TAMI – An intuitive approach to the learning of trigonometry

TAMI (Tangible Mathematics Interface) is an interface that facilitates the learning of the basics of trigonometry. Comprised of a tabletop display and a series of physical controllers, users can manipulate mathematical parameters and see the results on-screen in real-time. This direct, physical manipulation of digital elements enables the internalization of abstract concepts through an embodied and multisensory approach, making better use of pre-existing motor and cognitive skills.

As opposed to the traditional way of teaching trigonometry (and mathematics in general), TAMI enables an intuitive, playful, and collaborative approach to learning. The interface is designed so multiple users can interact synchronously with the same trigonometric concept, which fosters exploratory behaviors that lead to collective formulation of hypotheses and rapid evaluation of diverse alternatives.

TAMI is an educational tool for both teachers and students. During the experience with the interface, the teacher acts as a facilitator, proposing questions and fostering students to explore, discuss and discover the answers by themselves. The experience is supported by a script structured in scenes, where each one examines very precise trigonometric concepts. The experience builds up from the simplest to the most complex subjects, scaffolding on the previous scenes to introduce new content through specific interactions.

The experience purposely avoids the use of mathematical jargon until conceptual understanding is achieved. For instance, the terms “sine” and “cosine” are intentionally replaced by “red bar” and “blue bar” until there is a conceptual understanding. In this way, participants internalize the inner-workings of concepts before associating them with their name, facilitating students to incorporate the new knowledge with less resistance. 

The main controller is a 32-centimeter rotatory ring called “Rotary Wheel”. It controls the angle in a unit circle displayed on screen. Users can turn the wheel and see how the values of sine and cosine change represented with colored bars and numbers. TAMI supports a multisensory experience, making simultaneous use of vision, touch, and hearing. Sound has two roles: First, to highlight relevant information. For example, when a special angle (0, 30, 45, 60 or 90 degrees, etc.) is reached by turning the Rotary Wheel a beep sound is triggered, indicating the user that there’s something about that value that is worth exploring and analyzing; The second role is to represent trigonometric concepts as sound (e.g., sine waves represented as a variable tone to understand frequency).

The hardware includes rotation sensors, Arduino, Raspberry Pi, buttons and sliders. The Arduino gets data from the sensors and sends a constant report to the serial port. The processor, that can be either an external computer or a Raspberry Pi, receives and interprets the data through a custom software developed in OpenFrameworks, which is responsible for performing the graphic and auditory output that is displayed through the monitor.

TAMI was created by Francisco Zamorano and Catalina Cortes at the School of Design at Universidad del Desarrollo

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Team: Francisco Zamorano, Catalina Cortes, Maria Elena Errazuriz, Mauricio Herrera, Francisco Fuentes, Joaquin Dominguez

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