Giving students opportunities to ground mathematical concepts in physical activity has potential to develop conceptual understanding. This study examines the role direct embodiment, an instructional strategy in which students act out concepts, plays in learning mathematics. I compared two conditions of high school geometry students learning about similarity. The embodied condition participated in eight direct embodiment activities in which the students represented mathematical concepts and explored them through their movements. The observer condition participated in eight similar activities that did not involve physical activity. The students in the embodied condition had greater learning gains on a pre- and post-test, and those gains were driven by larger increases in conceptual understanding. There were also differences in the way the two conditions remembered the activities. On a survey given at the end of the unit, students in the embodied condition were more likely to write about the activities from a first person point-of-view, indicating that they had likely adopted a first person viewpoint during the activities. The embodied condition was also more likely to switch points-of-view when writing about the activities, indicating that they had likely translated among multiple viewpoints during the activities. This suggests translating between viewpoints is one mechanism for learning through direct embodiment. Students in the embodied condition also wrote more about the activities, which suggests that they remembered more about their experiences. Their survey responses included more mathematical and non-mathematical details than the responses from students in the observer condition. / text