12. A computer-based method for training a user in the operation of an abacus comprising: generating a series of mathematical problems without displaying the mathematical problems to a user; converting the mathematical problems into corresponding hand movements for manipulation of beads of the abacus; generating animations of the corresponding hand movements; displaying the animations to the user without displaying the mathematical problems to the user; accepting user input describing the mathematical problems, which have not been displayed to the user; comparing the user input to the mathematical problems to determine the accuracy of the user input; formulating a measure of user mastery based on the accuracy of the user input; and adjusting the series of mathematical problems based on the measure of user mastery.
12. A computer-based method for training a user in the operation of an abacus comprising: generating a series of mathematical problems without displaying the mathematical problems to a user; converting the mathematical problems into corresponding hand movements for manipulation of beads of the abacus; generating animations of the corresponding hand movements; displaying the animations to the user without displaying the mathematical problems to the user; accepting user input describing the mathematical problems, which have not been displayed to the user; comparing the user input to the mathematical problems to determine the accuracy of the user input; formulating a measure of user mastery based on the accuracy of the user input; and adjusting the series of mathematical problems based on the measure of user mastery. 23. The method of claim 12 , wherein: the corresponding hand movements for manipulation of the beads comprises a series of different hand positions and finger movements of human hands moving the beads of the abacus to execute the mathematical problems, and the animations are of the hand positions and finger movements.