notions he has, as it were, what he knows to be valuable gold ore in his possession. But the latter must be refined before it can be brought into relation to human needs, before it can be used; so with knowledge; the non-essentials that are mixed with the essentials in concrete facts must be separated from these before the latter can become adapted to our use. That itself is a very important part of instruction. In arithmetic it is not left to one or a few examples worked to suggest of themselves the arithmetical rule; that would involve too much risk. It is a matter of vital importance to compare the steps taken in adding different groups of fractions in order to discover what must always be done, i.e. what the rule is. This is the case, too, in all study. The first and second great steps of instruction give command at best of well-arranged series of individual facts; from these the general truths are still to be drawn; and unless this is done the instruction of the teacher is, as a rule, largely in vain. So far as knowledge is concerned, general truths are the teacher's harvest; just as the reaping and threshing of wheat are essential parts of wheat raising so the careful reaching of generalizations is an essential part of good instruction.

While the acquisition of concrete facts may be regarded as a single large step, it was found to consist of two minor acts, each of which involved a large number of valuable considerations. So the

progress from individual to general notions is not simple; enough has been said to indicate that the individuals must be compared in order to discover in what respects they are alike and what properties are essential to all; then must follow a collection of the essential characteristics of the class and an expression of the same in words in the form of a definition, maxim, or proverb, etc. Hence, there Two steps in may be said to be two stages in proceeding from

generaliza

tion.

individual to general notions: one, the stage of comparison and abstraction, the other, of definition; the former would then be the third, the latter the fourth step in the mastery of general notions, since, as shown above, two are necessary in acquiring the concrete data.

Third Step

Comparison presupposes a knowledge of things to be compared; one cannot well hunt out resemblances and differences among objects before these themselves have been separately studied. The argument for this statement is well worth thinking out, it would require too much space to be presented here. The opposite practice is quite common.

The extent to which the comparison is carried must depend upon the number and nature of the data furnished through the second step, or through other similar experiences acquired either in or outside of school. Few problems involving addition of fractions need be solved before their comparison can

take place with the view of reaching the rule. This The ease or difficulty of is because one problem is quickly recognizable as reaching gentypical of all others. Likewise the metamorphosis eralizations. of one insect readily represents that of others of the same class. The moral of a story may easily be reached from the one narrative when the theme is simple and when it recalls numerous past experiences tending in the same direction. This is the case with the Golden Touch. Children who are quickly susceptible to the force of the underlying truth must necessarily have been led already to reflect on the occasional uselessness of gold; for instance, they have found Crusoe rightly preferring a jack-knife to a whole bag-full of money. And such experiences, coupled with the narrative, indeed compared with it unconsciously, cause the moral to seem easy and capable of being reached at a single bound. However, as already shown, it is reached much more effectively if time is taken to recall other related experiences and compare them all.

But some of our great classics furnish remarkable examples of a common inability to "read between the lines." Pestalozzi's "Leonard and Gertrude" was undoubtedly regarded only as an interesting story, not as a work on education, by the great majority of its multitude of admirers during the previous century. Even to-day students need to be cautioned that it is educational in its aim before they are inclined to discover in it educational truths. One hundred years

ago people wanted many of the experiences that must be put alongside those of this story in order to bring out clearly its fundamental thought. Now they have plenty of them, but easily fail to call them to mind and to associate them with the contents of the book. Hence it must be a part of the instructor's duty to call up such experiences and suggest, through them, the generalizations intended.

Pestalozzi's book furnishes an excellent example of a properly realized second step; i.e. there is an abundance of incidents or particulars so presented as to be very clearly seen and to appear interesting; but while there is no fault to find with it in that respect, the reader must extricate himself from this mass of details and discover the great truths that the essential parts of the story indicate before he has really read the book or gotten its worth.

In general, this step of comparison must be a considerable abridgment of what is necessary in a complete induction. It would be agreeable if a great number of individual valleys, trade centres, and stories teaching the same underlying thought as the Golden Touch, etc., could be studied in detail. But want of time, in school at least, forbids. Only a few wellchosen types can there receive such close attention, and they must represent and explain in a rough way the entire class to which they belong. It is for the home and later life to supplement this work of the school.

advantages of comparison.

If these individuals have been accurately and in- The various terestingly taught, the comparison that follows can awaken much life. It is interesting to note how a cat or a dog runs across the floor; but it is more interesting still to note how the former is fitted to do it so much more quietly than the latter. We enjoy observing just how the sheep, the cow, or the horse clips off grass from the meadow, but we enjoy still more the comparison of them to discover why one prefers long grass and another grass that is very short. Tennyson's poem of "The Brook" is very attractive in itself, but after seeing what message a little stream carries not only to one poet but to two or three, it is especially attractive to compare these messages and their various styles of expression. The old Greek heroes were wonderful men; so were our own pioneers. A class that has formed a close acquaintance with both sets of men is likely to become especially stirred in determining which had the greater difficulties to meet and which were the nobler.

Such comparisons increase not only the interest in knowledge, but its accuracy and definiteness as well. One serious defect in most instruction is that the facts taught are abandoned too soon for the sake of new ones, and in consequence they are neither thoroughly comprehended nor even retained in memory. But the moment we begin to compare animals or poems, or men, etc., they must be recalled vividly to mind; thus a careful review is instituted. But more