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!
Monday, April 28, 2014
Saturday, April 26, 2014
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
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
Wednesday, April 23, 2014
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
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
Tuesday, April 22, 2014
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.
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.
Monday, April 21, 2014
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.
Thursday, November 14, 2013
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.
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.
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.
Tuesday, November 5, 2013
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
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
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