Math Game
by Myles · in Game Design and Creative Issues · 12/28/2004 (12:55 am) · 8 replies
I posted a plan on this. I would like comments or suggestions, as this is ment more for discussion at this point than anything else.
Most people can grasp a mathmatical concept; however, mathmatics, like anything else, takes practice, and thats were alot of students fall behind.
The are several obsticales that keep students from doing the repetative operation needed to learn math. I mentioned a few in the full .plan. The idea is to make a game that uses math as a primary tool for advancement in the game. It is also a goal to make a fun game.
The target audience would probably be middle school, somewhere around 4- 7 grade. But the game should be fun so anyone is actually the target.
THEME:
Math, and tehcnology in general, have always been associated/confused with MAGIC. I think this is an excellent starting point to the game design. Math and magic have always been married, and this provides an entry point for math to take the main focus of a video game, without the player/student initially realizing it.
Games themselves are generally mathmatical models with some graphical or contextual veil to make the player think they are not doing math. The goal would be to expose more of the math and keep some of the veil.
'Magic' symbols could be employed. Math deals with typographic symbologies and has little to do with numbers, and the game likewise need not bother with typographical 'numbers'; but with Moons, stars, squares, triangles, flames, water drops, circles etc..
GENRE:
Magic systems usually are found in two game genres; RPGs and Adventure games.
Either one could suit the goals of the game; however, an RPG might be better. As said before math is all about building upon previously learned skills. So leveling systems usually found in RPGs could act as a vehicle for mastering a mathmatical operation before moving on to an operation built upon it.
This is not to say anything about the setting. An RPG, with Magic, does not automatically suggest a medieval backdrop. It could be modern day, something like harry potter or it could very well be medieval with dragons and all.
And of course this could also fit into any sort of puzzle type game. But them again RPGs and adventure games usually emply puzzles as plot obstacles or side games.
IMPLEMENTATIONS EXAMPLE: (one way to do the interface/game mechanics)
This is a very simple example, the game could be done a million different ways. But I think this example shows what the game might have as an objective.
The player Starts as a low level wizard apprentice, he has a spell book and a bag of magic symbols, given to him by his master.
The symbols are little stones with with some engravings.
The only symbols the player has are:
Two symbols that look like a negative sign.
Some strange symbol that looks like a flame.
In the spell book there are only three entries written: (the F and W are graphic symbols that resemble a flame and a water drop).
F = -W.
W=Liqu.
-Liqu=Flamo.
The player is instructed by his master to light the fire using magic, he is cold.
If the player clicks on one of the entries in the spell book the same symbols appear glowing, floating above him in the air. So the player clicks on the Entry 'F=-W' and sees it floating in the air.
Then he clicks on the 'W=Liqu' entry. and the Floating symbols change to 'F=-Liqu'. (every W is substituted with Liqu)
The Player then can Click on '-Liqu=Flamo', and the floating symbols change to 'F=Flamo'. (every '-Liqu' was substituted with 'Flamo').
At this point the Foating symbols shake and glow brightly brusting into flames, and a new entry is added to the spell book; 'F=Flamo'
If the player then said the magic word 'Flamo' (typing it perhaps). Then the flame symbol in the bag would disappear and be used And the Flame Spell would be activated allowing the student to lite the fire.
Most people can grasp a mathmatical concept; however, mathmatics, like anything else, takes practice, and thats were alot of students fall behind.
The are several obsticales that keep students from doing the repetative operation needed to learn math. I mentioned a few in the full .plan. The idea is to make a game that uses math as a primary tool for advancement in the game. It is also a goal to make a fun game.
The target audience would probably be middle school, somewhere around 4- 7 grade. But the game should be fun so anyone is actually the target.
THEME:
Math, and tehcnology in general, have always been associated/confused with MAGIC. I think this is an excellent starting point to the game design. Math and magic have always been married, and this provides an entry point for math to take the main focus of a video game, without the player/student initially realizing it.
Games themselves are generally mathmatical models with some graphical or contextual veil to make the player think they are not doing math. The goal would be to expose more of the math and keep some of the veil.
'Magic' symbols could be employed. Math deals with typographic symbologies and has little to do with numbers, and the game likewise need not bother with typographical 'numbers'; but with Moons, stars, squares, triangles, flames, water drops, circles etc..
GENRE:
Magic systems usually are found in two game genres; RPGs and Adventure games.
Either one could suit the goals of the game; however, an RPG might be better. As said before math is all about building upon previously learned skills. So leveling systems usually found in RPGs could act as a vehicle for mastering a mathmatical operation before moving on to an operation built upon it.
This is not to say anything about the setting. An RPG, with Magic, does not automatically suggest a medieval backdrop. It could be modern day, something like harry potter or it could very well be medieval with dragons and all.
And of course this could also fit into any sort of puzzle type game. But them again RPGs and adventure games usually emply puzzles as plot obstacles or side games.
IMPLEMENTATIONS EXAMPLE: (one way to do the interface/game mechanics)
This is a very simple example, the game could be done a million different ways. But I think this example shows what the game might have as an objective.
The player Starts as a low level wizard apprentice, he has a spell book and a bag of magic symbols, given to him by his master.
The symbols are little stones with with some engravings.
The only symbols the player has are:
Two symbols that look like a negative sign.
Some strange symbol that looks like a flame.
In the spell book there are only three entries written: (the F and W are graphic symbols that resemble a flame and a water drop).
F = -W.
W=Liqu.
-Liqu=Flamo.
The player is instructed by his master to light the fire using magic, he is cold.
If the player clicks on one of the entries in the spell book the same symbols appear glowing, floating above him in the air. So the player clicks on the Entry 'F=-W' and sees it floating in the air.
Then he clicks on the 'W=Liqu' entry. and the Floating symbols change to 'F=-Liqu'. (every W is substituted with Liqu)
The Player then can Click on '-Liqu=Flamo', and the floating symbols change to 'F=Flamo'. (every '-Liqu' was substituted with 'Flamo').
At this point the Foating symbols shake and glow brightly brusting into flames, and a new entry is added to the spell book; 'F=Flamo'
If the player then said the magic word 'Flamo' (typing it perhaps). Then the flame symbol in the bag would disappear and be used And the Flame Spell would be activated allowing the student to lite the fire.
About the author
#2
Also, it would make more sense if you called the "equations" something else, such as "conversions". I suspect that you don't really want the player to be stating that things are equal. Instead you want him to state that one thing is changing into another. So maybe it could be something like:
[original thing] -> [new thing]
So Goblin + Fire -> Burned Goblin. Or something like that.
If you're only going to have addition and subtraction, there's really no point. The problem is, what's the following mean?
Fire * (Goblin + Fire) -> Burned Goblin
What's Fire squared?
Having battles where wizards work on the same equation is fine, but it has to be obvious how the equation affects your character.
As I think about your idea, I see 3 main problems:
1) The "magic" has to actually require non-trivial math.
2) It should be pretty easy to select some sequence of symbols that will cause a specific effect.
3) There would have to be alot of possible spell effects if the game's going to be fun. And that would require alot of game development results (design, programming, and art resources).
If implemented properly, it would be cool. But if the player just has to memorize a bunch of silly sequences of symbols for no reason, it would be a terrible game.
12/28/2004 (7:05 pm)
It sounds like an interesting educational game, but you need to figure out some consistent way that the equations affect the game, which could be a real problem. If the player can use fire on one thing to make it burst into flame, he should be able to do the same with anything that's flammable.Also, it would make more sense if you called the "equations" something else, such as "conversions". I suspect that you don't really want the player to be stating that things are equal. Instead you want him to state that one thing is changing into another. So maybe it could be something like:
[original thing] -> [new thing]
So Goblin + Fire -> Burned Goblin. Or something like that.
If you're only going to have addition and subtraction, there's really no point. The problem is, what's the following mean?
Fire * (Goblin + Fire) -> Burned Goblin
What's Fire squared?
Having battles where wizards work on the same equation is fine, but it has to be obvious how the equation affects your character.
As I think about your idea, I see 3 main problems:
1) The "magic" has to actually require non-trivial math.
2) It should be pretty easy to select some sequence of symbols that will cause a specific effect.
3) There would have to be alot of possible spell effects if the game's going to be fun. And that would require alot of game development results (design, programming, and art resources).
If implemented properly, it would be cool. But if the player just has to memorize a bunch of silly sequences of symbols for no reason, it would be a terrible game.
#3
looks like a challenging task but as it is a unique one as far as i know you might get great benifits from completing it.
12/28/2004 (7:12 pm)
I think by not hiding the math you might make it more likely to be utillised by the education departments etc. also it would make your math more accessible to people of an advanced level.looks like a challenging task but as it is a unique one as far as i know you might get great benifits from completing it.
#4
Your comments are competely ON TRACK.
This is not an easy subject, and the game design would have to be VERY careful.
My example probably was not careful enough, but it was just to get the ball rolling. The math part is a huge discussion and one that the game would address:
Namely the distinction between the following:
A Typographical Axiomatic System.
Mathematics (Typographical Axiomatic System devoted to the exploration of numbers)
Geometery (A Spacial system, providing a definition of numbers)
Numbers ( a system all its own)
The real world (a physical non-deterministic system, that can be modeled with deterministic symbolic systems).
**************************************************************
Math is a discovery tool. The equals sign is a discovery tool.
You are correct. We cannot ever say THINGS are equal. If you say A rock is equal to another rock and have it be true, then there are not two rocks, there never were two rocks. If there were two rocks, then they would not have been equal.
The equals sign is like a question and an answer, but it has no action, it doesn't 'set' anything. In a programming sense, the mathematical '=' symbol is much more like the C++ '==' symbol.
The equals sign is part of a typogrpahical system. And it is only used within that system. It has nothing to do with anything 'real'.
And in the game the equals sign works with the equations. The equations would be a discovery tool, to learn things about the MAGIC system. But they, the equations and the MAGIC system, are completely seperate. Just like a typographic system and Numbers are Completely seperate. Math is a particular typographic system that has some rules modeled after some number properties.
To make this disctinction clear would be a great challenge for the game design.
The equations would never be dealing with ACTUAL objects, just like math does not deal with actual objects or even numbers. However, they use symbols that can represent actual objects to DISCOVER things.
***************************************************************
If you are talking about an actual physical fire, well, nothing. That doesn't make any sense.
If you are talking about 'fire' as a symbol, well, then it equals Fire Squared.
Mathematically of course fire (F) squared would be:
F^2=F * F;
This is a mathematical axiom. IT means NOTHING. It represents NOTHING. It is simply a string of typographical symbols.
**************************************************************
Some of the flow of the game would have to be thought out.. Introduction to NUMBERS would be mid-level.
The low level magic would deal with typographical operations and axioms.
What the equals sign means: Whatever string is on the left side of the equals sign, can be susbituted with a string on the right side, anywhere and everywhere, and vice versa, right substituted with left.
The strings can be moons, stars, pumpkins, etc..
An Example:
Here is a typographic axiom:
So complete the following:
Many people who have completed High-school algebra might not be able to complete the above. Becuase they are not directly tuaght how generic typographical axiomatic systems work in general.
Mathematics is a typographic system dealing with numbers. So there is some simple number theory thrown into the mix, and alot of this cuases confusion.
The place to start is with generic axiomatic systems. Then move on to numbers.
**************************************************************
Having a 'equals' spell would be unbelievably powerful.
12/28/2004 (8:32 pm)
@Steven.Your comments are competely ON TRACK.
This is not an easy subject, and the game design would have to be VERY careful.
My example probably was not careful enough, but it was just to get the ball rolling. The math part is a huge discussion and one that the game would address:
Namely the distinction between the following:
A Typographical Axiomatic System.
Mathematics (Typographical Axiomatic System devoted to the exploration of numbers)
Geometery (A Spacial system, providing a definition of numbers)
Numbers ( a system all its own)
The real world (a physical non-deterministic system, that can be modeled with deterministic symbolic systems).
**************************************************************
Math is a discovery tool. The equals sign is a discovery tool.
Quote: I suspect that you don't really want the player to be stating that things are equal.
You are correct. We cannot ever say THINGS are equal. If you say A rock is equal to another rock and have it be true, then there are not two rocks, there never were two rocks. If there were two rocks, then they would not have been equal.
The equals sign is like a question and an answer, but it has no action, it doesn't 'set' anything. In a programming sense, the mathematical '=' symbol is much more like the C++ '==' symbol.
The equals sign is part of a typogrpahical system. And it is only used within that system. It has nothing to do with anything 'real'.
And in the game the equals sign works with the equations. The equations would be a discovery tool, to learn things about the MAGIC system. But they, the equations and the MAGIC system, are completely seperate. Just like a typographic system and Numbers are Completely seperate. Math is a particular typographic system that has some rules modeled after some number properties.
To make this disctinction clear would be a great challenge for the game design.
The equations would never be dealing with ACTUAL objects, just like math does not deal with actual objects or even numbers. However, they use symbols that can represent actual objects to DISCOVER things.
***************************************************************
Quote:What's Fire squared?
If you are talking about an actual physical fire, well, nothing. That doesn't make any sense.
If you are talking about 'fire' as a symbol, well, then it equals Fire Squared.
Mathematically of course fire (F) squared would be:
F^2=F * F;
This is a mathematical axiom. IT means NOTHING. It represents NOTHING. It is simply a string of typographical symbols.
**************************************************************
Some of the flow of the game would have to be thought out.. Introduction to NUMBERS would be mid-level.
The low level magic would deal with typographical operations and axioms.
What the equals sign means: Whatever string is on the left side of the equals sign, can be susbituted with a string on the right side, anywhere and everywhere, and vice versa, right substituted with left.
The strings can be moons, stars, pumpkins, etc..
An Example:
Here is a typographic axiom:
So complete the following:
Many people who have completed High-school algebra might not be able to complete the above. Becuase they are not directly tuaght how generic typographical axiomatic systems work in general.
Mathematics is a typographic system dealing with numbers. So there is some simple number theory thrown into the mix, and alot of this cuases confusion.
The place to start is with generic axiomatic systems. Then move on to numbers.
**************************************************************
Having a 'equals' spell would be unbelievably powerful.
#5
A basic idea of concept order.
Symbols:
Symbols representing real objects:
Typographic Axioms:
Typographic operations (substitution primarily).
Graphical geometery: This could be accomplshed in a few ways that relate to the game ( think about drawing pentagrams).
Numbers (as defined by the geometeric number line).
Math.
Hopefully it is a little clearer what I am suggesting. The MAGIC part of the game, and the game play can be developed completely seperate from the math part, just like a regular game.
However, there would be this one interface/system, that is used to discover things about other systems in the game, just like math does in the real world.
Comments.. suggestions.
BTW- There is also a small discussion going on in the .plan
An snippet from there:
Sadly, I don't think there is a way aound this. In order to do math well, a student needs to be able to do operations like second nature. A student needs to go through a million examples so patterns start to emerge and are learned.
So when a student looks at a problem, it is just like reading a book. They see a whole story, where it has been, where is it heading. They can read that story becuase they have learned the language. (I myself am not close to mastering this, maybe a nice repetive game could help).
The goal of the game, would be to make that repative task either fun, or give some reward for doing it, other than a grade.
We start getting directly into more game related topic now.
OWNERSHIP: I believe ownership is a huge motivator in games. Players love to OWN things, build things, know things. These are all forms of ownership.
If you take the standard player taxonomy : Achiever, Explorer, Socializer, Killer.
Ther all like to own things, Killers just happen to love pwning other players. LOL!
This game would need to be designed like any other. With a set of rewards. The math is a big part of the game. But the design should make it not appear so. It is simply a vehicle to progress in the game.
One form of Ownership I have thaught about, would be to allow the player to actually design spells of thier own. The spell design process itself should be easy (interface) but not devoid of complexity. But would need to employ some math skills in order to design spells. The math part doesn't even have to be a game system. The player might just have to bust out pencil and paper for this one.
And here is a practical application. Using math to design spells.
12/28/2004 (8:32 pm)
So I think a good place to start would be to decide what order and at what player levels, to teach certain concepts, find a set of spells that are intersting but possibly reinforce the concepts.A basic idea of concept order.
Symbols:
Symbols representing real objects:
Typographic Axioms:
Typographic operations (substitution primarily).
Graphical geometery: This could be accomplshed in a few ways that relate to the game ( think about drawing pentagrams).
Numbers (as defined by the geometeric number line).
Math.
Hopefully it is a little clearer what I am suggesting. The MAGIC part of the game, and the game play can be developed completely seperate from the math part, just like a regular game.
However, there would be this one interface/system, that is used to discover things about other systems in the game, just like math does in the real world.
Comments.. suggestions.
BTW- There is also a small discussion going on in the .plan
An snippet from there:
Quote:
Your idea of enforcing repetitive tasks is also problematic. It's often synonymous with busy work which breeds frustration and creates road blocks to learning like still water breeds mosquitos.
Sadly, I don't think there is a way aound this. In order to do math well, a student needs to be able to do operations like second nature. A student needs to go through a million examples so patterns start to emerge and are learned.
So when a student looks at a problem, it is just like reading a book. They see a whole story, where it has been, where is it heading. They can read that story becuase they have learned the language. (I myself am not close to mastering this, maybe a nice repetive game could help).
The goal of the game, would be to make that repative task either fun, or give some reward for doing it, other than a grade.
We start getting directly into more game related topic now.
OWNERSHIP: I believe ownership is a huge motivator in games. Players love to OWN things, build things, know things. These are all forms of ownership.
If you take the standard player taxonomy : Achiever, Explorer, Socializer, Killer.
Ther all like to own things, Killers just happen to love pwning other players. LOL!
This game would need to be designed like any other. With a set of rewards. The math is a big part of the game. But the design should make it not appear so. It is simply a vehicle to progress in the game.
One form of Ownership I have thaught about, would be to allow the player to actually design spells of thier own. The spell design process itself should be easy (interface) but not devoid of complexity. But would need to employ some math skills in order to design spells. The math part doesn't even have to be a game system. The player might just have to bust out pencil and paper for this one.
And here is a practical application. Using math to design spells.
#6
Max
12/28/2004 (9:49 pm)
Ahh Ahh NO NO Don't make me learn! Lol, no, hmm I'm not so sure about this one.Max
#7
Yours is a good idea that, indeed, we are actually developing in the university where I work, but applied to psychology. We are creating a kind of first person adventure game in 3D, aimed towards the treatment of dyslexia.
In the game, the player walks around some environments (an enchanted mansion, a pirate island, the Moon...) looking for some lost friends, while he/she meets characters that throw at him some tests created specifically for the treatment of dyslexia (i.e. reading, audio tests, vocabulary... up to more than 20 tasks) in order to let him advance in his quest. As you said, this programs must be carefully designed if you want them to be functional. In our case, there is a full group of psycologists working on the script and task design.
Are you working in a university or similar or is it a personal project?
See you!
12/28/2004 (11:55 pm)
Hi Myles,Yours is a good idea that, indeed, we are actually developing in the university where I work, but applied to psychology. We are creating a kind of first person adventure game in 3D, aimed towards the treatment of dyslexia.
In the game, the player walks around some environments (an enchanted mansion, a pirate island, the Moon...) looking for some lost friends, while he/she meets characters that throw at him some tests created specifically for the treatment of dyslexia (i.e. reading, audio tests, vocabulary... up to more than 20 tasks) in order to let him advance in his quest. As you said, this programs must be carefully designed if you want them to be functional. In our case, there is a full group of psycologists working on the script and task design.
Are you working in a university or similar or is it a personal project?
See you!
#8
Your projects sound great. I am very interested in the study and creation of games that do 'work,' as the medium is far too powerful to be used just for entertainment, though I do love fun games.
Currently this is a personal project, and as you can see it is at the very beginning, and this thread is ment to have a discussion more than anything. Thanks for contributing.
I'm closing in on finishing my Undergrad for CS, and since I live in the Dallas/TX area I am contemplating The Guild Hall at SMU, or going for UTD 'Arts and Tech', to further my game studies.
Mathematics is a hobby for me, so eventually having a serious mathematician on board for consulting would be ideal. As my knowledge is far from superior, but complete enough to start a project as such.
My interest in education stems from the interest in games that provide a service.
Now some more thougts on the game:
Here is one way that I am approaching this. Comments are welcome.
Imagine a game that is provided with the minimalist of manuals. This shouldn't be too hard considering what most games ship with. The manual basicly covers the interface, and the setting of the game, backstory, whatever. But actual game systems are obscured.
However, there is a complete in-game manual. The in-game manual is a game system itself.
Using typographical systems and mathmatical systems, disguised in some context (ie a spell book), the player can discover insights and information about other game systems, (ie the magic system) and unlock features of those systems.
And alot of it is completely exposed;however, it might not be very obvious from the beginning, as it is written in some cryptic curios language of symbols.
Over the course of the game the player will learn to 'read' this curious language. (by read I mean understand, use, and manipulate).
As the player learns to 'read' this language, they will also be learning how to work with typographical systems and do math.
And as far as a game setting goes I think it could work with Magic. The Player character can be a student of magic, and over the course of the game the player becomes a powerful wizard, learning an arcane magical language.
12/29/2004 (12:45 am)
@Luis Your projects sound great. I am very interested in the study and creation of games that do 'work,' as the medium is far too powerful to be used just for entertainment, though I do love fun games.
Currently this is a personal project, and as you can see it is at the very beginning, and this thread is ment to have a discussion more than anything. Thanks for contributing.
I'm closing in on finishing my Undergrad for CS, and since I live in the Dallas/TX area I am contemplating The Guild Hall at SMU, or going for UTD 'Arts and Tech', to further my game studies.
Mathematics is a hobby for me, so eventually having a serious mathematician on board for consulting would be ideal. As my knowledge is far from superior, but complete enough to start a project as such.
My interest in education stems from the interest in games that provide a service.
Now some more thougts on the game:
Here is one way that I am approaching this. Comments are welcome.
Imagine a game that is provided with the minimalist of manuals. This shouldn't be too hard considering what most games ship with. The manual basicly covers the interface, and the setting of the game, backstory, whatever. But actual game systems are obscured.
However, there is a complete in-game manual. The in-game manual is a game system itself.
Using typographical systems and mathmatical systems, disguised in some context (ie a spell book), the player can discover insights and information about other game systems, (ie the magic system) and unlock features of those systems.
And alot of it is completely exposed;however, it might not be very obvious from the beginning, as it is written in some cryptic curios language of symbols.
Over the course of the game the player will learn to 'read' this curious language. (by read I mean understand, use, and manipulate).
As the player learns to 'read' this language, they will also be learning how to work with typographical systems and do math.
And as far as a game setting goes I think it could work with Magic. The Player character can be a student of magic, and over the course of the game the player becomes a powerful wizard, learning an arcane magical language.
Myles
The Symbols in the bag have two functions. One mathatical and one game play.
Game play the symbols work as reagents. You need a symbol to cast a spell. IF the player typed in 'Flamo' and didn't have a flame symbol then the spell could not be invoked.
The mathmatical element is if the player used the Flame symbol while the equation was floating in the air then a Flame symbol would be added to both sides of the equation. If the Player used the negative symbol, then both sides of the equation would be inversed.
Same for the spells in the spell book. Aquiring spells gains access to new magic words. Using them while an equation is up does symbol substitution.
This of course is an exmple of some low level play. The system could be used to solve puzzles are engaged in combat.
This could evolve into systems of equations.
Symbols could be included that do nearly all mathmatical operations.
Wizard battles could happen were a player fights another wizard, possibly even another player) by operating on the same equation.
Any comments suggestions are welcome.