Over A Thousand Virtual Hugs Given (Or A Blog Post About Nothing)

Place: Hacker Dojo, 599 Fairchild Drive, Mountain View, CA

Time: 6.30 pm

Monday evening. The team behind Mathbreakers – Morgan, Charlie, and Vivian – are half-way through their dinner. Morgan has Reddit open, and is pretending to be hard at work, when Charlie says, “Hey Morgan, Its your turn to do a blog post today.” 

“Mmmmm Mmph darumfff wamppppa,” replies Morgan, chomping down a rather large mouthful of burger. Which, Charlie and Vivian, having worked with Morgan before, rightly interpret to mean, “But I don’t wanna.”

What follows is the conversation they had..

Charlie: You should write about how we built the game from scratch.

Morgan: You mean how I met you and Vivian early last year, and how you guys had these cool prototypes for a Math game, though technically speaking not production stuff… And how I took on a role where I could advance that stuff in a maintainable way, and work towards optimizing and maintaining what we had?

Charlie: Also talk about the website.

Morgan: Remember, for a little while we had this impossible to maintain PHP version of the website that I wrestled away from you? I guess I could write about how we are using Django and jQuery.. Also, all the APIs we are using – the Mathbreakers game uses logins, assignments from the teachers which need to be tracked, the back-end purchasing system.. Yes, I could write about all that; but I don’t want to.

Vivian:  Maybe I could write the code for the site. I will only take five-times as much time than you guys.

Charlie: Remember all the time Morgan spent on doing Shaders! That was the time when he wanted to build this cool-looking bubbly shader for the numbers – giving objects in the game a ice-cuby effect? (Psssst, Ice-cuby is not a real word.)

Morgan: You can do all sorts of custom effects on object and game environment - cool things. Like the material you put on objects , light up when there is sun. See-through or reflective surfaces, for examples. We are a small team and did not have an art budget; so I tried to do most of the work using code.

Charlie: Which is why you built the hex grid system, this bunch of hexagonal tiles, that sort of pulled the game together visually.

Morgan: I think the way we built Mathbreakers was Charlie would have an idea and would start building a level for it.  He would also write much of the code for it. I would do tricky parts of the code,  make it more maintainable, for example. Then Vivian would come in, and make what we did look pretty.

Vivian: We built the game on top of Unity, which meant we did not have to do every little thing ourselves. Unity took care of the Physics for us. Like, when you go sufficiently close to a ledge, you automatically fall off.   

Charlie: I think Unity is kinda like Photoshop, but with way more interaction.

Vivian: I think you can say that about Blender. You can customize a lot of things very easily.

Morgan: Players can customize the characters in the Mathbreakers game, man. How cool is that! (Note: Vivian is not a man, but Morgan refers to everyone as ‘man’; be it man, woman, child or a pet cat.)

Vivian: I think the components-based model of Unity helped us a lot with testing. Larger game studios work in six-months sprints, they have to be able to figure out things many, many days in advance. We, on the other hand, were able to make a feature in a day or two, and test it out. If children loved a feature, we kept it. If they did not, we removed it.

Charlie: I thought having a marble in the game would be a good idea, but the kids did not like marbles all that much. The robots they loved!

Morgan: Speaking of, do you know we sent out roughly a thousand robot hugs?

Vivian, Charlie (in unison): Dude! A thousand robot hugs!

Morgan: Meh. Whatever.

(The End)

Editor’s note (Yes, this post has an editor): A thousand robot hugs! When the Mathbreakers team had this hugely successful Kickstarter campaign, they thought it would be a great idea to thank all the people who had supported them. They were at a party, and thankfully it was the kinda party that also had an unlimited supply of paper and pen, along with various cool beverages.

Having made sure they had enough pizza, Morgan, Vivian, and Charlie started drawing random robots on paper. Their friends joined in as well. Later, Morgan scanned some of the images, and wrote a quick JavaScript program that made it look like the robots were actually hugging people off their browsers. Everybody loved it!

Want to send someone a robotic hug? Fine! Here: https://mathbreakers.com/hug/absolutelyfree/

Mathbreakers Goes Global

Hey everyone! Hope you are all having a happy Labor Day! 

We have good news to share. We just had a very successful Kickstarter campaign. Yup. 469 backers, and we overshot our goals. How has life been after Kickstarter? We will tell you soon, and share pictures too. In the mean while, we have another exciting development we wanted to tell you about. Mathbreakers have gone global, people!

See, when we started working on the Kickstarter campaign, we were expecting responses from local schools, for the most part. We would have been happy with a couple of polite queries from a few schools in the East coast. Little did we expect Mathbreakers would get such enthusiasm from countries all over the world. We had teachers and parents write to us from UK, Canada, Spain, Singapore, Saudi Arabia, India, and Ethiopia, among other places! Not only did we have dozens of schools writing to us from faraway lands, we had a ton of queries from schools all over the US as well. We are happy to say Mathbreakers accounts are now in use all over the globe. How neat is that!

Very. Very neat. This is really exciting!

We are grateful for all the love. THANK YOU! Suddenly the mad hours, the moments of self-doubt, the pile of empty pizza boxes lining up trash cans because we were too tired to either eat healthy or take the trash out..well, all of it seems so worth it. 

It does not matter whether you go to school in Bangladesh or Brazil, Math fundamentals form an integral part of the curriculum. The Mathbreakers game is easy to set up, and can be played individually by two siblings at home or 1,500 children as part of a school district. If you're a teacher, you can request an early access trial at mathbreakers.com/trial.

The world is clearly ready for Mathbreakers. Lets get smarter the fun way!

Introducing Mathbreakers Labs: on Medium

Hey everyone! We added a Labs section to Mathbreakers.

Read all about it here: https://medium.com/@mathbreakers/mathbreakers-labs-a9b4e25b61d3

Mathbreakers is coming to your iPad, Android, and Windows devices (VIDEO)

We're reaching another big milestone soon, thanks to Raj and Helen at Microsoft -- they provided us a surface to develop on, and Morgan (our CTO and generalist wizard) has been hard at work to make the mobile build a reality.

We expect to be on iPad and Android by the end of the year as well. Which is good, because about half of schools use tablets instead of PCs now, and the trend is favoring tablets.

Here's a quick video demo of what we have working so far:
https://www.youtube.com/watch?v=5eaDKfaneXM&feature=youtu.be

Negatives are a No - No?

I just had a great meeting with a 4th grade math teacher and the lab specialist at a local Catholic school in Mountain View, and I got some very interesting feedback: Negatives were NOT welcome in the fractions levels that we had created!

This was not a total surprise to me, as I have gathered that Common Core pushed the learning of negatives back several grades, and as a result negatives are taught fairly late in elementary math education. However, in Mathbreakers, students are exposed to negative numbers right away; indeed it is one of the core tenants of our game, because in order to reach zero you must match positive and negative numbers together.

In practice, students don't have any trouble understanding that the light numbers and dark numbers with a "-" sign behave differently; they are able to work their way through all of the challenges of the game just by experimentation. This, to our credit, was exactly our goal -- to expose the concept of negatives in an environment where they "just worked", so that by playing around in this environment you could master the use of these positive and negative integers.

But there's a huge problem: Students have a difficult time translating this ability into solving a worksheet or chalkboard problem.

Although they had been using 1 + -1 = 0 literally hundreds of times, they did not make the connection that they could solve exactly the same problem on the whiteboard, because it looks different and they didn't realize it was the same problem.

This is a difficult, but not insurmountable challenge for us. The obvious solution to me is to (ugh) add a pop-up quiz at various points, probably at the end of the level, which clearly shows a visual relationship between 1 + -1 = 0 and the game.

This is, perhaps surprisingly, a common problem in mathematics: Context. Many math learners will totally understand a concept on paper, but be unable to perform the exact same math in the real world. The reverse also happens; Keith Devlin has an excellent book that covers this with third world marketplaces where children bargain and sell goods in the streets. The children perform with 97%+ accuracy in the market, but when presented with exactly the same problems on paper, they could not get a passing grade!

Overcoming this disconnect is going to be a cornerstone of how we add value to the classroom. When the students can make a clear relationship between the game and a worksheet, then students who play Mathbreakers will be able to translate those skills to paper, to make the test-makers happy.

Stay tuned for an update -- we will be testing again at the same school in June, and I'll post the results to this blog.

Lesson Guides for Mathbreakers @ Schools

When we set out to disrupt math video games, we were mainly thinking of the players. We expected parents to buy this game for their kids to enjoy and learn math. And they do!

But what about using it in the classroom? Millions of kids every day are stuck in front of some animated worksheet in their computer lab or classroom for math practice, and the vast majority of it is terribly boring. We wanted to get Mathbreakers in the classroom. So what were we missing?

Lesson plans!

OK, it's not really a plan, because once students start playing the game, they pretty much take off. But the teacher still needs to get them started, understand what's going on, and track their progress.

We created a Teacher Class & Dashboard for exactly this purpose. Any teacher who wants to supplement their kids' practice through Mathbreakers can get started in a matter of minutes. The lesson guides we created let them follow along with students as they progress through Integers, Negatives, Operations, and Fractions at their own pace.

Now, the Mathbreakers' team is working with schools across San Francisco Bay Area to make Mathbreakers a part of the math curriculum in the computer lab. Our sales pitch is really fun, because we have an awesome product and our entry price is many times lower than the competition.

Warning -- kids may have a higher expectation for math apps and/or get unreasonably excited about mathematics after playing Mathbreakers!

Shrinking the scope - how to go to market

OK .. breathe.

We've come a long way since we decided to make a 3-D video game about Mathematics. In some ways we bit off more than we could chew -- math is an enormous subject, and to explore it with a video game means we could only ever hope to cover a tiny slice of it. But which slice?

The short answer: Integers, Simple Operations, Negatives, and Fractions.

How did this happen?

We started by literally throwing things together in a world and seeing what stuck. What was fun to play with? Well, one of the core building blocks of math is numbers, so we started with 3-D numbers you could pick up and play with. That turned out to be pretty fun -- the default mechanic ended up being very simple. Just touch two numbers together, no matter which numbers, and they add together.

One of the major breakthroughs of our game was the Fraction Sword. I don't actually remember who came up with it -- the three of us were just brainstorming about cool things we could do, and we hit on the idea of literally cutting numbers in half to produce fractions. We implemented it and it was immediately fun! Boys and girls alike (and all three cofounders) love to cut integers and see fractions pop out. There's something deeply satisfying about this level of number manipulation.

Negatives came out of necessity. Since the only way to destroy something (like a wall or enemy) is to add until the result is zero, one of the two numbers must be a negative. We've heard that teaching negative numbers has been moved to Seventh grade -- outrageous! We've seen six year olds grasp the concept of negatives after just a few minutes with Mathbreakers.

Finally, we have operations. This was the logical next step after addition. Here's a gif of the number hoop in action -- it's a door you walk through that either multiplies or divides whatever numbers you have.

So there you have it. Through thousands of trial-and-error experiments, we boiled it down to a few simple mechanics that work together to strengthen your number sense, all in a vivid 3-D adventure that will have you leaving your math worksheets in the dust!

Aggh! Mistakes!

Part of being a 3-person team building a pretty complex product means that we mess up sometimes. For the past 7 days, the downloadable game on our website was not playable, because all the graphics had messed up. Oops! How did this happen?

Well, it's of course my fault for not double- and triple-checking each build I upload. But, sometimes a build is uploaded that was not thoroughly tested, which is surprisingly easy to do because we have an automated "build and upload" process. The exact cause of this mistake was that during our iOS development, Unity crashed while "switching" from Mac to iOS, and some assets were destroyed, but no error was given so we had no idea.

Fortunately, we were able to load the project from an earlier build (thank Godel for Version Control!), the problem was fixed, and we didn't end up losing too much work.

My personal apologies to anyone who downloaded the game between April 20 - April 27, because you got a broken build. There is a working build up now, and we are continually working to reduce bugs and improve the performance of the game.

Thanks to all the teachers, parents, and kids who use Mathbreakers for your support of our project! Our team is looking forwards to perfecting our product, and making it better each week for you. Stay tuned for more updates!

PRESENTING: Math Discovery Summer Camp

This summer, the Mathbreakers team is adding a new dimension to our business -- summer camps!

For one week, kids will get to have a hands-on experience with mathematics that will shape their attitudes towards math for years to come. With the help of Dora Lee, our crafter and maker of shapes, and Federico Chivalo, our math specialist, we have designed a host of games and activities to engage hungry young minds (and take them off their parents hands for a while! ;-)

One of the games we created for the camp is a wild take on the old classic, Tic-Tac-Toe.

Original Tic-Tac-Toe is ridiculously easy, and most games end with no winner ("cat" wins). But Multiples Tic-Tac-Toe is ... much different.

First off, there are nine boards, not just one. In order to win, you first have to win on a smaller board. Then you get an X or O over the whole 9 squares, and you're on your way to getting 3 in a row on the larger board.

But here's where it gets interesting. When you play, you can actually hit multiple squares at once. The board is laid out as the multiples for the integers 1 - 9. The first square has 1, 2, 3, 4, 5, 6, 7, 8, 9. The second square is for multiples of 2 -- 2, 4, 6, 8, 10, 12, 14, 16, and 18. Each square has nine multiples on it, all the way up to the ninth square which has 9, 18, 27, 36, 45, 54, 63, 72, and 81.

The savvy player will immediately realize that some numbers show up more than once! 16 shows up in the 2, 4 and 8 squares. So if you play a 16, you get to place three pieces (assuming none of them are already taken).

OK, one last piece of the puzzle! To play your number, you must pick two numbers between 1 and 9 to multiply together. If you want to hit the 16 square, you would choose "2" and "8". Now, the next player's turn, they can change only one of these numbers. So they could keep the "2" and change the "8" to, let's say, a "7" (and get 2 x 7 = 14 -- which unfortunately only shows up once on the board.) But they cannot change both numbers, so there is no way they could get numbers that are neither a multiple of 2 or 8, like 21.

The implication here is that you can "trap" your opponent by picking two numbers that are not useful to them. If they need a 21, and you pick "2" and "8", there is no multiple of either 2 or 8 that gets 21, therefore they cannot possibly get 21 on their next move.

And therein lies the core of the strategy -- you can control what squares your opponent gets to play next, while keeping in mind they will be controlling your next move as well.

This is just one of the many activities at our camp! If you're in the San Francisco Bay Area and would like to sign up your son or daughter, we have set up a camp website and signup form here: mathbreakers.com/camp

Stanford University Presents Jo Boaler's MOOC - for math learners nationwide

We are proud to add Jo Boaler to our board of advisors this year! She is the "teacher of math teachers" and works at the Stanford Graduate School of Education. She's also a founder of YouCubed.com.

This summer, she will be offering two online courses for mathematics -- one for math learners, and one for math teachers. Mathbreakers will be mentioned in both courses as a math learning tool for grade school level.

We clicked with Jo right from the beginning. She's a pioneer in math learning and recognizes that schools are doing it all wrong. Children are becoming calculators and there is no real internal driver to learn math other than grades. In math class there is No play, No experimentation, Worksheets, Tests, Memorize for the test ..

No, no no -- Math is something to play with, to have fun with, to use for your own ends, and it should be experienced as something fun and useful, not as a chore. "Of course!" we cried. "That's why we built Mathbreakers!" There are a host of new learning tools that fit into this new paradigm, and we are really excited that our game is ahead of the times. (Hopefully, not too far ahead. ;-)

It also helps that she has two children who absolutely love the game!

If you're interested in learning more about Jo Boaler's course, signups for students are already available. You can find them here: https://class.stanford.edu/courses/Education/EDUC115-S/Spring2014/about

New "Battery" Machine. Add fractions to get a whole

One of the most fundamental parts of understanding fractions is their relationship to whole numbers.

For the enlightened, 1/2 + 1/2 = 1 is obvious -- but for the new fraction learner, it's totally confusing! Where did the 2s go? Why does this happen?

Mathbreakers has a simple, visual solution to this problem, with the use of the Sword gadget and the Battery machine. Here's how it works:

Use the sword to chop numbers (or make enemy defeating fractions). You can easily see that chopping a 1 yield two 1/2s.

But what about adding numbers together to get a whole? True, you could just throw a 1/2 ball at another 1/2, and it would add to 1 (since the basic rule of Mathbreakers is that when two numbers touch, they combine and add together). But, there's no apparent reason to do this. That's where the "Battery" machine comes in. This machine takes fractions in, and only operates when you completely fill it up, usually to 1.

Here's an example of putting the final 1/3 into a battery that already has 2/3 in it. By adding the final 1/3, you can see the battery completely fill up, reaching the 1, and there is a satisfying sound as the gears whir and the bridge lowers, opening up your next path.

And that's it! This machine is used several times in Mathbreakers -- to operate the machine, you must fill it up with fractions to reach a whole number. Try it today -- the full game is available at Mathbreakers.com/#getmathbreakers.

One parent approached us at a party and told us her six year old son learned fractions because of our game. Awesome! If you have kids who are struggling with fractions, this could open the door for them.

New toy for the Mathbreakers world

Well, we did it again! A new toy for the Mathbreakers world, the Number Riser (ok, maybe the name isn't permanent):

This one came about because we wanted to teach about Greater Than Less Than as well as the Number Line, and equivalence, both for integers and fractions. This machine accomplishes it all. 

It works by taking an input number (any number you find or make) into the funnel in the bottom. Then the platform rises up or down according to the size of the number -- 1/2 is shorter than 1, and 3 is taller than 2, etc.

This teaches:

Equivalence. If you need to make a Straight Path Bridge, all the Number Risers need to be the same value -- but you can't just put "1" into every funnel, that would be too easy! Instead, we restrict you to having only /2 fractions in one zone, /4 fractions in another zone, and only integers in a third zone. This way, you must put 2/2, 4/4, and 1 into the risers to make a straight path.

Number Line: The risers can be used as stairs, but it only works if each one has a number incrementally larger than the last. For example, you can make stairs with 1/4, 1/2, 3/4, and 1. Once the stairs are created you can exit the puzzle.

Greater than / Less than: When two risers are next to each other, the size of the number inside each is obvious, because the height of the risers is different. If you want a riser to be higher or lower than another, you must find a greater or smaller number as the input.

The risers work with fractions and integers and are a great addition to the machines of Mathbreakers; a simple, easy to understand, visual, and yet very versatile toy to get your mind thinking spatially about number sizes.

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.

Analytics, Adaptive Learning, & Badges

Hey teachers!

Soon we will step into the next phase of development, and a big part of it will be analytics so that you can monitor your students' progress, incentivize students to complete all the math challenges, and help them where they need help the most.

Consider the following features:

• Student logins that will keep track of how many problems they did, what type of problem, and accuracy rate
• Badges to indicate skill or achievement level in specific subjects
• In-game suggestions for the student based on their deficiencies
• Leaderboards so students can know where they stand (and compete) vs. friends
• Simple online spreadsheet including all your students scores across the different math subjects

We need your help with this! 
We know the importance of smoothly integrating our game, and if it's going to work, it better do a good job of matching the students' learning experiences to their curriculum and test scores.

1. Do you use similar analytics for other games in your classroom?
2. Do you think these are good ideas listed above?
3. Is there anything that stands out as a potential problem with these ideas, that you would like us to address?
4. Did we miss anything?

Feel free to email us directly [ team@imaginarynumber.co ] or respond to this blog if you have any input!

Thanks!!

-- Charlie & the Imaginary Number Co. Team

Is Mathbreakers actually educational?

This is a question we get all the time, and it's one of our biggest challenges! Is Mathbreakers actually educational -- meaning that kids can learn new concepts and improve understandings of core concepts -- or, is it just a video game with pretty colors that they play around in until something happens?

This is a difficult question to answer, because Mathbreakers is a totally new take on education. Most of the time, the student is given two things: A lecture or a document explaining an abstract concept, followed by a worksheet or test so that they can practice. Mathbreakers has none of these -- it's simply a world, a toybox to play in, that is bound by the laws of math.

Let's stop for a minute and make an analogy -- to driving a car.

When you first started driving, surely you took a driver's test and read the manual. But, everyone knows that driving in the real world is a completely different (and often terrifying) experience. After some time of driving on actual roads, drivers begin to feel comfortable and confident in their vehicles. They learn things that the books try to explain, but you don't really know it until you've had to watch for people who were about to cut you off, slam on their brakes, or walk out in front of you. No amount of studying prepares your feet and hands to react in these situations -- only experience can.

Maybe it's a stretch, but bear with me. Mathbreakers is like driving with math. Because the whole world, and all its outcomes, depend entirely upon your ability to put numbers together in the correct manner, you will have the experience of solving problems in your head and making the right choice, as well as sitting around stumped on a puzzle for a while until an "a-ha!" moment hits you. Our goal is to have the player learn mathematics, not because it's written down and they're told to study it, but because they have to experience it in a simulated reality, and master it in order to thrive in this new reality.

But the fun (and learning) doesn't stop there!

Mathbreakers isn't just a single player game with only a few types of math that we put together for you. It's a whole new world of creation and competition. Players can use numbers in whatever way they wish to do totally novel things -- building a number castle, for example, or a bridge with numbers. Or knocking down your opponent's number castle.

Here's where things get interesting. In our current game, if there were two number castles battling, things like prime numbers, fractions, really big numbers, and multiples of specific numbers becomes *Very important* for survival. If you can realize that your opponent's wall is all a multiple of 5, you can use that to destroy her. If she makes her wall into very large prime numbers, however, it will become very difficult for you to do anything to them -- you'd have to destroy them one at a time, because prime numbers don't have any factors in common with each other.

Furthermore, math doesn't stop at factoring and fractions, and neither does Mathbreakers. We're building a world where *all* of mathematics is possible to play with, including things like Trigonometry and Calculus. Imagine the castles you could build, and the various ways they might be destroyed, if you had the power to graph in 3-D!

We realize this is a brand new approach to the education of a subject like mathematics, but it's just crazy enough to work!

• The better you become at math, the more powerful you become in the game
• Multiplayer opens up a whole new world of math competition (both speed and ingenuity)
• There is no upper limit to what is possible to build with 3-d mathematics

Design Overview - Arcade/Action

As noted in Part One, Mathbreakers has several types of challenges. This post is about our faster-paced action segments.

In some ways, we made Mathbreakers as a reaction to the state-of-the-art in educational games. Many other math games are great at teaching and testing certain concepts, but fail to be engaging to kids. We see engagement as important, not only because kids will enjoy the game more, but because this motivation greatly improves learning.

One of the ways we keep players in a state of tension and engagement is by using time pressure in our action/arcade puzzles. Sometimes you will be chased down by spikeys, or zapped by guards, or fall off cliffs if you don't react quickly.

Passing these challenges requires accurate calculation and planning in a short period of time. When designed well, they induce a flow state in the player. In addition to adding engagement and fun to the game, we use arenas for repetition and training of skills the players have just learned.

Designing Arenas

We like to use an arena format with a unique twist for action segments. One example:

Here, we have a prime zone which all the enemies stay inside of. This type of zone with turn any prime numbers into gems. This is how we make the conflict interesting - the player has to figure out an efficient way to turn all these enemy numbers into primes. Right now, the Multiblaster is loaded with 9s which will dispatch of the 20s (20 + 9 = 29, a prime number) but can't deal with the 15 or 9 guards. A player who has planned well can load up her Number Launcher with 2s to finish off the guards (15+2 = 17, 9+2 = 11).

Other arenas in our game require zeroing enemies, finding square numbers, making fractions, factoring large numbers, and so on.

Calculus in Mathbreakers

When talking about Mathbreakers one subject that always comes up is our level editor. We are determined to make it possible for someone to create any type of math within our game world. Calculus is a popular subject, because it is relatively complicated when compared with elementary subjects currently in the game. How could we interact with something like Calculus in a 3-D game world?

I just had a great conversation with my dad, who is a software engineer, about how Calculus could work in the game. I was pretty surprised to see him getting excited about it -- he is definitely not a gamer, but when we started getting into the details of Calculus, he was suddenly very interested.

What we talked about was a giant wavy field of blocks. These blocks would represent a 3-D graph. Now, one of the key parts in understanding Calculus is taking the area under a curve, and breaking up a graph into smaller and smaller bits is a way to get a more accurate area. Well, in a 3-D world this has some very interesting results. Together we invented an idea of how a multiplayer Calculus match would stack up:

• You cannot see your opponent because the graph is too "coarse". You're standing on a 3-D graph with big blocks, and some of them are blocking your view.
• You can take some action to break the blocks up into smaller chunks. One block becomes 8 blocks (instead of 1x1x1, it becomes 2x2x2). Now, because some of the bigger blocks have disappeared and been replaced with many smaller blocks, the graph is more smooth and you can see more clearly.
• But maybe your opponent moved to a *different* part of the graph where it's still coarse.
• If you want to aim something like a projectile, you can use a part of the graph that has a curve that would cause a projectile to hit some object in the air, perhaps a power up. By making the graph more smooth, you increase the accuracy with which you can hit these targets.
• By taking the integral or derivative of a graph, and then graphing the result, you can create a more wavy or less wavy landscape, which can achieve game goals such as making your opponent slide into a pit, or create a staircase where you can reach a higher level.
• You can enter a 2-D or 3-D equation into a graph generator, which will change the 3-D landscape you're playing on.

The list goes on. There are lots of neat ways to represent Calculus in a 3-D game world, it turns out, and we can't wait to try some of them out!

Musical instrument for mathematics

We just had the pleasure of seeing Keith Devlin's talk at AC3ME in Berkeley on Mathematics in Video Games. Right up our alley!

His talk spoke to me on a deep level; especially when he related mathematics to music throughout the presentation. As a lover of both music and math I could really appreciate the analogy.

He talked a lot about "Where is the math happening?" There was a slide with a blackboard and a human brain. Is the math on the board, or in the brain? He asked us to make an analogy to sheet music and a piano. Is the music on the sheet of paper, or is it in the activity of playing the piano? The answer is obvious: Music comes from playing the piano, not the representation of it written down in notation form.

Math is the same way. It is written down (beautifully) in many different ways, but where is the piano for mathematics? Where is it played? Maybe a calculator .. but that's a pretty boring instrument. He likened his game, Wuzzit Trouble (available on iOS), to an instrument. Instead of writing equations, you are simply playing with math on a 1-to-1 level with inputs and outputs. It is like playing with music.

This was my favorite part of the talk. "Exactly!" I wanted to shout. That's exactly what we've done -- made an instrument where mathematics can be played. In fact we've made several instruments! My favorite right now is the Multiply Wave, although a 5th grader had a great idea for a "Positive negative boomerang" and another one said something about a "Fraction laser" that sounded pretty awesome.

Anyway, the point is, Mathbreakers is a world for mathematics, like a music store is a world for music. There are of course some annotated sheets you can look at and decipher. But more importantly, there are instruments everywhere, for you to pick up and start playing immediately! You might not be very good at first, but you can definitely participate and make a sound with little more than casual human effort. That's what we bring to mathematics -- the ability to play with it.

Prototype Testing at a private school

We just finished our 8-level prototype and tested it on 22 fourth graders this week. The results were amazing! The kids, aged 8-10 and a mixture of boys and girls, played the game for a full two hours. They needed very little help from us, and spent most of their time answering each others' questions about the math they were encountering. Specifically, some students knew more about primes and squares than others, and helped teach each other during gameplay.

The level of reaction was just unreal. We heard multiple random outbursts of "This is the most awesome game EVER!" and "Can I buy this?" When asked how many students would buy it at home, 18 of them raised their hands enthusiastically. Overall they loved Mathbreakers more than we could have anticipated. They even refused to leave for a 5 minute break halfway through the session -- a sign of true engagement.

What surprised us the most was how much gameplay time our levels provide. (none of them got past more than 2 levels during the full 2 hours). First, each section kept them quite busy; not only did they have to solve the math, they also had to think their way around our logic puzzles, which mainly consist of doing things in the right order to achieve the desired result.

But more than that, they just spent a lot of time playing with the different gadgets. Several times we heard "I got 500!" or "I got 6,352!" For some reason, getting big numbers is instantly gratifying, and kids often go out of their way to create them for no other reason.

They were all very excited to return for test session #2 next week.

All in all it was a smash success. We're looking forward to doing more testing! Contact us if you'd like to join in!

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.