Math Game Design Group

Join the game design email group organized by Colleen King of Math Playground

"Games are thus the most ancient and time-honored vehicle for education. They are the original educational technology, the natural one, having received the seal of approval of natural selection. We don't see mother lions lecturing cubs at the chalkboard; we don't see senior lions writing their memoirs for posterity. In light of this, the question, "Can games have educational value?" becomes absurd. It is not games but schools that are the newfangled notion, the untested fad, the violator of tradition. Game-playing is a vital educational function for any creature capable of learning."
Crawford, The Art of Computer Game Design

Connecting math and mechanics

Use this form to capture good connections between math concepts and game mechanics.

Examples so far:

Live and Interactive Meetings

Login & Recording
June 16th at 9pm ET
World Clock

Math Trek photography game: discussing the mechanics

Randall Fujimoto, Maria Droujkova

Full recording: voice, text chat, web tour


The goal of this group is to develop and publish an innovative, online math game. To get started, I thought we could answer some questions that will get us all thinking about game design. You can respond here on the wiki or send your responses to me privately. It will be interesting to see how similar or dissimilar our ideas are. - Colleen

The initial game review and brainstorm in the weekly Math 2.0 events series is here and a later meeting here .

  1. What makes a game good?
    1. "Princess rescuing application" is my favorite presentation about good serious games/apps. - Maria Droujkova (MariaD)
    2. My game design hero is Tom Malone What makes Things fun to learn: Heuristics for game design who influenced my thinking about games back in 1980. Unfortunately, his paper costs $15 to download. (Thank you, ACM.) (Discussion of Malone hereTonyF). He made me aware that the math should be intrinsic to the game design and that kids really want to learn the math in the context of the game. He used the game Darts for his research. See Jason Sayre's Flash applet version which I encouraged him to write. His decimal version is great too. -Ihor
    3. When I think about good games in an educational sense, Seymour Papert's hard fun concept comes to mind. The goal of the game has to be one that is meaningful to the player. The path to the goal should be sufficiently challenging and within the player's reach. Successive game plays should then move the player closer to that goal. Ihor, I've seen the dart game and agree that it's very good. I've been thinking about how the math concept itself could be the game. That's something we should keep in mind during the design process.-Colleen
    4. There is a class of drill-type games I actually like. What makes those good is some openness (creativity? game-ness?) in the questions. For example, in this subtraction game you need to find two numbers that result in the given answer. It calls on memory skills, attention and reasoning in the way no exercise of the 5-2=? variety ever can: web/games/SpeedGrid/ Subtraction/urikasub1res.html >> - MariaD
    5. (New) I listened to Hasslebring's keynote about math subskills research at the FETC conference 10/22/09 yesterday.Tom Snyder sells a product called Fastt Math based on this research. He confirmed a theory that I believe. Those math blaster drill games are fun for the kids but they only help in reinforcing skills that students already have. Without further intervention they won't learn facts they don't know from these games. -Ihor (10/23/09)
    6. Mark Overmars' tutorial describes some of key ingredients in creating good games. - TonyF
  2. Have you seen examples of good math games online?
    1. Set! online (a puzzle game). Sand (a meditation/mood game I use to set the atmosphere in Math Clubs). Zoombinis (an offline logic game that could be ported). - MariaD
    2. My favorite is (though not really a game in the traditional sense) is Green Globs. I've written a lot about it including here It's an excellent example of a software environment that motivates kids to want to learn math. (Woops.. There currently is no online version of Globs, but there are some that are similar, but nowhere near as good. (See Shooting Balls - Freudenthal i.e) -Ihor
    3. Phun is a great sandbox game to explore physics and a good way to introduce some math concepts too. How close does a slingshot need to be to knock over a tower? Given two "vehicles" (that students can design themselves) that move at different speeds starting at different locations, which will win a race of a certain length? -Chris Hazard
    4. Just about any sandbox game which requires proportional reasoning or concepts of variation and causality, Phet, Fantastic contraption, Linerider1, Crayon Physics, Elastolab, Falling sand, Orbiter, Soda constructor, Armadillo run, Bug brain, Game Maker sims, Physics, TonyF
    5. I don't have any good examples. I would like to know more about Lure of Labyrinth. I believe Scot Osterweil (Zoombinis) was behind this project. Have you played this game? I can't seem to get past the wandering around stage. I've yet to see any math challenges. Chris, that's a great idea that we can complete in a reasonable amount of time.-Colleen
    6. Mainstream games can be used for mathematics. For example, using the auction house in World of Warcraft is a good way to learn maths. TonyF
    7. ...
  3. What are some examples of poorly designed math games? What must we avoid?
    1. "Solve a problem, shoot an alien" as a genre. Any game where game mechanics are not intrinsically connected with the math concepts it supposedly teaches or reinforces.- MariaD
    2. There are plenty out there mostly written by groups that dont pay much attention to good game design. -Ihor
    3. A poorly designed math game is also a poorly designed game, so my answer will be general. Avoid games that do not continually challenge the player in some way. If there is a dominant strategy or a simple way to complete every level, the game fails the player. Similarly, if a game is too challenging, players get frustrated. The trick is to find one that is consistently engaging to the audience. The game should progressively teach the player and the player should continually use things they have learned throughout the game. -Chris Hazard
    4. I agree with all three of you. I wonder why these types of reinforcement activities continue to be very popular with teachers. Even enlightened educators speak very positively of these games. Are poorly designed games so prevalent that they have become the accepted norm?-Colleen
    5. Chocolate coated broccoli is a term used to describe educational games which attempt to dress up boring content with a thin layer of fun. "much educational software is like broccoli in that in order to make it appealing, it has been "sweetened" with chocolate. This is like Papert’s "Shavian reversal" where the child inherits the worst of both parents." Does Easy Do It? Children, Games, and Learning The ten minute PhD, TonyF
    6. ...
  4. What should be the purpose of our game? Do we want to teach a new concept, reinforce concepts already learned, or create an environment where kids can interact with math objects and ideas?
    1. I'd like an environment where kids can interact with math-rich objects in ways relevant to purposes intrinsic to the game. For example, in Zoombinis it's passing through a series of logical gates on the basis of external in-game character features. Also, making your own "levels" would be nice. For the content area, I'd like multiplicative reasoning, because I've been studying it for 10+ years - MariaD
    2. Games that do what Globs does.... engage kids in the math using a powerfully engaging context. I like to focus on developing fractional, proportional reasoning concepts - not skills so much - because that tends to narrow the context too much. The worst examples Ive seen are the ones that try to model division of fractions. Its terribly difficult to do right. I usually avoid any formal instruction there, just build on the students intuitive ideas of division in general.
    3. I'm partial to an exploratory setting rather than a single objective user interface such as the one in the Dart game. However, these are more difficult to develop. A Dart type game could be programmed in a week once the rules and objectives were determined. An open ended environment would be a long term project. My practical side thinks our first game should be less ambitious without sacrificing quality.-Colleen
    4. ...
  5. What do we want to accomplish? Should we select a specific skill such as multiplying whole numbers or dividing fractions? Or should we create a game that uses many ideas from a larger area of math such as algebraic or geometric reasoning?
    1. We could make a series of specific skill puzzles that "add up" to a larger area. But they got to be genuine puzzles, not drills or exercises. Here is a proportional reasoning puzzle I like: fish puzzle. I can see a game based on Universcale ("where in Universcale is Carmen S.?") - MariaD
    2. I don't have a particular preference other than the one I mentioned above. Proportional reasoning is the key to success in math learning. -Ihor
    3. I'm on board with proportional reasoning. This topic would cover a large range of grade levels. We could create levels within the game. Elementary age students could begin the game. Middle school students could potentially get all the way to the end.-Colleen
    4. More on proportional reasoning. Mathematics is a language, a system of symbols which have meaning. Like written language, it acts as an amplifier to our cognitive abilities. Lemke has written on typological and topological languages. Mathematics, Lemke says, is topological, it "distinguish(es) variations of degree (rather than kind) along various continua of difference" I would be happy with anything which explores variation in a symbolic way. This is a similar to the idea of proportional reasoning. TonyF
    5. ...
  6. Is it important to relate the math concepts in the game to real world applications?
    1. I think it's important to relate math concepts to SOMETHING significant and meaningful; it can be utility (applications), beauty, community and friendship, or in-game meanings. - MariaD
    2. Not necessarily, fantastical worlds are just as good as long as its well done.
    3. I think there is room for both. If the game is internally self-consistent, it can be an unusual world or experience for the player to explore (e.g., Crayon Physics Deluxe). Also, some games, particularly those devised in game theory and economics, can have important real-world implications even if they are very abstract. For example, the following games are great for engaging the class: Keynesian Beauty Contest, Minority Game, Iterated Prisoner's Dilemma. In each case, the basic principles are easy to grasp and can be used to teach concepts as easy as what an average or summation is, but can be used as practical examples to teach more advanced concepts such as exponential discounting. When teaching about auctions and game theory, I've sometimes used trick decks of cards that are of all the same value (e.g., 50% jacks). That way, when the students see me deal out one card to each of 8 students, they assume that each student has a different valued card. They then play as if they do, even if they do not, which is a great way to teach things about assumptions. On the other hand, seeing a direct mapping between a game and a real-world setting or practical application can entice a student to apply their knowledge accordingly. -Chris Hazard
    4. I think the challenge itself is more important than the setting. -Colleen
    5. ...
  7. Should the game be part of an overall engaging story? Does the game need a setting?
    1. How about the notion of "levels" or "dungeons" with the same character(s) or other common elements, but different circumstances? MariaD
    2. An engaging story would be great, but may be too challenging for a first group project. Some of the Math Forums POWs are good sources for games some of which became applets. -Ihor
    3. I don't think it necessarily does. Tetris and other puzzle-type games don't always need a story and are still engaging. If the material is dry, then a setting and story can help make it digestible. I think it would work best when the story or setting is closely related to what concepts are being taught. However, adding a story and setting that aren't engaging can actually be worse than not having a story if it turns out to be distracting or superfluous. -Chris Hazard
    4. Ihor, do you have examples of POWs that became games? -Colleen
    5. Colleen - I was thinking of the Broken Calculator game. When the Math Forum had funding for their ESCOT technology POWs, I was involved with group of participants that suggested making the broken calculator activity into a game. I don't think they made any progress on that. Here's how I used the Broken Calculator activity in my CIESEmath project:
    6. There is some evidence that girls relate better to narrative styles and boys action styles. In USING STORYTELLING TO MOTIVATE PROGRAMMING, the Storytelling Alice programming environment was used to to create computer-animated movies inspires middle school
      girls’ interest in learning to program computers. Collaborative gameplay is especially important for girls, Playing Together Beats Playing Apart, Especially for Girls, TonyF
  8. How can our game be unique? A lot of online games have essentially the same game mechanics housed in different settings.
    1. A large list of game mechanics. Also, Chris Hazard's time mechanics. -MariaD
    2. We should collectively make a list of games that are good and unique and go from there. (It would start up a nice discussion on what we mean by "unique".) -Ihor
    3. In the gaming industry, some companies focus on well-polished games that are balanced and fun to play without being particularly unique, others produce innovative mechanics, and some do a little of both. Just because a game isn't unique doesn't mean it is a bad idea. When teaching a particular unique concept, particularly mathematical, unique mechanics may benefit the student if the mechanic and concept are closely intertwined. One approach is to examine the concept to be taught and see how you can turn it into a puzzle or otherwise engaging experience and have the player build on their knowledge to move forward. You can then adapt previously known game mechanics or make a new blend that fits the problem. -Chris Hazard
    4. By unique, I meant a game design that has not yet been used to teach math. When games such as Crayon Physics first appeared, the concept of actually drawing the game elements was unique. I am more concerned with avoiding overused game formats than inventing a new genre of games. I do think it's ok to improve an existing design. -Colleen
    5. ...
  9. How important is competition in a game? Do educational games obscure the idea of enjoying math for math's sake? Students play the games because they want to get the high score or reach the next level or gain something that is external to math. Is this something we should move away from? Is it possible to create an educational game in which students don’t win in a traditional sense? The “winning” is the gameplay. What might that look like?
    1. There are cooperative games, meditation games, and hybrid (e.g. team vs. the environment) games. I like to think in terms of games that provide set goals, vs. games where players can set their own. I vote for a goal-oriented game with the "zen mode" (no scores, minimal hazards) available. - MariaD
    2. Personally I don't have a problem with competitive games. I've gotten way too much good mileage over the years by playing game with my classes. Most kids love them. The trick is to make good ones that boys and girls love to do together and that everyone comes away feeling good about it and they learned some math. A game I used to play was How the West was one+two x four (Sunburst). We would play it backwards which was great for learning about negative intergers.
    3. You can further divide the type of games into zero-sum games (purely competitive with a distinct winner and loser), cooperative games (individual score is perfectly correlated with the social score), general sum games excluding the first two types (like an economy where players are incentivized to increase their score, but there is no prize for the highest score and no ranking), and single-player games (compete only against the levels or computer). Then there are sandbox games where the player explores on their own without goals. There are other taxonomies of games and a handful of games purposefully that try to break such molds. I'm less aware of how well these different pedagogical environments work with younger students (I've taught primarily college age and some gifted & talented high school), but the basic principals of game theory with respect to repeated games can be useful to predict how a particular game design will unfold in practice. I've seen collusion between students in some otherwise zero-sum (perfectly competitive) games I've run in my classes, and have even pointed it out as it happened and later discussed how it affected the end results. -Chris Hazard
    4. I know that some students are very opposed to time limits. Interestingly, time limits are one of the hallmarks of poor educational game design. Many designers think that by adding a timer, any drill activity automatically becomes a game. Competition, however, is alive and well.-Colleen
    5. ...
  10. What age group should we target?
    1. Like "Alice in Wonderland" book! - MariaD
    2. I'm a middle school kind of guy which means - almost anything done appropriately is game for me. - Ihor
    3. I'm partial to grades 4-8 though, as Maria suggested, a game that appeals to everyone is a great goal to have.-Colleen
    4. ...
  11. What skills or knowledge will you contribute to this project?
    1. Pedagogical content knowledge, gaming experience, some experience with game design with Math Club kids. - MariaD
    2. I've been thinking about (math) games for most of my adult life which is interesting given that I am not a big game player myself. I've looked at and used a lot of math software game over the past 20 years as maths project manager at CIESE at Stevens Tech in Hoboken, NJ. -Ihor
    3. I'm currently stretched pretty thin across my various commitments, so at this stage I unfortunately won't be able to offer significant development/programming/code architecture work. I will be able to offer advice from my experience designing and developing games, my knowledge of game theory for aligning incentives, and my experience designing and running games (the offline kind) in game design and game theory classes I've taught. While I don't have time to play as many games as I used to, I have some familiarity as to what is out there in the gaming industry. Further, as my company moves forward, we'll look at possible opportunities of using our time manipulation engine for pedagogical purposes like this. -Chris Hazard
    4. Ihor, I think about math games a lot and, like you, I am not a gamer (see question 2). My contribution would be programming, organization, and game design experience with children. We could use someone with artistic skills and we may need a second programmer if some advanced elements are needed.-Colleen
    5. Pedagogical content knowledge, using game programming to teach mathematical concepts. 1 2 3 4 Currently helping with the development of Turtle Art.TonyF

Thank you all for your very thoughtful responses. I will check the links that were mentioned and play some of the games. If there are discussion points that I've missed, please feel free to add them to this list. I think our fundamental ideas about game design are strikingly similar.

Step 2
The next step is proposing specific game ideas. What do you want kids to learn and how will your game help them achieve that goal? What is the action in the game? What does a player actually have to do? Contact Maria Droujkova droujkova at gmail dot com to join the discussion.