Find It!

Design
The call: a game for 5th graders just starting with fraction multiplication.

I look at my games. Fraction version of the Product Game... great fun, but more for practice than introduction. The crazy Ant Man game ... fun, good for calculator use, but also dividing fractions, so probably not time for that. Hmph.

Answer the question
(this was the first one)

Get it right to get a chance to
shoot past the goalie.

I look around on the web. Googled fraction multiplication game and got a lot of really awful drill "games." Glgkh - they left an awful taste. Some are obviously just quick flash mass production, but there are a couple that people really put time into looks and animation. For a quiz set to 8-bit music.


So, I'm on my own. Often with introduction time I try to think about representation. One of the things to love about fractions are all the many representations.  I think the discrete models are underused, so I thought about about students claiming fractions of a common pot (similar to the GeoGebra percent game I posted recently) - but it was difficult to figure out how to keep to intuitive numbers and overcome the disproportionate effect of going first. Also, I had trouble thinking of a game context that would get students to see it as a fraction of a fraction instead of a fraction of a whole number.

Then I thought about the area model. I imagined carving up a rectangle, having kids carve up rectangles. Scoring a total... connecting two points... then I had a connection. Cutting down bit by bit, it felt like searching for something. I tried a 12x12 grid, and my first pass at a mechanic worked pretty well: rolling a die to get halves, thirds, fourths. I thought of a context - searching for a lost hiker. Too scary if you've been lost? Finding a lost pet... maybe. It was a little too direct. Is it a competition? It was starting to feel like Battleship (a fine game), and that was good. I tried finding multiple objects; 2, 3, 4... and 4 was right. Oh! They could come up with the context - and that would give them the opportunity to add rules of their own. That's worth a try!

Here's the handout on Google docs: Find It!

Playing
I launched the game with my own context:

They managed to find all three, before... well before nothing. I was pleasantly surprised by how engaged they were just trying to find the rings. Like spontaneous applause when someone found one. (Playing with the whole class, I have them pass the die to someone who's ready of the other gender. Usually works.) Afterwards, I shared how maybe I needed more rules. Or the Mandarin's searching also. Or if you roll two 5's the Mandarin finds a ring. Or...

It was clear this was going to work because there was immediately a crowd of students trying to tell me their context, Minecraft, aliens, how it fit into the story she's writing about two wolves who turn into humans. It was exciting. They experimented with more than 3 objects and asked me why I had chosen three.

The wolfgirls.

Quite complex. This was played on two boards,
with interaction between the heroes and villains.

The minecraft game.
This had hazards as well as the goal.

The zombie game, which also had a hazard.
You had three lives, and had to find the zombie solution
before you lost all the people in your party.

The playing went well also. I was impressed by students ability to divide regions equally, and the many ways they found to do it. They started inventing their own terminology for how they were doing it, like the strips or plus method for dividing into four.  They used horizontal and vertical divides, and one group experimented with non rectangular regions. One group played like Battleship, competing to find all three before the other team did.

In feedback, everyone gave the game a thumbs up (mostly) or so-so. (Rare to have one that no one dislikes.) They liked the Battleship connection, the feeling of searching and the multiple objects to find. They were very excited to tell about their context and rules variations.


Game Evaluation

1. Goal(s) - good - experience with representation, dividing up rectangular pieces into equal parts. Plus a context for future questions and rephrasing.
2. Structure - works well.
3. Strategy - puzzle like. Choice in which region to divide up with which fraction. Choices for where you hide the objects. Not the strongest element of the game, though.
4. Interaction - good and so-so. One person/team being the mechanic for revealing spots and checking the other team's work on dividing was good mathematically. But Battleship isn't strong on player interaction.
5. Surprise - die roll, so okay.
6. Catch-Up ... depends on the variation. It's a bit methodical doing the search, but there's no time element in the basic version. The chance to get lucky with a search or a roll will help.
7. Inertia - works for this. Students were anxious to play more.
8. Rules - toughest element is the dividing up equally. Once you've got that idea, rest is simple.
9. Context - here's the winner. Students being able to set their own context was very engaging for a vast majority.

Math Evolve

Math Evolve - a basic operations fluency game for iOS. Free Lite version to try out, full version $1.99.

Somehow Math Evolve came across my radar again this week; it's an iOS app for elementary math. I'm always willing to give those things a try. Tired, frustrated with other stuff, I tweet:

And didn't think any more about it.

The next day, Adam tweets back, very politely. Immediately I feel like a heel. If I was speaking to someone in person, I wouldn't express myself that way. So I want to apologize to Adam here.

I had high expectations because the app store page has the following:

★ Winner of BEST EDUCATIONAL GAME OF 2011 (2nd Place) in the Best App Ever Awards.
★ “The holy grail of edutainment math apps.” Editors Choice, 5/5 Score -Best Apps for Kids 

In Math Evolve you are an alien organism, completing number sentences on a quest to grow and return to your people. At the beginning of a level you fill in the first blank, then the second blank after the operation, then finally the result. Later you pick the first blank and the computer provides the second. (I always get the first one of those wrong as I don't notice when the switch occurs.)  All the while you are dodging combatants and trying to shoot them out of the way. You control your position on the screen by moving your character with a touch. Finally the boss appears and asks you to compute particulars.

Another part of why I expected/hoped for more is that it is slick. Trying to develop ParabolaX (or rather, watch while Alejo and Kevin program ParabolaX) has given me an appreciation for the work that goes into slickness in iOS.  Is there a role for a practice app? I think so, but I don't value it anywhere nearly as highly as one that helps students learn. After all, if they need practice, typically there's room for greater understanding.

I'd love a practice game that gave more for students to notice. Like asking 7+3, 6+4, 5+5, ... or 4x5, 5x5, 6x5... or 5x6, 6x6, 6x7... Noticing and generalizing are things that I value more about math.

Given the context, the practice mode could have meaning of the operation.  Gathering or eliminating to add or subtract, repeated groups for multiplication... lots of possibilities. I do like how at first you're gathering all the equation elements, then the game fills in the second spot, then the boss poses a computation. The incorrect answers are not particularly problematic, and the boss doesn't seem to use missed problems to pose problems. Maybe at higher levels? Ways for added difficulty could be including choices that are not computable, such as choices between 3, 6 and 7 when you have 21÷___.  I did only play the Lite version, so possibly some of these things come later.

Boss level.

I love how open and interested Adam is in improving the game, the context and game mechanics are well developed and suitable, and the game is fun enough that students will be happy to play. And he is obviously a far better internet citizen than I am, but hopefully he's taught me to watch my oafish responses.

As I think about evaluating math games and apps
Objective: facts practice, four operations, including negative numbers.
Gameplay: fun enough. Think Galaga/shoot 'em up.
Aesthetic: great. Cute characters, good effects.
Pedagogy: beyond difficulty selection, no visible fact strategies or support for learning. Minimal math practices.

I'd love to hear what you think of the app, and what do you feel like would make for a good facts learning game.

Multiplying Game Possibilities

I saw this quick and clean multiplication game suggestion from the Math for Love blog, and really thought it had potential.

• Roll three dice
• Pick two to add
• multiply times the third

A little bit of choice, clean mechanic... great. But I thought that it could be jazzed up a bit. Then I thought that this was a great opportunity for the students to do game design.

The warm up problem that Mr. Schiller had suggested was pure serendipity: what is the largest area rectangle with whole length sides and a perimeter of 30 units. Maximizing a product with a constraint on the factors with multiple choices - perfect! I couldn't resist asking them after they found 7 x 8, "what if it didn't have to be whole numbers?" One student said - maybe 7\(\frac{1}{2}\)? They verified the perimeter, and I showed them a way to find the area. (Area model for multiplication is definitely one of my favorite representations.)

I shared the game and introduced the idea that we could rebuild it, make it better than before, with these prompts.  (Here is the handout I gave them.)

• Is there a context that would fit or a story to go with it? Climbing, racing, building, digging, fighting, shopping?
• Should it be a set number of rounds? How many?
• Or play to a total? What total?
• Any special actions or situations or rules? 
• Is there a way to get people to try and make something besides the biggest score? Like a bonus if you get to a total that ends in zero, or something that depends on the story.

They were bursting with ideas! We shared a couple and then they got working. They quickly decided 100 was too small. A few students went completely away from the idea. Rolling a die to shop from numbered stores, or just a roll and move that many spaces game. Still a lot of pride of ownership, and some good problem solving to make the game work. Others liked the game just fine the way it was, and figured out the right total to play to; as low as 200 and as high as 1000 depending on the group. Some instituted catch up rules for if you got too far behind. (Glad to see that come back from the Spiral Races.) Others added some player interaction by being able to buy out your opponent's roll.

One group made an Escape from Planet of the Apes game, where you race to 100 (pick the locks to escape the cages), then to 300 (escape the village), then to 600 (back to your space capsule for the final escape); this was humans escaping the apes. It's a madhouse! Actually another group also made a Planet of the Apes game, but they didn't share.

One group made a really complicated scheme where you start with 400 points, roll for more, and spend your points on chess pieces that represented bad things for your opponent. First player to zero loses. I would be very surprised if these guys are not future gamers.

Several players made gameboards for the race, with some special rules. One group's game that I got to play had a route through town with obstacles like a storm cloud, mud puddle, etc. that you had to use your points to buy, and you got points by rolling the dice. There was no really clear explanation on how you decided where you were on the path, other than gradually moving forward. These girls were less concerned with that, and it almost felt like a role-playing game. One of the designers repeatedly reassured me, "it's not rigged. At all!"



Another player made/recalled a game from her uncle, a press your luck game. I think you could make a multiplication game out of it.  Here are some slightly cleaned up rules. I love how she wrote an example.

Multiply or Bust!

Roll 5 dice. Scoring rolls are:

• each 1 = 100
• each 5 = 500
• 3 or more 2's = #x200
• 3 or more 3's = #x300
• 3 or more 4's = #x400
• 3 or more 6's = #x600

Set aside your scoring dice. You can reroll any remaining dice. If some of those score, add to your set aside dice. You can reroll non-scoring dice as much as you want, but if you ever roll no scoring dice, you end your turn with zero points. You can only keep scoring rolls, so you cannot set aside two 6's and hope to roll a third. Winner is first player to 5000, or the player with the most points if multiple players beat 5000.

A very really interesting idea came from a designer who wanted a guessing game. Her initial try involved turning out the lights, but after some discussion we got to a really fun little game. Not something either one of us would have thought of by ourselves.

Masquerade - 2 players
Roll three dice but keep them hidden. Add two then multiply by the third and tell your opponent the score. They get three guesses to try to win your dice. If they guess a number right, they get the die and score that many points. After the third guess, players switch who is the roller and the guesser. Each player gets five turns guessing. Highest point total wins.

We closed by students sharing their games. I often encouraged students to write out their rules, which was an interesting ELA activity.

I also had a couple ideas inspired by their warm up question. Here's what I would try.



The main benefit of the grid is to make non-maximal multiplications more interesting. Hopefully it adds a layer of strategy.

Of course, it would be a nice variation to play on the same grid. More interaction, more strategy, and I think the little products are bound to be better. I'll be trying these out!



The game design aspects of these 5th grade lessons has been pretty powerful. We lose a bit of focus on the mathematical objective compared to all playing a set game, but the engagement is high, and the mathematical practices are strongly present, as well as having more math done than in many traditional math lessons. Even comparing the energy the students invested in the warmup problem, which correlated roughly with their mathematical self-identity, with the very similar problem of figuring out the sum and product of the dice in the initial game was a stark contrast.

Katie Salen

Katie Salen is a professor at DePaul in Design, and director of the non-profit Institute of Play, which runs two public game-centered schools in Chicago and New York called Quest to Learn. I have a fantasy of getting to work with these schools at some point, or being part of a similar project here.

She spoke this year at SXSW in Austin, and they put up the audio of her presentation. I was so interested and engaged I started taking notes. That led me to do some rewinding (so to speak) to get some of it right and listen with intent.  Finally I decided to share them, in the hopes that it might support others in going to listen to the talk. If you're interested in applying lessons from other areas to teaching, this is for you. You do not have to be interested in games to get a lot out of her talk.

I was not so focused on whom she was quoting and missed some of the companies or games they made. Sorry!

Notes:  Dr. Salen says...
Make learning irresistible now.

• Not about preparation for the future
• Not about efficiency and productivity of education (i.e. teaching more kids more quickly or for less money)
• About engagement, present potential of people including children.

Play is rooted in the now.

Design principles: the idea is to take theory to forge design principles that synthesize and apply the theory.

Sometimes listening to a presentation, there’s a single sentence as a takeaway that helps. As she has listened to game designers, she's noted 'what do game designers think about that resonates with design for learning.' (This talk is her overview of the best takeaways she's found.)

• how to engage people
• structure for challenge, motivation, feedback, and to incentivize

Portal: Trying to move someone through a level, to hit the beats. There was an early level that players couldn’t get through. They can’t see the door directly in front of them, if there’s too much drama.  What they learned was “Don’t shoot the player while they’re learning.” Create a safe-space when people are trying to learn.

Shift from design for learning to design for engagement.

Little Big Planet: created a badge for building levels so players built spam levels. Never incentivize things you expect players to do. Instead incentivize the unexpected and original.

Failure: practice as repeated failure. Musicians know bad practice and good practice. Take the thing you’re failing at, and keep hammering at it. Make it hard for yourself. This turns failure into a positive act of creativity. You make decisions about the things you need to fail at vs. failure as a thing to avoid at all costs.  So start with state standards, but design classroom experiences that do not look like taking tests.

Media Molecule: in the original Little Big Planet there were not enough tutorials, because of the push to publish. But players chipped in. Now for Little Big Planet 2 they intentionally left space for contribution. They expected codesign. Supported it by having the “Elite Creators Group” in Little Big Planet 2 who designed great levels, but also tutorials at the same time. Leaving a gap. Applying to teaching, consider what can young people teach each other? Value peer to peer exchange. Design community. It’s not the product, that’s their material. If social interaction matters, you have to design the community for interaction. What do cemetery rows of desks support? Communication of one to many.

Valve: developing levels and puzzles, and how they are playtested. Single player puzzles were designable, but they couldn’t make the collaborative puzzles hard enough. Fundamentally different design problem. Most challenges today in classroom only deal with individual problem solving, fueled by individual assessments. Assessment people can’t solve the free rider problem, how do you know someone is not participating and letting others solve the problems. So they make assessments individual, secretive affairs.

LBP: share, communicate and collaborate is opposed to the idea of sorting and classifying, which is common in school, primarily because of assessment.  The problems in design for community belong to design for interaction. (In general she kept referring to the design space for x belonging to the design space for y. I want to think some more about how this applies to teaching teachers, and how common teacher problems generalize.)

Design Principles
1)    Create a need to know. (Games do this well.)
2)    Create a need to share. (Opportunities and need.)
3)    Create an infrastructure to enable sharing. (Designing mechanics.)

There were several comments that relate to assessment:

• Valve: new feature allowing players to playtest each other’s levels. Game design isn’t theoretical, you have to build it and try it. Whole curricula are designed and distributed before testing.
• John Beech: value of feedback to the designer. “A computer can’t say if art is amazing.”
• Games are rich data spaces. The danger of moving to stat-driven models is focusing on what machines are good at assessing.

Alex: bias towards and emphasis on jamming. Jamming is a common game-design culture, but less common in education. Put in constraints. The original LBP had infinite depth, but the final version only had 3 levels, because the restriction pushed designers. Game designers understand the importance of rules. Rules are so natural they are unseen, or they push the players to develop excellence. Might go from a lot of rules to less; constraining how many things are possible. This increases challenge, laying the groundwork for jamming. (A problem worth solving. Lord knows that in education we have plenty of these.)

Some games work on the 3 Pass Rule for learning outcomes for players:
1)    Learning one thing.
2)    Practicing that thing and learning another.
3)    Synthesizing what you’ve learned.

Are schools putting in constraints that push creativity or shut students down?

Design for collaboration is linked to design for play. Students feel imaginative, are hard working and collaborative. We want them thriving now, not being prepared to thrive.

Lonely Planet: Empowerment. Giving people the ability to make something. I remember making my first computer game in Basic on my first computer. Made copies and sold them at the playground for 1 lb a piece. That feeling for me is what I mean by empowerment.

Not about stuffing content in games, or games as a substitute for textbooks, but that feeling.

Takeaways. These are here big points gleaned from all these game designers.
1)    Design for friendliness. Environments that are well and healthy. Interactions are reciprocal and positive. This doesn’t mean they are noncompetitive. (Starcraft 2)
2)    Enable good practice. Students are skilled at finding out what’s on the test, which
3)    Qualitative feedback.
4)    Keep challenge constant.
5)    Make sharing a gift.
6)    Minding the gap. Design opportunities with holes that give students opportunities to fill the gap. Don’t make gaps around the wrong things.
7)    Don’t shoot the player while they’re learning.


In the questions and comments, two particularly education relevant points were raised.

• This is what Dewey was advocating at turn of the 20th century without the infrastructure to make it realizable.
• Higher ed? Grad school has a lot of these features. Baccalaureate? Not so much.

Summary
Just having listened to this, it came up multiple times in response to an observation today. Some of the ideas are powerful, especially as relate to engagement. I encourage all teachers to give it a listen, as your students love the games these designers have made. But if you are also a fan of games or game design, or game use in education, it becomes a must listen.

Need video to pique your interest? Here's a couple year old clip of Dr. Salen from Edutopia.




Photo credits: Portal - hunterseekerhk, Sack Boy - Simon Owen Design, StarCraft - Kim Pierro; from Flickr.

Game Evaluation via NCTM

The Product Game (pdf)
aka Times Square (online)
still my choice for best math game ever.

This is a quick post comparing NCTM's math game evaluation criteria with my design framework, based on Mark Rosewater's game design criteria.

I just stumbled across the NCTM's Tips for Teachers page on Math Games. Definitely check it out, they have solid links to games at the end.  After a brief motivation about why to use games, they give their criteria for evaluating a game. I've reworded and reorganized them here, as the lack of any organization and structure was a wee maddening to me.

Mathematics:
M1. Does the game reward engaging in mathematical processes? (They connect with strategy.  NCTM’s Process standards)
M2. Does the game's structure or context support the mathematics?
M3. Does the game promote conceptual understanding?

Game features:

G1. Does the game have a random component or choices to make with clear outcomes? Are students empowered?
G2. Does the game reward replay? (Variety in tasks or different pathways to the end.) Does the game have clear scoring?

Teacher and Student:
S1. Does the game give feedback throughout?
S2. Does the game support players through the most challenging parts? (Can they get stuck?)
S3. Does the game have teacher support for classroom use? (Extensions, connected lessons, chance to track students' progress.)

Learning environment:

L1. Does the game promote positive competition and a safe learning environment?
L2. Does the game promote social play? (Competition, collaboration, and communication. )

I want to compare it to the framework I've been using lately. Both to see

1. Goal(s) - M1-processes, M3-concepts
2. Structure - M1-processes (representation), M2-game mathematics, S3-extensions.
3. Strategy - M1-processes (problem solving)
4. Interaction - G1-choices, L2-social play
5. Surprise - G1-randomness
6. Catch-Up - G1-randomness
   
7. Inertia - G2-replay, S2-support as needed.
8. Rules - S3-teacher use.
9. Context: Fun-Flavor-Hook. G2-replay, L1-positive,

What the framework handles well: 

• Math goals.
• A lot more clarity on gameplay.
• Covers their characteristics in a usable format.

Do I need more?

• I've got to think about the feedback throughout (S1). That feels important for an educational game. In some games it's just your success.
• Similarly, support through the challenging parts (S2).
• Classroom support (S3). 

These are basically the education specific characteristics, though S1 is worth thinking about for games in general. It makes sense to me that if the framework is lacking it's in the context of educational games, since its origin was more general.

Note also the slides Maria Droujkova captured from Keith Devlin's math game webinar. His principles have a lot of overlap with the NCTM checks, but are expanded and better suited to multiple platforms. I think there is a place for skills mastery, though, as I would much rather have that in the context of a game than in drill and practice.

Spiral - So-So

I've never seen a spiral board... wow!

Since Vi Hart released her Christmas time spiral celebration, I've been digging spirals again. I made a GeoGebra sketch to go with her video (link includes a link to her video), that I quite like. My tumblog is where I post one-off math and reblog other Tumblr math. So when I got the word from Mr. Schiller that this gameday the "Topic will be polygons/angles/rotational symmetry," it didn't take me too long to get to the idea of a spiral game.  The way it worked out, though, has me wondering: how good does an educational game have to be?

Click for full size

There are lots of things to recommend it: kids think spirals are cool, it makes a nice race track, it allows you to see circle connections to angle, and that angles have the same measure whether small or big in size. I like race games for practicing with quantities, because it gives some repeated experience with a variety of the quantity, and gives you a reason to talk about the quantities. The GeoGebra I used to make the Archimedean Spiral (as opposed to Vi's logarithmic spirals) is posted on Tumblr, too. Then I just used GeoGebra's export as image to get the track into Word.

The problem with race games is that many of them devolve into chutes and ladders (American; snakes and ladders elsewhere).  This one definitely did. I thought a one die game might be easiest, and after some practice settled on moving 15º times the die roll. It included right angles and gave some nice opportunity for mental multiplication. I justified the simplicity of the game to myself by adding a game-design objective. The winner adds a rule; that rule has to help with the catch-up characteristic of the game.


In addition - since the game was simple - I wanted to have another option. I brought some triangle grid paper and an eightfold diagram (links to Google docs) to support the students in making an art project with rotational symmetry.  As I told the students, math art is as close to my heart as math games. I explained how to color a piece and then imagine it turning, or on the 8-fold to color in 1, 2, or 4 wedges and then copy it.

The students gave the game a good try, and they seemed to meet many of the objectives quickly. Watching them play, the game seemed a bit too long. One student who had gotten disengaged was willing to collect data for me on how long a game took. His results: 27 turns for a full game. 16 turns for 1.5 loops shorter.  After one try, some people played on, many moved on to the math art, and a few pulled out the games they made in December.  Mr. Schiller and I agreed it was too long, though the class was just barely in favor of okay-as-is.  In terms of new rules, some students modified it to have 2 dice. Others added rules for if you land on someone +15º, an "if ahead, out one loop line," a -30º spot and similar. Several students were proud to share their art. Not many tried the triangle paper except for making free designs. 

A revised, shorter game is at the end of this post. In general, it was so-so. The whole experience really raised for me the question of how good does an educational game have to be. These students have played some really good games so far, and I think they were disappointed that this one was more regular.  I've definitely thought that educational games have a lower bar, since you're not interested in replay on many of them once your objective is met.  My experience has been that any sort of game is a welcome change.  But maybe if games are regularly played, the bar rises. I'd be interested in your opinions below, by twitter or email.

In terms of the game design framework I've been trying, and my rating of Spiral:

1. Goal(s) - good concrete objectives.
2. Structure - the spiral really fit the objectives well.My main question here is if the board should have angle measures on it. (Definitely, if polar coordinates are the objective.)
3. Strategy - no real strategy. Real room for improvement here.
4. Interaction - with no choices the interaction is limited to the racing.  It's a hook, but no way to effect your opponent.
5. Surprise - not really relevant to this game.
6. Catch-Up - this game has it, both through randomization of the die and the board structure; but it's of the candyland/chutes and ladders variety.
   
7. Inertia - main reason for shortening the game. Overstayed it's welcomed. I think race games, in particular, probably need to be mindful of pace.
8. Rules - clean, simple. The add-a-rule rule was a big hit. I'll be using that again.
9. Context: Fun-Flavor-Hook. The spiral is a start to this, but some context for the spiral might have helped here. With all the spirals in nature, it shouldn't be too hard to add something. Maybe birds flying to the eye of a tornado? Hurricane?

The warning sign for this game is being weak in the green characteristics. Mr. Schiller and I were excited about it because of the strength in the yellow areas. If I was thinking about a commercial game,  I think I'd make a deck of cards for movement, that would give more strategy and interaction. But that's a lot of printing for a one-off classroom game. Maybe you could simulate that with multiple dice? Make the rules a bit more complex, but worth it for gains in the green. Maybe roll three dice, pick one to use that you'll reroll next time. Trade for an opponent's die with one of yours that is higher.  Worth a try! It will even increase angle use.

The modified game is up at Google docs.


Snakes & Ladders Image: Smabs Sputzer @ Flickr

Holiday Game Design

#mathchat last night (twitter stream, wiki) was on "Games: Where's the math? How can we use games to teach mathematics?" One of my favorite topics, and a good discussion. There are so many things I like games for in mathematics: playing a game is quite like math, strategy is an excellent context for problem solving, engagement level for repeated exercises or tasks, etc. But one of the things I like best personally is making them. (That's definitely one of the appeals of collectible card games; building a deck is a lot like game design.)  The amount of math that goes into making a game can be quite a bit greater than playing it.

So today for the 5th graders I brought a half-formed game based on the Traveling Salesman problem. Georgia Tech has a nice Traveling Salesman Problem site, with a few games of their own, nice explanations and history of the problem. It was inspired by the ultimate Traveling Salesman: Santa Claus. Every home in a night? Mathematician Elves on the job.  I eventually changed the game to running Christmas errands in town here, and intentionally left it rather drab.

We played a few turns of the game to get the idea. Then I shared how I wanted them to be game designers today, and we discussed possible things to work on.


Game Design To Do:
1) Playtest

• Are the rules clear? Do they need to be changed? 
• Are the mechanics of the game okay? (Right number of destinations, how to move, placement of stop, dice to roll…) 
• Is it fun enough? How can you make it more fun? 

2) Develop

• Should there be obstacles on the map? 
• Decorate the board; add fun details or pictures. 
• Make nice game pieces. 

3) Create!

• Make your own map. 
• Change to the world map or the US map. 
• Change the story of the game. Santa, UPS, mail carrier, … 
• Completely new game idea: 12 days of Christmas, Christmas tree, Hanukkah Candles, Winter Break, … 

I also brought a blank grid, a polar map (to do a Santa Claus version) and a United States map. (Click for full size. PDF of the whole document on Google Docs.)


Nobody used the polar map - poor Santa!  The class had many people make improvements to Santa Haven, and several who made their own game.

Some of the improvements: new goals, like get all the presents to Grandma's house.  Board alterations, like road block, traffic jam, hazards, stop signs, school zones, etc. Some quite clever, like a gas station (you have to go in if you pass), or a muddy spot that divides your speed by 2 until you get to the car wash. Play alterations, like the bank after every present, or a specific chore list (home, school, presents, back home then school then home). One student made walking and driving rules; driving was double speed, but had school speed zones and roads they had to stick to. At the end we talked about how this was mathematical modeling, where they tried to take real life stuff and figure out what they would be like in the game.

The new games included 2 Risk variations on the US map, variations on the traveling salesman with all new maps, and a candy cane math game with problems on the spaces.










Quite a lot of creativity, so much enthusiasm. And, I think, a nice lead into designing some of their own games later.