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# Tangible Metaphors Activities

Upper-division physics requires students to use abstract mathematical objects to model measurable properties of physical entities. We have developed activities that engage students in using their own bodies or simple home-built apparatus as metaphors for novel (to the students) types of mathematical objects. These tangible metaphors are chosen to be rich, robust, and flexible so that students can explore several properties of the mathematical objects over an extended period of time. The collaborative nature of the activities and inherent silliness of “dancing” out the behavior of currents or spin ½ quantum systems certainly increases the fun in the classroom and may also decrease students' fear of learning about these mathematical objects. We have found it useful to use tangible metaphors in several physics subdisciplines including electromagnetism, quantum mechanics, and thermodynamics.

A cognitive motivation for doing kinesthetic activities is to help students develop geometric reasoning skills. Many of these activities emphasize spatial relationships and motion. The classroom and the students become a toy model of some interesting physical phenomenon, and it is hoped that this concrete model encourages students to make connections between visualization and conceptual knowledge. Furthermore, some cognitive theories describe a kinesthetic mode of learning, based on experimental evidence that visualization and kinesthetic experience are cognitively linked. From this perspective, kinesthetic activities reinforce students' visualization skills.

The social aspects of these activities make them particularly effective teaching techniques. Putting students on the spot by asking them for some kind of response creates an urgency in understanding the central idea. Having students play a role in a demonstration may also give students a sense of ownership of the activity, furthering a need to understand the central idea. This is like what happens during a comedy show when the comedian interacts with a member of the audience. If you're that audience member, it may be a bit uncomfortable at the time, but it's the most powerful and memorable part of the show.

They provide an alternative representation that engages a different part of the brain.