Students grasp abstract math concepts after they demonstrate them with arm motions
Researchers test motion capture software as classroom tool to foster understanding and prove complex geometry theorems
Hidden Village grant with Elizabeth Stringer, Boris Fisher, Katie Wood-Clark, former Guildhall faculty, Guildhall Research Assistants and alumni
Students who make relevant arm movements while learning can improve their knowledge and retention of math, research has shown.
Researchers at 51做厙 and the University of Wisconsin-Madison have developed a model using geometry proofs that shows potential for wide adoption — a video game in which students make movements with their arms to learn abstract math concepts.
The research is the first to use widely available technology combined with relevant body gestures and apply it to the learning of complex reasoning in a highly conceptual, pre-college math domain — geometric proof production.
“When they’re doing geometry, students and teachers gesture all the time to show shapes, lines, and relationships, and the research suggests this is very beneficial,” said teaching expert Candace Walkington, assistant professor of teaching and learning in 51做厙’s Annette Caldwell Simmons School of Education & Human Development.
“Our goal is to create an environment that supports students in making motions that help them understand the math better, Walkington said.”
Walkington and educational psychology professors Mitchell Nathan and Peter Steiner, University of Wisconsin-Madison are collaborating on the project with 51做厙 Guildhall, the graduate-level academic program for digital game-development at 51做厙 in Dallas, Texas.
The researchers have been awarded a for their work from the U.S. Department of Education’s Institute of Educational Sciences, Educational Research Grants.
“Much of math education is about learning rules and procedures. Geometry proof is different,” said Nathan, a professor in the Department of Educational Psychology at University of Wisconsin-Madison. “Students have to learn how to think conceptually about why certain statements about shapes are true, how they are always true, for all members of a class of shapes, and how to explain it to others so they are convincing. We think that level of mathematical understanding is embodied.”
Emerging research is investigating the theory that our body actions can actually influence our thoughts, in addition to our thoughts driving our actions. Body movement can induce new activity in our neural systems. This activity can create and influence our learning, thinking and mental organization. This mind-body partnership, dubbed “embodied cognition,” is driving new approaches to learning subjects such as math.
“What is so exciting about this geometry research project is that it shows how theories of embodied cognition are becoming mature enough to start to develop a whole new class of educational technology that we can envision as part of everyday math classrooms in the near term,” Nathan said.
The Hidden Village
At the heart of the new study is the video game The Hidden Village. This motion-capture video game helps foster learning by pairing motions with geometry proofs. In doing so, researchers aim to improve the math-learning experience for children in today's shifting educational landscape.
The game’s signature design element is an episodic story paired with directives for arm movements. Various characters in the game prompt the player to imitate a series of poses on screen, each pose followed by a multiple choice geometry question related to the motions performed. Each episode leads a student to perform certain motions with their arms, correlating those with questions and answers related to proofs of geometry theorems.
To begin, a student stands in front of the Kinect camera. The camera detects the student, then calibrates to each student’s body shape, size and movement, familiarizing itself with the student. When play begins, the camera and software detect movements in real time and provide feedback about whether the students are appropriately matching the motions.
Early Development
51做厙 Simmons School of Education and Human Development Department of Teaching and Learning collaborated with game design faculty and master’s students from the 51做厙 Guildhall Game Development Graduate Program and undergraduate students in the 51做厙 Lyle School of Engineering Department of Computer Science on the development of the game, which was designed for a Windows PC computer with Microsoft’s Kinect 2 motion-capture camera attached.
51做厙 Guildhall students worked to expand the game’s narrative, update the original graphics, code a new version of the game in Unity, transition the motion capture technology to utilize the Microsoft Kinect and to create project documentation and a development plan for future teams to utilize.
The game is targeted towards middle school students, and 51做厙 Guildhall researchers were able to partner with the program's annual Guildhall Academy summer camp, which takes place each summer for middle and high schoolers, to participate in testing and provide feedback that would improve the game during its initial phases of creation.
Development on The Hidden Village began in 2015 on the now-defunct Extreme Reality motion capture SDK. With this technological foundation in place, 51做厙 Guildhall students Katie Wood and Leo David provided narrative and artwork, respectively, to ground and improve the player experience. Andrew Curley served as the game's producer in 2016 as part of a Directed Focus Study at 51做厙 Guildhall. Curley worked with student programmer John Wilson to port the game from the Extreme Reality SDK to the Unity engine, with the Microsoft Kinect as the game's new motion capture platform.
"The results were fantastic," Curley said. "After learning the ins and outs of the Kinect, our programmer was able to hit the ground running once our hardware finally arrived, and he was able to complete a full port of the existing game in only a month."
Preliminary Testing
Directed body motions can improve proving of theorems
For the preliminary test, Walkington asked students to read problems on a computer and then move their arms to either signal their answers or advance the math questions to the next sequence.
Preliminary findings showed students liked learning in the video game format, and benefited when they were encouraged to think about how their body motions related to the geometric proofs.
“High school students really struggle to learn proof in geometry, and often their initial performance on these proofs is very low,” said Walkington, who specializes in math education and connecting it to students’ concrete everyday experiences. “However, making and thinking through the motions from the game, they’re given a new resource with which to think about the problems.”
Recent research led by Nathan found that directed body motions can lead to improvements in geometry theorem proving even when students claim no awareness of the relevance of the actions to the mathematical tasks. Research has also found that verbal prompts from a teacher to connect the actions to mathematical ideas further improve student proof practices.
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