Penta defends MS thesis on video game creation for mathematical learning

On November 17, 2011, Computer Science graduate student Michael K. Penta successfully defended his Master's thesis, entitled “Video Game Creation as a Platform for Mathematical Learning.” Penta had previously earned a B.S. degree in Computer Science from UMass Lowell (2006).

Penta’s work was inspired by an experience he had teaching video game design in a summer camp held at the university. Two of his students were trying to position a cannon ball at the end of a cannon, which could be positioned at various angles. Near the end of a day, the students asked Penta how to do this, and he told them, “That is just a bit of trigonometry. I will show you tomorrow.”

Penta was then surprised when, the following day, the students had solved the problem on their own. As he described it:

I learned that they had gone home and introduced themselves to trigonometry by searching the web. ... These students had taken responsibility for their learning, and became self-directed problem solvers. They had taken a subject disliked by most students and [...] learned the essence of an important math concept. ... They were motivated by their own problem, a problem within a context about which they cared, the game they were making.
Penta used this insight as a jumping-off point for his Master’s project. He set out to develop an intentional learning environment where students would be encouraged to build their mathematical competencies through video game creation.

He then evaluated three different learning environments: an in-school mathematics classroom, an after-school game design workshop, and an after-school mathematics-focused game design workshop. Using a design-based research methodology, Penta created a series of evaluation tools to measure students’ learning, and refine the learning environment in each iteration.

Ultimately, Penta argued that because of curricular constraints, in-school time is not suitable for student video game design projects. He concluded that interventions should be structured around authentic video game design with integrated, focused mathematical design challenges. Finally, he demonstrated that students developed improvements in their understanding of mathematical concepts including plotting Cartesian coordinates, using negative numbers, and finding functions from patterns.

Penta’s work was advised by Prof. Fred Martin. Douglas Prime (College of Engineering) and Prof. Marvin Stick (Mathematical Sciences) were thesis readers. A copy of the thesis is available on Proquest or as a local PDF.

Video games were programmed in MIT Scratch and Game Maker. In this Scratch program snippet, a student has used knowledge of X and Y coordinate axes, and positive and negative numbers, to program a game character to move up, down, left, or right, in response to arrow key presses.

“Haunted Mansion,” a student-created game in response to the maze challenge. Student games had to have a “hero” character which moved using the arrow keys, and at least two “good” and two “bad” non-player characters (NPCs). When the hero struck a good NPC, its number of lives had to increase, and when it collided with a bad NPC, it would lose a life. When all lives were lost, the game had to end.

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This page contains a single entry by Martin, Fred published on December 15, 2011 9:07 PM.

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