The B.E.A.M. is a tangible user interface designed to help teach mathematical concepts. This research considers the role of Montessori pedagogy and traditions in the design of new, digitally enhanced educational manipulative materials.

From learning to stand and walk to solving complex physics problems, balance is a concept we encounter and adapt throughout life. This research aims to enhance the lessons along this path by creating a tool to reflect physical and symbolic implementations of a balance system connected with various virtual simulation results. The system will consist of a tangible portion for physical reaction to the manipulations of quantity and placement, and a software counterpart to relay information to and from the physical portion to illustrate and define the physical input.

Balance plays an important role in studying and defining cognitive development. Various forms of the balance beam have been used to understand children’s perception of conservation, representation of knowledge, comprehension of rules, and the communication of conscious and unconscious knowledge. Through such studies researchers have identified various phases of development that children achieve through balance exercises.

The B.E.A.M. provides elementary aged children with a dynamic manipulative environment for creating and understanding physical and mathematical balance concepts. Through work with this material children experience algebraic lessons on balancing terms of equations, as well as physical lessons in torque. The design allows for expansion into more complex concepts such as balancing chemical equations, and basic circuit comprehension.