Multiplication is vexation,
Division is as bad,
The Rule of Three doth puzzle me,
And Practice drives me mad.
Never will such lines express the feelings of properly taught children.
It may be convenient to work out the process of teaching arithmetic on strictly psychological principles.
Concrete teaching first.(1) From the concrete to the abstract. Let the children learn to count with the actual things.
Once the teacher would have set the child down to a slate, taught it to count, and write down the figures, and work sums in addition and subtraction, and then to learn the multiplication table. Now the child has actual things—stones, coloured beads, sticks, bricks—anything but marbles (which one of H.M. Inspectors recommends) or things which run about freely. A box of china buttons, which cost only a few pence the gross, is perhaps best.
(2) Associate doing and knowing. Let the child add actual things: Mary has 3 buttons, Anna gives her 2, she now has 5.
(3) Put thoughts into words. Get the child to say exactly what addition is—“giving to”—and let her find out from words she already knows or may know, as donation, donor, etc., the meaning. The sign + for addition may also be given.