Note that the subjects enumerated fall into different groups. Counting, arranging, observing, are different phases of the natural development of the mind. Instruction does not create these activities; its business is merely to accelerate them. At the beginning, therefore, our mode of procedure must be as much as possible analytic. On the other hand, reading and writing can be taught only synthetically, although on the basis of an antecedent analysis of speech sounds.
(1) Arranging--commonly neglected, though wrongly so--is an exceedingly easy exercise in itself, and facilitates the performance of many other tasks. It is therefore appropriate for children. That three objects may change places from right to left (from front to rear, from above to below) and _vice versa_--this is the beginning. The next step is to show that three objects admit of six permutations in a straight line. To find how many pairs can be formed out of a given number of objects, is one of the easiest problems. How far to go, is a matter to be determined by circumstances. Not letters, however, but objects,--the children themselves,--should be changed about, permuted, and varied in position. The teaching of a subject like this must in a measure have the semblance of play.
(2) The first observation exercises begin with straight lines drawn vertically or cross-wise. Use may be made also of knitting needles variously placed, side by side or across each other, of domino checks, and of similar objects. Next comes the circle, subdivided and presented in manifold ways.
(3) For arithmetic, likewise, concrete objects are needed,--coins, for example, which are counted and arranged in different groups to illustrate sums, differences, and products. At first the highest number employed should not exceed, say, twelve or twenty.
(4) For work in reading we may avail ourselves of letters and numbers printed on cards, which lend themselves to a variety of arrangements. If children are slow about learning to read, the blunder must not be made of neglecting their mental culture in other directions, as though reading were its necessary prerequisite. Reading often demands a large amount of patience, and should never be allowed to produce a feeling of aversion to teachers and books.