Math Learning Embeded into Game Design Process
PlayMaker School, funded by the Bill and Melinda Gates Foundation, just launched in Los Angeles on September 7, with 60 students in 6th grade. Like Quest to Learn, the game-based school in New York, PlayMaker will incorporate principles of game-based learning into the entire instructional model, but with an additional focus on making and discovering. The goal is to engage students in both high-tech and low-tech games and modular, instructional activities.
Operated by GameDesk, a non-profit organization that seeks to reshape models for learning through game-play and game development, the new school utilizes a variety of digital games and tools. Among them, MathMaker is a significant program for making games and enforcing mathematical skills at the same time. MathMaker had successfully improved the math scores of predominantly low income and minority students in Los Angeles.
From the evaluation report on this curriculum: (can be found here)
In the MathMaker curriculum we created, students engage in a carefully structured series of activities that require them to grapple with and apply mathematics standards to a variety of game development based contexts. Students begin very simply by sizing their character and getting the character to move. From the start, students apply simple fractions and proportions to increase and decrease the rate of their moving character, and strategically control its size and relative proportion to the game environments’ fixed pixel resolution. In this way, students immediately begin to cultivate the meaning of fractions in a variety of different contexts and procedures.
Exemplar MathMaker Methods for Embedding Mathematics in Game-Creation are :
Converting game values for distance and rate: In certain instances, a math concept will be required to author certain values within the game. For example, ratios and conversions are used to go from a general value to a value that the game recognizes (e.g., pixels-per-second converted to pixels-perstep for rate of movement). Unit conversion is used for myriad design and development needs, such
as setting characters to move at different speeds and “jump to” [GameMaker function] specific distances to create a relationship of movement between auxiliary characters, the environment and another player’s character.
Math as a game design mechanic: Math concepts are also essential for creating successful game designs. For example, in a game like Food Frenzy the player has to eat the right amount and type of food to progress to each level. Within this context, ratios become the core game balancing design practice in ensuring that all the food types and weights are proportional to the totals within the game.
If the ratios are not properly configured, the game will become too easy, too difficult, or even impossible.
Math explicitly used for programming: In later instances, a mathematical concept will be explicitly tied to the programming. For example, in one of our advanced pilots, students learned the quadratic formula in order to generate a parabola that defined the jump style of their playable character. The students used the quadratic equation to determine the vertex and overall form of the parabola within the Cartesian plane of the game environment.
Relative distance to optimize a global variable: Linear equations are used to create an optimization formula in a simple 2D airplane flyer game to determine the shortest distance across a set path for landing the plane for a refuel. In this process, the application of the mathematical concept is repeatedly facilitated as a programmed “global action” throughout a game level based on the airplane’s location and the island on which it is to land.
Known technology language leveraged to reveal an essential math concept: To correctly configure a game for different devices (PC screen, plasma screen, the iPhone), the student must understand factoring, resolution and aspect ratio to calculate a game screen size that is compatible with different aspect ratios. Students come to a concrete realization that a ratio is a comparison of two numbers. They come to realize that certain resolutions share the same factors and can be reduced to the same ratio. The authentic context in this case naturally lends itself to variation in procedure, and our research has leveraged that affordance to give students the opportunity to develop conceptual understanding in concert with practical skill.
Extracting a general rule: Game authoring is an authentic context for recognizing and abstracting patterns. For example, when moving a character across the game environment using the “jump to position” command, the character moves at different fractions of distance across the screen. Given a certain fraction and room size (pixels of resolution) students must determine the proper x and y values to properly position the character. By varying the fraction and room resolution, students have opportunities to recognize and extract a general rule for calculating the jump distance. In this instance, the students make a series of calculations from which they extract a general pattern and then rule (in this case an equation).
The conclusion, quantitative survey results demonstrated a clear increase in students’ attitudes toward math and their own ability to be successful in math and engineering. Importantly, this project demonstrates the effectiveness of game-making for teaching and engaging students in STEM fields, and contributing to a necessary revision of our educational model.
[vimeo http://www.vimeo.com/28634159 w=400&h=300]