Teaching devices for use in teaching and learning basic mathematics are known, and include devices using marbles to represent numbers. For example, U.S. Pat. Nos. 2,875,529 and 3,400,472, incorporated herein by reference, disclose marble-based teaching devices with relatively limited capabilities. The teaching device disclosed in the '472 patent is designed only for use in teaching addition. The device in the '529 patent is described for use in teaching addition, subtraction, multiplication, and division. However, the '529 device is relatively constrained in its application, and limits the tactile and aural involvement of the student in the learning process. More specifically, the flow of marbles in the '529 device is caused by the gentle tilting of the device, and the marbles are retained in partially enclosed channels. The gentle slope limits the impact-generated noise as the marbles move from one position to the next. The enclosed channels limit the ability of the student or teacher to touch or otherwise interact with the marbles.
Accordingly, there is a need for a computational teaching device that can be used to teach and learn counting and all four of the basic mathematical operations, and that will provide the opportunity for significant student involvement in the problem-solving process. There also is a need for a device that easily will demonstrate the connections between basic mathematical problems and patterns, fractions, different number bases, graphing, statistics, and negative numbers.