: When Math is Out of Context

When we first started building a math game, we thought it would be easier compared to other subjects since we wouldn't encounter any discrepancies in interpretation. (Imagine trying to tackle a history game!) After all, mathematics is supposed to be the universal language -- a common tongue spoken across diverse cultures with little variation (even though the level of literacy may differ). We figured that we would do all the fun, creative game design stuff and leave the math-y heavy lifting to our code. Mathematics = calculations, and therefore the computer can handle the execution because the answer can only be right or wrong. Right?

Wrong.

Here's the thing -- math is not just about performing calculations, and neither is it a universal language. We have merely come up with a near-uniform set of symbols to represent mathematics, refined over centuries of standardization. The "universality" of this system crosses terrestrial borders but, as far as we know, does not extend beyond human civilization.

Math itself is subjective. While calculations may produce consistent outcomes, there could be a myriad of different meanings and associations attached to the math depending on who's doing it. Those meanings and associations are probably not innate; rather, they're developed in the learning context. In the Western education system, that context is generally the symbols and calculations themselves, and students typically don't attach any other meanings to math until they start applying these concepts in the "real world." That could mean counting change as a cashier or leaving tips after a meal (I still mess that up constantly and could use a little help… level designers, are you listening?) Or, if you're a lucky duck like my surfer friends, math could mean optimizing surf times through complex calculations of wind velocities, tide changes, etc. (Although these same people are thoroughly perplexed by basic arithmetic, go figure.)

Dr. Keith Devlin's research has shown that children in developing countries that help their families run market stands could perform complex calculations on the fly with over 90% accuracy. When asked to do the same calculations on paper, that accuracy rate drops to about 40%. Conversely, Dr. Devlin gives an example of American students on a field trip to Mt. Diablo -- in a class full of trigonometry aces, not one could figure out the height of the mountain based on its distance from where they were standing. For each of these kids, math has been taken out of context.

Context gives math meaning. I'm not saying that mathematics must be attached to real-world applications in order to have meaning at all -- abstraction can be a beautiful thing and even a fun toy to play with -- but you'd have to be able to wrap your head around it first. The question is, how do we bridge that gap between the concrete and the abstract and vice-versa? When we say we want to build a game that teaches math, what we're really trying to do is help players make the logical leap when they transition from one context to another.

In the Mathbreakers world, we started off by making our numbers "tangible" -- whack a number with a Factor Hammer to get its prime factors, blast it with a Fun Times Wave to multiply it, chop it with a Halving Sword to literally produce two halves -- you get the idea. This approach removes the player from a typical symbolic context and lets them play with mathematics as though it's something tactile. We thought that was good enough (actually, we thought it was quite brilliant) until Dr. Devlin wisely pointed out that each gadget is but one way to teach a concept, and a single concept needs to be reinforced in many different ways before students can begin to grasp the abstraction.

Does this mean our math gadgets could essentially shape the meanings that our (young and malleable) players associate with the corresponding operations? While we would feel pretty proud if a child instinctively reached for her Halving Sword whenever she needed to do division, we're probably not helping her learn math by giving her just one or two tools for performing each operation. Every math gadget is really just a subjective interpretation of its inventor. We need to aggregate all sorts of different subjective interpretations of one concept in order to form an objective abstraction. If that's the case, no one can ever saturate the demand for gadgets that teach division or any other concept -- and our math toy box grows infinitely bigger.

Mathbreakers Kickstarter Kickoff!

Welcome to the next step in our plan to rule the world! We've made a ton of progress of the past few months, and are announcing the launch of our Kickstarter campaign beginning November 1st!

Find out why we're running a Kickstarter campaign & more in the Q&A session with our CEO below.


Jennifer: Why is Mathbreakers running a Kickstarter campaign?

Charlie: Other than raising money, we're looking to get exposure to our game on a mass scale and test the game with a larger audience. We want to build our initial player base and create a community around that.


Jennifer: What's the goal of the game?

Charlie: An evil number empire is attempting to destroy all the transcendental numbers to prevent higher-level math from ever being done again. You must rescue the transcendental numbers before the bad guys reduce them to zero. Transcendental numbers are non-algebraic numbers such as π (3.14) and e (2.71). If you save the numbers a little late, and the bad guys have begun reducing them, you still have a chance to save the world by completing a challenge level and returning the transcendental numbers to their true irrational values.

Jennifer: What's the coolest thing about your game?

Charlie: All the ways you can chop, smash, combine, and modify numbers with magic weapons! The bazooka launches numbers and returns the sum of everything in the blast radius. The sword slashes numbers in half (literally). Or, you can smash numbers with the factor hammer, and even control swarms of flying numbers with a magic staff. The game makes you think about math in a different way, and you learn to look for opportunities based on the tools and numbers available.

Most importantly, there are no "What is 6 x 7" problems. All the numbers exist in a world on their own, and you decide how to play with them.


Jennifer: How does Mathbreakers play into the EdTech community?

Charlie: Mathbreakers fits nicely with the standard math curriculum for grades 1-6, including arithmetic, negatives, fractions, factoring, multiples and powers. It can be played at home or at school; the action-packed 3D world that approaches mathematics in a new way, and repeated play helps develop a strong intuitive understanding of mathematics from different angles.

Mathbreakers brings more to the ed-tech community in two ways:

1. Math is a property of the game world, not an additional problem set. This means that instead of hundreds of repetitive worksheet problems, the student works in an environment where simple interactions lead to more complex behavior. This builds a strong foundation to build on, and allows for multiple different solution paths.

2. It's not just a game — it's also an editor and level builder, where students can invent their own math machines and puzzles for their friends. We believe this creation process engages the brain at a higher level, and fosters a deeper understanding of math concepts than practice alone. You know a student really understands factoring if they can make their own factoring puzzle!


Jennifer: Those are exciting claims, but has anyone played your game?

Charlie: Yes! Over 100 students have tested our game at various workshop settings. We've received great feedback from kids and parents, and had a significant amount of questions like "Is the next version ready yet?" It's a great feeling to see kids continue playing the game after the workshop is over, and they are constantly asking us for the next level set!


Jennifer: What are you going to do with the money you're able to pull in from Kickstarter?

Charlie: The funds will be used to finish development of the Alpha version, with the level editor and multiplayer as potential stretch goals. We will also amp up our advertising and reach out to other organizations for strategic partnerships. Our short-term goal is to launch by Christmas 2013 and get our game in the hands of as many students as possible, gather their feedback, build the community and make the game better.