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Students grasp abstract math concepts after they demonstrate them with arm motions

July 12, 2016

Students who make relevant arm movements while learning can improve their knowledge and retention of math, research has shown.

Now researchers at Southern Methodist University, Dallas, 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 SMU'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 SMU Guildhall, SMU's graduate-level academic program focused on digital game development.

The researchers have been awarded a four-year $1.39 million grant 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.

Video game fosters learning by pairing gestures with geometry proofs

At the heart of the new study is the video game "The Hidden Village." A motion-capture video game, "The Hidden Village" helps foster learning by pairing motions with geometry proofs. Designed for a Windows PC computer with Microsoft's Kinect 2 motion-capture camera attached, the game's signature design element is an episodic story paired with directives for arm movements.

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.

A demo of the latest version of the video game is available at https://www.youtube.com/watch?v=g_qspP2Uu0Y, with an explanatory video here, http://blog.smu.edu/research/2015/07/21/mustang-minute-simmons-researcher-tests-if-video-game-motion-capture-can-teach-math/.

Directed body motions can improve proving of theorems

The previous version of the game was tested at a high school in Dallas in February with positive results. The researchers are presenting those results in early November at the Psychology of Mathematics Education conference in Tucson, Arizona, http://www.pmena.org.

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.

The new grant, "How dynamic gestures and directed actions contribute to mathematical proof practices," runs from July 2016 through June 2020.
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Southern Methodist University

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