1. A method for teaching arithmetic on an electronic calculating device having a processor, input means and a display, comprising the steps of: receiving, via said input means, a selection of first and second operands and of an arithmetical operation to be performed upon said first and second operands, the arithmetical operation being addition; displaying upon said display the first operand as a first collection of icons whose number is equal to the first operand; displaying upon said display the second operand as a second collection of icons whose number is equal to the second operand; displaying upon said display a grid for facilitating visualization of a computed answer to said arithmetical operation in a base ten format, said grid comprising multiple rows or columns of ten cells each to represent said base ten format, each occupied cell representing a unit of one in the computed answer, the cells initially being unoccupied; using the processor, moving the icons of the first collection to occupy cells of the grid, each icon occupying a single cell, said occupying being performed row by row or column by column and resulting in one row or column respectively being only partially occupied by icons, the number of occupied cells in the partially occupied row or column being equal to the ones place value of the first operand; using the processor, regrouping the icons of the second collection into two groups, the first group containing a number of icons equal to the number of unoccupied cells in the partially occupied row or column, the second group containing the remaining icons of the second collection and being made visually distinct from the first group; using the processor, moving the icons of the first group to the unoccupied cells of the partially occupied row or column so as to create a fully occupied row or column, each icon of the first group occupying a single cell; and using the processor, and following a noticeable pause after the moving of the icons of the first group, moving the icons of the second group to partially occupy the next row or column, each icon of the second group occupying a single cell, wherein said moving of the icons of the second group provides a visualization of arithmetic carry-over and wherein the pause enhances the visualization of the arithmetic carry-over or of the regrouping.