Posts tagged games

Good calculation games

Here are games that work well with arithmetic tasks. By “work well” I mean:

  • Mechanics provide players enough agency and freedom to develop tactics, so that the overall activity is still a game (rather than a quiz)
  • Mechanics produce strong, pleasant flow, as evidenced by popularity
  • The overall feeling of the game is vaguely mathematical (this one is hard to define and requires human judgment with some artistic license)
This gets two and a half out of three on my “quality math game” definition (attached).
Examples:

Join my math game design online event February 3rd

 

I summarized some of my thoughts on math game design for the upcoming online event February 3rd, which is a part of CO12 (Connecting Online 2012) conference. In particular:
- Defining intrinsic math game mechanics, and why we want them
- Taxonomies for math game designers
I would very much like comments about my slides, which are here:  https://docs.google.com/presentation/d/10gG23rJdWKwdDh4sWgj9uYptx4XSiFKmYbeAk0YUT94/edit
The presentation will happen online on February 3, 1pm Eastern Time, and is open and free. You can log in here: http://www.wiziq.com/online-class/701943-math-game-development-communities-and-networks

Games and revolutions

Games devoted to fluency rather than creative mastery or exegesis of the subject matter are tools of continuity. They attempt to maintain a firm, secure grip on the generational transmission of information. The grip is slipping in the digital, co-produced, post-book world.

Kids These Days (TM) write and otherwise author several orders of magnitude more than kids used to author.

Can drill games maintain the continuity? Is this one of the reasons it’s sort of hard to find financing for games that can teach kids to lead interesting lives through developing a subversive attitude toward the status quo?

My rules for judging learning games

This is a comment at a LinkedIn conversation in Game-Based Learning (a closed group).

I have a few criteria I use. If game designers get these things right, most of the time everything else is good, too.

  1. “No Jeopardy” rule: Game mechanics are intrinsically related to target concepts.
  2. “No drill” rule: Players can make better or worse strategic choices with engaging in-game consequences, rather than being told they answered a question wrong.
  3. “Conceptual reward” rule: Players understand something bigger, better and at a whole different conceptual level about the target concepts from the strategy of the game, than they do from the tactics (individual steps).

99% of learning game designers can’t manage to pass these criteria.

Defining game mechanics: Part 2 of 2

Part 1:

Game mechanics are metaphoric structures defining actions, objects and their relationships within the gameplay.
Intrinsic game mechanics in learning games use the same metaphors that define concepts the players are studying.

The practical framework for designing intrinsic mathematical learning games stems from the above definitions.

  1. Identify the target concept
  2. Analyze the concept to find a mathematical metaphor for it
  3. Model the metaphor in particular objects and actions
  4. Match game mechanics to the model
  5. Compose the game out of mechanics

Let’s use the framework to analyze a few math games from the same conceptual field, the coordinate plane. In the first two examples, you can see how the same metaphor can lead to different game mechanics, when modeled differently.

  1. Concept: Coordinates
  2. Metaphor: Ordered pairs (of qualities)
  3. Objects and actions: A grid with qualities constant within each row and each column; finding positions, cell entries, or labels of the grid by other known data
  4. Game mechanic: Matching objects with a given pair of qualities to a position in the grid
  5. Game: Zoombinis Mudball Wall

  1. Concept: Coordinates
  2. Metaphor: Ordered pairs (of numbers)
  3. Objects and actions: A grid with numbers constant along each vertical and horizontal line; finding positions or labels of the grid by other known data
  4. Game mechanic: Walking to a safe position on the grid
  5. Game: Robot and Maze

  1. Concept: Graphs of linear functions
  2. Metaphor: A (laser?) ray
  3. Objects and actions: A line going through a particular point, with a particular slope, aiming for particular positions in space
  4. Game mechanic: Optimizing line position to hit as many of the targets as you can
  5. Game: Green Globs

Visit Math Future Game Design Group for more ideas and discussions.

Defining game mechanics

Game mechanics are metaphoric structures defining actions, objects and their relationships within the gameplay.

Game mechanics are related to, but separate from, rules of games, user interfaces, tactics and strategies, and genres.

Intrinsic game mechanics in learning games use the same metaphors that define concepts the players are studying. For example, one of the grounding metaphors for “equation” is “balance.” Intrinsic games for learning equations that are based on balance game mechanics can involve characters piling weights on a balance scale, walking along a fulcrum, or adding weights and balloons to a dirigible. Each of these mechanics can be used in different game genres, such as puzzles, platformers, race games or roleplaying games.

On the other hand, a game where players shoot correct answers to equation problems out of the sky is extrinsic. The game mechanics (choice and shooting) have nothing to do with the topic of the equations, and could be used for anything from matching capitals and countries to learning Latin roots.

There are more discussions and examples specific to mathematics at the Math Game Design group: http://mathfuture.wikispaces.com/GameGroup

Part 2 explains how to make games on the basis of this definition.

Visit Math Future Game Design Group for more ideas and discussions.

Lowering prices or making wealth? Games and math

This is my answer to a discussion Colin Chambers started at his game developer group Symbiotic Learning. Colin’s prompt was:

Please read the passage below, and then read it again, swapping GAME for SCIENCE, and decide whether you believe it applies to either games, science or both. I strongly believe gaming, as outlined by Jane, has a strong relation to science. What about you?

A GOOD GAME HAS:  (Jane McGonigal)

1. A goal
2. Rules
3. Feedback
4. Voluntary participation

“Playing a game is the voluntary attempt to overcome unnecessary obstacles” ~ Bernard Suits

Let us talk about the concept that’s important for “voluntary participation” – PRICE OF ENTRY.  The price is in several currencies, including time, money, and reputation.

For example, the proverbial rocket science or brain surgery science have very high price of entry in all three currencies. You need to study for years, it costs a lot of money (yours or the society’s) and you need to gain a lot of reputation as you go along to be supported in any serious experiments and publications.

Environmental science or nutrition science have lower price of entry, and in fact, there are many citizen science projects in both.

Let us look at games. Eve Online has a monthly fee, requires about 30 hours before you understand what’s going on, and in-game connections to corporations to have any sort of fun with it. As games go, it has one of the highest price of entry. Not coincidentally, it involves rocket science.

World of Warcraft has the same monthly fee, but it is fun to play from the first five minutes, can be played solo, and supports casual gaming. It has much lower overall price of entry. Both are excellent games, but the difference in price of entry correlates with the number of players, which is about fifty times higher in WoW.

Now take Farmville, with five times more players still than WoW… You see where this is going!

Right now, mathematics is like “Eve Online” – the price of entry is such that, for example, only about 5% of adult Americans are algebraically literate.

Should we lower the price of entry for education? Should we aim, instead, of making people wealthier in all currencies so they can pay high entry prices?

Math games and anti-social behaviors

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This blog post originally appeared on Technology Integration in Education, where I am a guest blogger. More interesting is Colleen King’s response – she’s the author of the widely stolen games.

I am absolutely thrilled when new math resources that include interactives appear online. Cataloging, annotating, tagging and making collections can add value to interactives. These jobs don’t necessarily have to be done by the same people who program math games or applets.

Right? Right?!

Here is an altogether positive example of a resource catalogue: MathForum’s Internet Math Library, the Software page. It provides tagged, searchable short reviews of sites with math interactives. One big minus of the library is that it does not deep-link individual games.

Deep-linking even many resources can be done appropriately. Take a look, for example, at MathsOnline blog. It links and categorizes several hundred math games created and hosted everywhere. Each game has a short (original?) review, a screenshot, tags, and the link to the site where it is hosted. Here is another example of such a site.

Some people object to deep-linking to their sites, especially if no content (no value) is added by the process. I confess it is annoying to find the same interactives, with the same descriptions, indexed by the same category and tag set, in gazillions of places. Instead of providing service to educators, this practice wastes time when people click link after link only to find the same content.

Then there is outright stripping of credentials. I don’t want to call this “theft” if it is done to something that is already freely available to anyone. It is not about property. It is, however, a deeply anti-social, anti-community behavior.

Consider an example that recently came up in a discussion of math games. “Percent shopping” is a game Colleen King created for her site Math Playground. It features a kid shopping at a store called “Troy’s Toys.”

There are automated content-aggregating sites, apparently dozens of them, that not only embed the game without any attribution to the author, but also offer its embed code to their visitors.  Some examples:
http://www.wordfreegames.com/game/percent-shopping.html
http://www.home-games.org/game/116/Shopping-at-Troy_s-Toys.html
http://www.freekidsmathgames.org/game/18/Shopping-at-Troy_s-toys.html

The sites sell ads. Using other people’s content. Without adding value to the content. This is bad.

The problem is also self-propagating, because new aggregating ad-selling sites, which are built automatically, simply take content from old aggregating ad-selling sites. Also honest but newbie site builders may take content from these “free and nameless” collections without realizing anything is wrong.

A consolation: math is now so hot that thugs break laws for its sake.

One may be a strong proponent of the Pirate Party on the grounds of making content available to people in need. But this situation is different: the content is already available.  The only other freedom some of these sites provide is making the content embeddable – but they strip the credentials in the process! Cory Doctorow recently wrote, in his Guardian column:

In my world, copyright’s purpose is to encourage the widest participation in culture that we can manage – that is, it should be a system that encourages the most diverse set of creators, creating the most diverse set of works, to reach the most diverse audiences as is practical.

Piracy, arguably, can encourage wider initial participation – but discourage large and expensive projects. In my mind, games that are already available for free, on a well-organized site without ads, don’t require any further liberation. Or do they?

Is easy embedding such a big deal? Here, I took a screenshot of Colleen’s game and linked it to her site. Is this significantly worse for promoting wide content creation than the ability to embed the game right here?

Colleen King’s response to the original post


It isn’t often that I’m mentioned in a blog post so I was very curious to read this. I wonder if people are aware of just how prevalent this problem is.

I agree with your description of this practice as “deeply anti-social, anti-community behavior.” And I agree that it’s not about property. And while this isn’t theft in the traditional sense, since I am still in possession of the original games, I think the consequences of such actions are more destructive than people may realize.

I’m going to describe a fictional but more real world example that depicts what is taking place and the potential harm it may cause.

Imagine that a group of people decide to organize a community theater. The idea is to create original, short films and show them free of charge to people who enjoy such productions. The group writes stories, builds sets, licenses music, rehearses, records the action, edits the film, and finally presents its work to the community.

Everything is wonderful. The theater group is doing what it loves to do and the community is enjoying the films.

Eventually, the theater group must face the economics of providing a free service. There’s rent and utilities, licensing fees, and editing software to consider. And demand has become so great for these films that the theater group is working practically full time without any compensation.

The group considers its options. It could begin charging the public to view its films. The group argues that doing so would prevent some members of the community from seeing the films for financial reasons. That didn’t seem like the right thing to do. Then someone suggests asking local businesses to sponsor the community theater. The group would place ads from local businesses in its brochures and show ads to the audience before viewing films. This seems like a win-win situation. The community theater covers its expenses and can even pay its members a small salary. Local businesses are gaining new clients and customers. And the community is enjoying wonderful films free of charge.

Flash forward.

Mr. X has been watching the success of the theater group from afar. He thinks this is something he’d like to do. However, Mr.X doesn’t know how to make films and doesn’t wish to spend any time learning. Besides, he rationalizes, the theater group already created a good product. And Mr.X is really only interested in the profit potential of the community theater. Providing a service is just a secondary benefit.

Mr. X finds some low cost space for his theater, comes up with a catchy name, and makes the theater attractive and comfortable. He then pays a visit to the original community theater group. Mr.X finds copies of all the films the group has ever produced and proceeds to take one of each. He wastes no time adding the films to his own theater’s list of events. The idea is working! Mr.X is earning money while providing a terrific service. Businesses are doing better than they ever have and the people in Mr. X’s community are thrilled to have such wonderful films to watch free of charge.

Meanwhile, Ms. K, one of the members of the community theater group decides to do some traveling. And in her travels, she stumbles upon Mr. X’s theater. Enjoying films as she does, Ms. K decides to go to an afternoon show and, much to her surprise, the film is one she made some years ago! Ms. K looks through the theater’s listings and finds nearly every one of her films on the list. But there is no mention of her work or anything at all about the community
theater group she founded all those years ago. Then Ms. K finds something even more disturbing in the brochure. Mr. X is giving away copies of the films! She tries to contact Mr.X but he is nowhere to be found. Feeling somewhat helpless, Ms. K returns to her theater group to discuss the matter.

They view a graph showing the number of people attending the theater over time and spot a disturbing trend. Traffic has been diminishing. People no longer think it’s necessary to visit the original community theater since the films can be viewed elsewhere. The group then looks at profit charts and observes a similar pattern. When traffic declined, local businesses no longer saw any benefit in sponsoring the community theater. The theater began earning less and was struggling to cover its expenses. It could no longer afford to produce new films thus depriving the community of its unique and innovative work.

The story of the community theater is a sad one but I wonder if it had to be so. Could the community theater story have a different ending?

How can organizations protect themselves from unauthorized distribution of their creative works, apart from invoking the law? Would the community theater prosper if it had decided on its own to distribute its work under a creative commons license? I can see how that might return control of creative works to the organization but I wonder if it would eliminate or even reduce the attribution problem. Is it beneficial to have copies of creative work available in hundreds of locations? Online, the concept of location is mostly inconsequential. There are exceptions but generally we have access to the original work and every location that stores a copy. What’s the benefit of multiple copies?

This is a very interesting problem with many subtleties to discern.
I’m really like to hear what others think.

3 Large Math Applet Communities

This is a guest post for Technology Integration in Education. I review three large active online communities centered on sharing applets, widgets, interactive models, and other pieces of “executable mathematics.” What other applet-making communities are currently alive, active and promising? Please add to the list!

  1. Scratch from MIT, the most popular descendant of Logo, currently has about 130 million applets. There are two very good reasons for this popularity. First, the programming environment itself is visual, intuitive, and so simple I used it with kids under three and they got it. It looks and feels like building with Legos.

    scratch code

    Second, Scratch has excellent tools satisfying all principles of community building. Applets are shareable with one click of the “share” button, as you make them. Each applet gets its own linkable and taggable page with comments, information about the author, ratings, tags and other community feature.  Applets are remixable, with automatic tracking of previous authors. I use Scratch to show kids what is open source software, as you can open any applet’s code in your editor with a click of a button on its web page. Also, applets are easily embeddable. Here is one of my students’ favorites:
    Scratch Project

    Because Scratch community does not have any top-down taxonomies, categories, or quality controls, it may be hard to find applets that satisfy a particular set of topic, level and quality requirements – what teachers need for lesson planning. On the other hand, kids can usually find what they need, such as games with particular game mechanics.
    There is also an educator community ScratchEd, and International Scratch Day celebrated in May by hundreds of local communities, and online.

  2. GeoGebra is a powerful platform for making sketches and animations, solving problems, and supporting rapid development of math interactives. Its particular strength is the dynamic connection between a computer algebra system and geometric constructions. Drawing with Euclidian tools is automatically or easily linked with graphs, functions, formulas and tables of values. A lovable feature is the ability to remember any multi-step geometric construction as a custom tool. For example, once you build a star using Euclid’s construction axioms, your next star can be created with a click of a button.


    GeoGebra community has a strong support for local groups through GeoGebra institutes and regional conferences, and has applet-sharing wikis in 27 languages. Applets are shareable, embeddable, and remixable, but community tools, such as an active forum, are not applet-specific. This promotes creation of many different communities for aggregation and discussion of GeoGebra content in groups, such as the wiki where I first met the above animation.

  3. Wolfram Demonstrations requires software with a somewhat steep learning curve. This means every Demonstration is made by a math geek, with the obvious implications for quality. Mathematica software is not free (the viewer is), but volunteers for Wolfram used to get a free copy. Volunteer tasks are accessible to novices."Rhombic Enneacontahedron with 30 Icosahedra" from the Wolfram Demonstrations ProjectDemonstrations are linkable, and their code is available for remixing. There are no other social features, such as discussions of applets, tags or ratings. The site uses top-down categories for browsing applets. The sense of community is sustained largely through academic connections of authors, and isn’t apparent from the site.

Problems and their camp followers

What is a problem for one person can be a puzzle or an exercise for another. A smart teacher can turn an exercise into a problem by being “less helpful.” Many curricula and educators also work hard on turning all problems and puzzles into exercises by attaching a step-by-step guide to every one, and by formalizing math before solving as such begins. Lockhart comments on the results:  “I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.”

Video: Dan Meyer on being less helpful.

  • Problems are mathematical questions for which the solver has no readily available methods of solutions, but has ways and the intrinsic intellectual need to figure them out. In particular, solvers do not know all mathematical concepts or formulas they will use.
  • Open-ended problems have multiple correct solutions, often infinitely many of them. The correctness of open-ended problem answers is determined by the mathematical qualities of the solution, such as rigor, logic, definitions, and aesthetics.
  • Exercises are mathematical questions for which the solver knows what methods, concepts and formulas will lead to the solution.
  • Closed-ended problems and exercises have answers known exactly ahead of time. For example, multiple-choice questions are always closed-ended.
  • Puzzles in mathematics are similar to problems in that the solver does not know which methods, concepts and formulas to use. The difference is that problem solving involves eventually developing a mathematical method for solution, whereas puzzles require intuition, finding a trick, or guessing, and may not involve any methods at all. There is no clear line between puzzles and problems, and most collections have a mix of both.

Relationships between problems and puzzles are complicated. Consider the nine-dot puzzle, a classic. Join all nine dots, using four straight lines, without lifting your pencil from the paper.

nine dots in three rows

The difficulty of this puzzle is psychological: most people assume that lines have to start and end inside the assumed square. Once solvers start to experiment with lines that go beyond the square, the solution usually presents itself soon. There is no general math method involved. Unlike another classic, “the wolf, the goat and the cabbage,” or the nine-coin puzzle that open the door to the whole class of interesting math problems and investigations, the nine-dot puzzle stands by itself.

The nine-dot puzzle helps to make a powerful problem-solving point about assumptions. Puzzles may have a powerful role in mathematical problem-solving, similar to “the Mozart effect.” Puzzles support mathematical values and develop the mathematical sophistication, on a meta-level. I do not consider puzzle-solving the same activity as problem-solving. Evidence: quite a few people like one and hate the other, or are good at one and not the other.

What to make of pastimes like Sudoku and KenKen? Their combinatorial complexity quickly overwhelms human processing capacities, such as memory and attention. Human solvers are forced to develop and use intuition-based strategies, which is a puzzle trait. Yet there are also consistent, formulated strategies and rules solvers develop and use, which is a problem-solving trait. Finally, individual steps are routine exercises. The balance between puzzle, problem-solving and exercise traits in Sudoku, in particular, hits the sweet spot for millions of people. Chess and several other abstract games are similar in their balance.

I have a gut feeling, not yet supported by readings or experiments, that there is some sort of 3d flow channel among problems, puzzles and exercises. Each person has particular needs for the balance between the three to develop mathematically. The balance shifts with time. I have no idea how to visualize 3d flow channels.