Numbers Land game mechanics
Jan. 11th, 2007 11:01 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
bnewmanAs I mentioned in my previous entry, I've been thinking lately about Numbers Land, an arithmetic CRPG of which I mean someday to write a new version.
In the orginal Numbers Land, the combat system was very simple. In each encounter, you would face one monster. During each round of combat, you would answer one arithmetic problem. All problems were drawn from the same random distribution of two-digit addition, subtraction, multiplication and division facts, and were roughly comparable in difficulty. There was no time limit (it would have been difficult to implement one). Answer correctly, and you would hit the monster, doing damage depending only on your level (no random component). Answer incorrectly, and it would hit you, doing damage depending only on the type of monster. That was pretty much the whole game.
For the new Numbers Land, I have something much more complicated in mind, which raises a number of interesting questions about what pedagogical goals such a game can address, and how to make the game fun for players at a variety of grade/skill levels while encouraging all players to improve their math skills.
More variety — the new game will feature a much wider variety of problems, with somewhat more variation in level of difficulty. In addition (ha ha ha) to basic arithmetic facts with integers, I plan to include fractions, decimals, percentages, primes and factoring, and some basic statistics (mean, median, mode, range) and geometry. I would like for there to be a thematic association between the problem types and different regions of the game world and types of monster.
I would also like to open up the possibility of fighting more than one monster at once — maybe. This would call for a more involved combat system, since the original, one problem, you hit it/it hits you system won't work if there's more than one of it. The system I'm considering gives you one problem for each attack — to dodge the enemy's attack, or to hit with your own. The type of problem depends on the enemy (and some may have more than one kind of attack) or on your equipped weapon/technique, respectively. The disadvantage of this system is that, if you're outnumbered, you'll do a lot more "dodge" problems than "hit" problems, and doing a problem just to avoid taking damage is less exciting than dealing damage yourself.
On the other hand, if you face several monsters, but you hit each one that doesn't hit you, how is that different from taking them on one at a time? One possibility is time — you might have a certain amount of time per round, so more enemies would mean more time pressure. But I feel that time limits should be used with caution, since I imagine that solving speed varies a lot among students.
Speed is one of four dimensions of proficiency that I can think of, along with size, accuracy, and type. Speed means doing the same problem faster. Size means doing a more difficult problem of the same kind (more digits, more steps, etc.). Accuracy means getting the problem right more often. Kind means solving a different sort of problem entirely. I'm a bit worried about kind — how standard are math curricula? At what grade level can students be expected to have been exposed to which concepts? In games like Number Munchers or Math Blaster where the types of problems are independent of the plot and each challenge is separate from the next, concepts the player isn't expected to have learned yet can simply be skipped, but in Numbers Land, how are players who haven't learned about graphs going to get through Cartesia, for instance?
Balancing the game, difficulty-wise, is going to be tricky in any event. In a typical CRPG, the player character's combat ability is determined by stats which improve when the character gains a level. The more you play, the stronger your character gets. But Numbers Land is about the player getting stonger (at math), not the character — if the game is going to dynamically make itself easier, it should do so when the player is doing poorly, and this should not be construed as a reward.
However, being able to do more damage is a reward. This means that improving your character's defensive and offensive abilities will be covered by completely separate systems. You'll gain defense experience points when you get hit, or lose a battle, and these will go towards increasing your hit points and extending the time limit (if there is one). You'll learn offense techniques by passing a training exercise (quiz) at one of the world's many training centers (your character is a kind of arithmetic martial artist), and this will allow you to choose different kinds of problems for your own attack, including bigger problems that deal more damage. The most skilled players will collect all the techniques without gaining any levels.
I'm not sure where the genre-traditional equipment fits in this system, but the genre does recognize a martial artist character class who uses techniques rather than weapons. Still, it would be nice to have some items to collect beyond the handful of necessary McGuffins.
So... if you have any thoughts, be they from an RPG or a pedagogical point of view, I want to hear them.
In the orginal Numbers Land, the combat system was very simple. In each encounter, you would face one monster. During each round of combat, you would answer one arithmetic problem. All problems were drawn from the same random distribution of two-digit addition, subtraction, multiplication and division facts, and were roughly comparable in difficulty. There was no time limit (it would have been difficult to implement one). Answer correctly, and you would hit the monster, doing damage depending only on your level (no random component). Answer incorrectly, and it would hit you, doing damage depending only on the type of monster. That was pretty much the whole game.
For the new Numbers Land, I have something much more complicated in mind, which raises a number of interesting questions about what pedagogical goals such a game can address, and how to make the game fun for players at a variety of grade/skill levels while encouraging all players to improve their math skills.
More variety — the new game will feature a much wider variety of problems, with somewhat more variation in level of difficulty. In addition (ha ha ha) to basic arithmetic facts with integers, I plan to include fractions, decimals, percentages, primes and factoring, and some basic statistics (mean, median, mode, range) and geometry. I would like for there to be a thematic association between the problem types and different regions of the game world and types of monster.
I would also like to open up the possibility of fighting more than one monster at once — maybe. This would call for a more involved combat system, since the original, one problem, you hit it/it hits you system won't work if there's more than one of it. The system I'm considering gives you one problem for each attack — to dodge the enemy's attack, or to hit with your own. The type of problem depends on the enemy (and some may have more than one kind of attack) or on your equipped weapon/technique, respectively. The disadvantage of this system is that, if you're outnumbered, you'll do a lot more "dodge" problems than "hit" problems, and doing a problem just to avoid taking damage is less exciting than dealing damage yourself.
On the other hand, if you face several monsters, but you hit each one that doesn't hit you, how is that different from taking them on one at a time? One possibility is time — you might have a certain amount of time per round, so more enemies would mean more time pressure. But I feel that time limits should be used with caution, since I imagine that solving speed varies a lot among students.
Speed is one of four dimensions of proficiency that I can think of, along with size, accuracy, and type. Speed means doing the same problem faster. Size means doing a more difficult problem of the same kind (more digits, more steps, etc.). Accuracy means getting the problem right more often. Kind means solving a different sort of problem entirely. I'm a bit worried about kind — how standard are math curricula? At what grade level can students be expected to have been exposed to which concepts? In games like Number Munchers or Math Blaster where the types of problems are independent of the plot and each challenge is separate from the next, concepts the player isn't expected to have learned yet can simply be skipped, but in Numbers Land, how are players who haven't learned about graphs going to get through Cartesia, for instance?
Balancing the game, difficulty-wise, is going to be tricky in any event. In a typical CRPG, the player character's combat ability is determined by stats which improve when the character gains a level. The more you play, the stronger your character gets. But Numbers Land is about the player getting stonger (at math), not the character — if the game is going to dynamically make itself easier, it should do so when the player is doing poorly, and this should not be construed as a reward.
However, being able to do more damage is a reward. This means that improving your character's defensive and offensive abilities will be covered by completely separate systems. You'll gain defense experience points when you get hit, or lose a battle, and these will go towards increasing your hit points and extending the time limit (if there is one). You'll learn offense techniques by passing a training exercise (quiz) at one of the world's many training centers (your character is a kind of arithmetic martial artist), and this will allow you to choose different kinds of problems for your own attack, including bigger problems that deal more damage. The most skilled players will collect all the techniques without gaining any levels.
I'm not sure where the genre-traditional equipment fits in this system, but the genre does recognize a martial artist character class who uses techniques rather than weapons. Still, it would be nice to have some items to collect beyond the handful of necessary McGuffins.
So... if you have any thoughts, be they from an RPG or a pedagogical point of view, I want to hear them.
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(no subject)
Date: 2007-01-12 04:21 pm (UTC)If someone asks you to do a math problem, you're aware you're doing a math problem. That's no farther removed from a real life combat scenario than rolling dice, but it is one step closer to the homework/test environment. It's math-in-a-vacuum. Whereas if you're in a more traditional RPG, keeping track of your stats and modifiers on the fly, you're still getting some of the basic arithmetic but also internalizing math-as-applied-skill.
(no subject)
Date: 2007-01-14 04:02 am (UTC)(no subject)
Date: 2007-01-14 05:06 pm (UTC)(no subject)
Date: 2007-01-12 09:20 pm (UTC)Well, I guess I wonder why you want to open it up to multiple monsters. In my CRPG playing experience (which, as we know, is skewed a little younger than your own - less NES, much more PSX), games with multiple monsters tend to have multiple characters in your own party, as well. Is there a reason why, if you're adding multiple monsters, you couldn't also have multiple player characters? That way, sometimes you might be outnumbered, sometimes there would be an even balance, and sometimes the monsters might be outnumbered.
(no subject)
Date: 2007-01-13 01:14 am (UTC)It strikes me that a lot of interesting properties of numbers (and shapes, etc.) can be expressed as sets. (Which isn't too surprising, since set theory is a popular foundational system for math, although not my favorite.) Anyways, for any set, like "divisible by three", "prime", you could have a weapon that attacks only those numbers/shapes. Thus, both of those "weapons" would work on 3, but only the "prime" weapon works on 37. This does at least mean multiple "weapons" can work at some point.
If this is to be open source, I recommend sourceforge.net.