## 7 games for 7 algebra concepts

Talking with other people about games really helps to get some perspective and to get me thinking. Reading the “Game Design Concepts” blog has also been very helpful. Ian Schreiber makes the important point that sometimes setting constraints on the design of a game can actually help in making the many design choices involved. So, and in the spirit of rapid prototyping, here are 7 game concepts. See if you can spot a common theme.

### Pilings

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.

### Pipeline

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?

### Piezo

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.

### Plug ‘n Chug

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.

### Pilot

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.

### Pinning it Down

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.

### Prove It!

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.

## Rapid prototyping

So my proposal to present at the MCTM conference in Duluth was accepted and I need to get cracking. Fortunately I have some outstanding coworkers that want to help figure out where we can go with using games in the classroom. I proposed that we use Ian Schrieber’s great blog class on Game Design to get started.

## 15-minute game

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!

## Proposal to present at MCTM conference

[the Minnesota Council of Teachers of Mathematics has its annual Spring Conference in Duluth on April 26 – 27]

## The Multiplayer Classroom: Using Games to Enhance Learning and Teaching Algebra

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)

## Problems and possible fixes

So after one trimester of using the Pirates game and the Spies game in my College Algebra and Algebra 2 classes, respectively, I can see some problems that need to be addressed.

## Not enough time to use the game

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.

## Some students disinterested in the game

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.

## Some students unsure of what’s going on or the value of skills or items

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.

## Notes on the spy game

We just had parent teacher conferences and one of the students who came with her mother made a special point of showing what we are doing with the spy game. So this is a good time to talk a little about what’s happened so far. In Algebra 2, the students are collecting XP towards leveling up their 1930’s spy avatars.

### The story so far

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.

### Chaotic storytelling

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).

## What works so far

**The XP system motivates the students**– Students see the updated leaderboard each day and see the results of their completion of assignments and successful mastery of concept quizzes. When they reach certain milestones and level up, they get an item for their avatar and they can improve their skills or player traits. Since the levels are easy to achieve at first then require more XP, weaker students are also leveling up.**Students have a different attitude to the class**– Because I push the line between game and class, students pay attention to changes in the classroom environment. What new clue is there somewhere in the classroom? How does this assignment possibly relate to goals in the game?**The game gives opportunities for situated learning**– Like Jasper Woodbury, when students are engaged in a story, a drama, then the problem solving takes on a different meaning for the students. Not always, but often enough, I see a sense of ocus on solving an applied math problem that connects to the pirate story or the espionage narrative.**The teacher really looks at the material and is better motivated**– Like other teachers, I seem to have a million tasks involved with teaching. But figuring out new items, new artifacts, new puzzles motivates me. Is anyone researching what motivates teachers to teach well? At least I have a different answer to “when will we ever use this?’

## Notes on the pirate game

In my College Algebra class (concurrent enrollment), I began the trimester with the students creating their avatars. They needed to create pirate/scholars that could explore, problem solve and fight. The students weren’t quite sure how the game would interact with the class. I am still figuring it out.

### Character generation

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.

### What students like most

Next blog.