Singleplayer. Beginning with simple levels, the player has to find the right length for caissons to balance a lintel-like oil rig. If they find the wrong value, the rig topples, maybe with a satisfying boom. There are given units and a picture of the two sides of the pilings. Concept: 2x + 3 = 4x – 5.

Single player or multiplayer kinesthetic version. Given a time distance graph, try to program a robot, perhaps traveling down a pipeline, to match the graph. If it’s not possible, explain why. Or act out the graph, using a proximity sensor. Concept: is this graph a function?

Multiplayer or timed singleplayer. Two numbers flash on a screen under two columns, x and y, and then fade. No pair of numbers will be shown a third time until all pairs are shown at least once. When a player sees a pair for the third time, she yells out “Piezo!”, gives the domain and range and states if it’s a function. Concept: given input-output find domain and range and if the relation is a function.

Singleplayer or multiplayer. The player(s) get a list of functions down the left side of the page with two input values for each one. Most of the page has a graph with a train tracks winding down through it. Players decide which of the two values puts the output between the rails of the track. Concept: Evaluate a function.

Singleplayer. The player tries to keep his plane, or maybe a ship into harbor, on course. For example, given an input of 6, the needed correction is 14 to keep on course toward 20 and an input of -2 needs a correction of 22. At higher levels, an input could get multiplied before the correction, which could also have a multiplier effect. Concept: recognize and graph linear functions.

2 player. One player is black, the other green. Each turn the two players draw cards of their colors. A black card might be a coal mine or oil field while a green card might be a wind farm or new biofuel. Players use first, second, and third order effects to calculate marginal profits. Black will have relatively low first order costs but higher second and third order costs (i.e., pollution).Green will be reversed. Players try to play cards that make it more difficult for the other player to get a final marginal profit. Concept: find the slope from a table or graph.

2 or 3 players. Two arrays of cards with numbers are laid out, face-down. On a player’s turn she turns over one card from each array. If she thinks the right hand number times m + b (given at the beginning of play) equals the number from the left array, she keeps the pair. If not, she turns them back over. Other players can challenge, saying “prove it!” If the number pair does not work, the challenger keeps the pair. If the challenge is unsuccessful, the challenged player takes another turn. Concept: Graph each line given slope and y-intercept or write the equation of a line from the graph.

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The first lesson has a great challenge: make a race-to-the-end game in 15 minutes. Just think a bit, make a path, write a few rules, and play! Here’s my first attempt.

**Jungle Treasure** – Take your band of pirates into the jungle in search of treasure. But be careful of hidden traps! A game for 2+ players

SETUP – A piece of paper with fifteen spaces in a path between the start space and the “treasure space.” Each player rolls to see who goes first. Players then place a die in front of them with the 6 face up (the size of their band at the beginning). Write 100 near the treasure spot (increase for more than 4 players).

PLAY – Starting with the first player, and then clockwise, a player may move from 1 to 5 spaces toward the treasure. When a player lands on a spot (including the treasure spot) they must check for traps. If they roll one d6 higher than the number of spaces they moved, they’re safe for that turn. If they fail to roll higher then they set off a trap and lose a member of their band. The player turns their die to show the new number. Mark that space because if a trap is sprung, the space becomes safe for other players to land on without having to roll. EXAMPLE: a player decides to move three spaces to a space where no one has sprung a trap yet. If the player rolls a 4, 5, or 6, they’re safe and it’s the next player’s turn. If they roll a 1, 2, or 3 a trap is sprung and they lose a member of their band and clear the trap for other players.

WINNING – Once a player lands on the treasure spot, they roll as many dice (d6) as the number of remaining members of their band. The player adds up the numbers and collects that much gold. Subtract the total from the remaining amount of gold. If the number rolled is larger than the remaining gold, that player gets the remaining gold and the game is over. Each turn players are at the treasure spot they can roll for more gold as long as there is still some remaining. The player with the most gold at the end wins!

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Jeffrey Jones

In this session I will explain how I use the multiplayer classroom in the teaching of high school algebra. I will present a short sample lesson where participants can create an avatar, complete a mathematical task and possibly “level up.” Then I will discuss the benefits and possible drawbacks of game-based math education, along with ways to design and implement a multiplayer classroom.

**Books referenced:**

*The Multiplayer Classroom: Designing Coursework as a Game*, Lee Sheldon (2011)

*5 Practices for Orchestrating Productive Mathematics Discussions*, Mary Kay Stein, Margaret Schwan Smith (2011)

*Implementing the Common Core State Standards through Mathematical Problem Solving: High School*, Frances Curcio, Theresa Gurl, Alice Artzt, Alan Sultan (2012)

*Using Games to Enhance Learning and Teaching*, Nicola Whitton, Alex Moseley (2012)

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Feeling the curriculum crush that probably all high school math teachers feel, it would seem like many days or even weeks would go by without the students doing anything with their avatars. A leader board and leveling up has some positive effect but it needs the heft of the game to make the new skills and items important. **Fix:** smaller but more frequent game episodes, particularly at the beginning of the class. While students are working on warmup problems, they can roll dice to see what random event happens while they are questing. Plus more students get involved at the same time with moving the game forward. In a typical RPG like Dungeons & Dragons, a party might be three to five players and a game manager. In a typical classroom that would mean a lot of students just watching while a few make decisions and roll dice.

If a student doesn’t think the game is interesting or fun, then the game becomes demotivating. Some students can question whether there’s a point to the game and can even break the “magic circle” for others, jeopardizing the point of using the game in the math classroom. **Fix:** in addition to shorter episodes of play, more tightly integrate the play scenario with the math “story problems.” For instance, in the pirates game the students were sailing around Jamaica and were presented with navigation problems. Solving the Pythagorean Theorem or trigonometry problems gave their characters in the game an advantage. As much as possible, blur the line between game and class work.

In the spy game in particular, I got a bit carried away with creating a multi-layered mystery with multiple clues and characters. I think that the “chaotic story telling” technique could have worked better without such a complicated storyline. **Fix:** Edit and use smaller missions that use a wider range of skills and items. This ties in to the fixes above. Also, I made a website with documents (like character sheets) online. The skills list now has tool tips that give more information on what a skill can be used for. As a bonus point opportunity, I had students pick a skill and describe it in a paragraph.

We will relaunch this week and put students back to level one. Students got invested in their characters but for purposes of the class (getting a separate grade for each term), I have to start everyone at the same place. More later on the new beginning.

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Students created their avatars with combat, stealth and technical skills. They divided 30 points among strength, dexterity, stamina, perception, and charisma. They also picked a art skill (Antiquities, Old Masters, 18th and 19th century art, Modern Art, and Tribal & Indigenous Art). I made some collector cards (from the period) and each student got one. Why an art skill? This is their cover, that they are working as art consultants, based in London. They were told that someone was trying to steal British naval secrets.

I read about this solution to the problem of the GM having to dump a lot of story and details on the players, namely, giving the players multiple pieces that they actively piece together to create the story. This aims to bring the student/players more in to the story. So I made little cards that had some of the background and distributed them to the students. The students read them and discussed them. I told them they would receive “mission points” based on their engagement (very valuable to have later on). Then I started weaving clues in different places in the class (more later).

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I used a technique for creating a back story from here. The students stepped through different stages of their life before they become pirates. They add languages and one trait from each of combat, stealth, and technical traits. As students complete assignments and take quizzes, they gain and XP. When they get enough XP to level up. they add to their traits.

Next blog.

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In some ways the class wasn’t that different from other algebra classes. I taught, students did activities and homework assignments. They took quizzes (more of this later). But about every other day, sometimes for just 2 minutes, sometimes for 20 minutes, they were involved in a role-playing game. This made the levels meaningful as the students’ avatars got items and increased skills with each level. The items [little pieces of cardstock] were pirate-related like a telescope, jewels, or a blunderbuss. The skills were things like swordsmanship, swimming, carpentry, or lock-picking.

Two reasons. First it was an investment in student participation in the whole idea of assignments and quiz scores turning into leveling up. Second, and more importantly, it was an opportunity for the students to participate in math in context. For example, the students had to decipher the secret message about the Spanish ship they were searching for. One of the students choose an “Arabic manuscript” by Al-Kindi that explained frequency analysis. She took “Arabic” for her next skill when she leveled up and asked me what the “manuscript” meant. Her guild helped her assign probable letters and decipher the clue. My goal then and now was to blur the lines between a game and doing math.

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I took inspiration and ideas from multiple sources for the game. Like Seventh Sea, I told the students they were in a parallel world to Earth. I did this so that we could be a bit anachronistic and have roles for women and different nationalities than the pirates of the golden age. I decided on a simple skills based game, borrowing from Five by Five the idea of using dice multiplication. Each level meant the player got a new random item and could either add a new skill, upgrade a skill, or add a new language.

I didn’t want the effect of the XP to be just a progress bar on the wall (although most students really liked this and would check their spot each day). I wanted to give students another reason (besides a grade) to get XP. I also wanted to blur the lines between students playing a game and doing algebra problems in a math class.

Promising, fun for me and most of the students, more focus (I think). I will explain more in the next post and talk about what is happening this year.

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But I can’t make a video game for Algebra 2. So I decided to try an experiment and take a page from The Multiplayer Classroom: Designing Coursework as a Game. In the spring trimester I picked one class and made it a multiplayer classroom. My next post will go over what happened.

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