Let’s Teach Geometry in the Gym

As a kinesiologist, I always look for ways to connect learning to movement. This week’s readings were right up my alley. Especially considering I had just tried Leap Motion technology and a 3D geometry activity with my class.

The question:

How could you use what is developed in these studies to design learning experiences for younger learners that incorporates perception/motion activity and digital technologies? What would younger children learn through this TELE (technology-enhanced learning experience)? Fit perfectly with what I was working on.

In the readings for week 11 a good foundation for using motion and perception with teaching in math was laid out. For example, Winn (2003) stated “once we start to think of cognition as the interaction between a person and their environment, it is necessary to consider how that interaction occurs. This, in turn, requires the consideration of how our physical bodies serve to externalize the activities of our physical brains in order to connect cognitive activity to the environment (p. 93).” Students need to use their bodies to interact with the environment and the concept they are trying to understand. Geometry, including 3D geometry is an excellent example of this. If students do not get a chance to understand how objects move in 3-dimensional space how can they be expected to learn this on their own? Looking at a rectangular prism on paper is much different than holding one in your hand and manipulating it by sliding, flipping it or rotating in in real space.

As modules continue students will scaffold their learning from concrete to abstract and then consolidate their actions into gestures so that deeper learning, as well as easier transfer and recall will occur. Novak et al. (2014) stated that “gesture promotes transfer of knowledge better than action, and suggest that the beneficial effects gesture has on learning may reside in the features that differentiate it from action (p. 445).” Lindgren et al (2013) reported “there is increasing evidence that body movement, such as gesture, can serve as a “cross-modal prime” to facilitate the retrieval of mental or lexical items (p. 447). Finally, Pouw et al (2014) found that:

  1. Under certain conditions, perceptual and interactive richness can alleviate cognitive load imposed on working memory by effectively embedding the learner’s cognitive activity in the environment (Embedded Cognition claim).
  2. Transfer of learning from manipulatives does not necessarily involve a change in representation from concrete to symbolic. Rather, learning from manipulatives often involves internalizing sensorimotor routines that draw on the perceptual and interactive richness of manipulatives (Embodied Cognition claim) (p. 53)

As a kinesiologist I have always benefitted from doing rather than imagining. My body is the instrument I use to understand my world and my place in it. As an educator, I want my students to rely on their bodies as a learning tool. If the use of manipulatives enriched learning, imagine the leaps and bounds that could be made if at an early age students kinesthetically understood what these terms implied? For example, with students as early as kindergarten and continued through primary education what if we take geometry on a cross curricular journey into the gym.

Using the technology of a white board or projector the teacher could introduce the idea of translations (sliding across a surface), rotations (spinning their bodies right, left, forward, backward) and flipping an object in the same manner. Students could use their bodies to change their shape, curl up into a ball, spread out into a star fish. Once the idea of the movement in three D space has been introduced large scale objects could be moved, such as yoga balls, large cardboard boxes, large cylinders. As students become more comfortable with the movement of the object the size of the object can be diminished until it fits in their hand. A final step would be to use technology (with programs such as the Leap motion 3d geometry app) to have students manipulate virtual objects.  Following these steps would build and reinforce neural pathways and eventually students (as they mature) would be able to use this information to try and do the manipulation mentally.

Kim et al (2011) noticed that students in their study often naturally gravitated to using their bodies to mimic actions. They state “her thinking develops in and through her gestures, and her gestures further develop her thinking. Her gestures constitute the thinking with and about shapes and motion (p. 230).”

They found firstly “that children’s bodies (bodily orientations and gestures) constitute an integral part of knowing, thinking, and learning supporting the appropriate of geometrical concepts before the age thought possible (p. 233).” Secondly, the children’s co-emerging gestures allowed new concepts to be enacted for themselves and others and, thereby, for new concepts to become reflexive objects available to individual and collective inspection (p. 233).”

If students benefitted from using their bodies while seated in a classroom imagine the possibilities of using their bodies in the 3D space of a gymnasium.

Kim et al (2011) conclude that “as children think, develop, and express knowledge through their bodies, their bodily engagement needs to be realized as integral to student learning. Their bodies are necessarily engaged in coping with the abstractness of knowledge. Their bodies embody the knowledge of science and mathematics and become part of knowing itself (p. 235).”

As I noticed when my students tried the Leap Motion 3D geometry technology and app in the classroom (in groups) they were moving their bodies through space, helping each other visualize the end result of a manipulation in space. The collaboration seemed to help them solve problems and persevere more than when students worked alone. This coincides with the research by Hwang et al. (2013) that students were more successful when collaborating using new technology (p 318).

Finally, by observing students at each of the various steps outlined above there would ample opportunity for the teacher to evaluate or assess the students’ knowledge in a new way. Bodily movement and the manipulation of objects using technology can be assessed over a paper pencil test. This unit would also provide an excellent way for students to document their growth in the math using a digital portfolio, digital story or digital movie or interview. Can’t wait to give this a try.



Hwang, W. Y., & Hu, S. S. (2013). Analysis of peer learning behaviors using multiple representations in virtual reality and their impacts on geometry problem solving. Computers & Education, 62, 308-319.

Kim, M., Roth, W. M., & Thom, J. (2011). Children’s gestures and the embodied knowledge of geometry. International Journal of Science and Mathematics Education, 9(1), 207-238.

Lindgren, R., & Johnson-Glenberg, M. (2013). Emboldened by embodiment: Six precepts for research on embodied learning and mixed reality. Educational Researcher, 42(8), 445-452.

Novack, M. A., Congdon, E. L., Hemani-Lopez, N., & Goldin-Meadow, S. (2014). From action to abstraction: Using the hands to learn math. Psychological Science, 25(4), 903-910.

Pouw, W. T., Van Gog, T., & Paas, F. (2014). An embedded and embodied cognition review of instructional manipulatives. Educational Psychology Review, 26(1), 51-72.

Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition and Learning, 1(1), 87-114

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