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the budding mathematician will be suppressed or depressed by any innovation for the benefit of his less gifted fellows. On the contrary, there is no doubt that the new movement is bearing fruit in the highest classes of our schools and universities. There, as in the ordinary school classes, the process of attaching a purpose to the work is adding interest and sanity to the whole study. The subject is no longer an artificial programme to be read through with a view to answering questions set in challenge at a future examination. It is recognized and is treated as a great Science arising out of human needs, carried forward by a burning desire for knowledge of the truth, and applying itself in turn to the satisfaction of further human requirements. To the genuine mathematician, the purely intellectual interest is often far stronger than considerations of utility, but he suffers not one whit by the realization imparted in early youth of what consequence his study is or may be to mankind. Such a consideration tends to make him more careful in his thought, more precise in his statements, more intolerant of all that is slipshod, and, let us hope, more indulgent towards those who have not yet attained the same intellectual eminence as himself.
BY JAMES FAIRGRIEVE, M.A., F.R.G.S.
Introduction. It is impossible to discuss the teaching of geography without being sure of what we wish to do.
Methods which are entirely suitable when one idea of the subject holds the field may be entirely unsuitable when another ideal is held. Methods in vogue two centuries ago were not the methods of thirty years ago ; methods of thirty years ago are not the methods of the New Teaching, partly because there has been a change in all teaching methods, but also partly, possibly to a greater extent, because that which is taught is not the same and demands new methods. Geography could then be taught from a text-book that contained a list of capes and bays, mountains, counties and county towns, with a few brief statements as to what the towns were noted for. All that was necessary was that these should be learned. The methods employed to induce the pupils to learn were very different from those of to-day, when the aim of teaching geography is to enable the pupil to place himself in and on the world, to realize precisely where he stands. It is not sufficient, for example, that he should be able to say that the world is round: he should be able to feel that it is round with his feet firmly planted on one spot, to imagine, not as something external but as concerning himself directly, this globe turning under him and wheeling onward on its course round the sun. We wish our pupils to imagine accurately the conditions of the great world stage on which they play their parts. Book-work, though necessary, is not sufficient. The emphasis must be laid on the making of mental images as nearly as possible corresponding to the actualities. The methods of teaching must be different because the conception of geography has changed. The New Geography demands New Teaching
Geography deals with Real Things.—It is essential that teachers should know what their aim is; they must know what is important and what is less important. What is important at one stage of the pupil's advance may be less so at another. It is important, of course, that what is known should be correct. Pupils should not speak of the Rhine when they mean the Rhone : names should be used correctly ; but 'confusion of names is of much less importance than lack of ability to recognize that names stand for real things. It is this that must be taught first, last, and all the time. Very much geography as taught now does not deal with real things but with things that have no manner of resemblance in essentials to the real things. If geography did deal with realities pupils on the point of leaving Secondary Schools after a full course would not make statements like the following, “Heligoland commands a view of the northern Atlantic and the North Sea," "The Nile flows up to the Mediterranean Sea,” “The water after surging and boiling in the great heat of the Gulf of Mexico escapes in a north-easterly direction,” “The chief occupation of the inhabitants of Surrey and Kent is hop-picking in summer,
" " Canada
is one of the countries owned by Britain.” It is just as difficult to teach the new geography as it was easy to teach the old. Geography and history are different from all other school subjects in that they deal with things that cannot be brought into the class-room. Perhaps history is the more difficult as no history worth the name is possible without a working time scale and an understanding of adult passions. These from the nature of the case children cannot have during the earlier years of school life. Geography deals with things which if not so impossible are yet almost as difficult of realization. Nothing geographical is adequately realized unless the pupils have some kind of idea of the size and scale of the world and its several parts, and not even the greatest traveller has even seen the whole world in a long lifetime. No one can see a large area like England all at once so as to take in all its relationships. These must be imagined, and imagined accurately. Inaccurate imagination, at any rate in essentials, is worse than useless.
All this makes the teaching of geography extraordinarily difficult, but it does not absolve us from attempting to do the best we can. One thing that the teacher can do is always to have visions of real things before his mind. Unless he makes an effort to visualize the things he is speaking of he will insidiously suggest by a word here and a phrase there ideas of things that do not correspond to the actualities. He must deal, and feel he is dealing, with the world as it exists and not with some picture of it. This is the first necessity in the New Teaching of geography.
Objects of teaching Geography.—The objects of teaching geography are mainly cultural in the best sense. This does not, however, exclude the possibility that geography may pay directly : it has a cash value. The old geography was of very little value to any one, but it is obvious that those who have been trained to make accurate mental pictures will not be satisfied with sham presentments. They will not be satisfied with appearances, but will be accustomed to look for real things in the world. They will not make the error of mistaking the sham for the substance. And this will be not merely because they are accustomed in a general way to deal with realities, but because the actual things of which they have learned and with which they are familiar in geography are those in the main with which commerce is concerned. They have a knowledge of facts which will enable them to check reports from other lands and estimate their value. Those who have been trained to think of real things on the earth's surface will make better business men as well as better citizens.
The Grammar of Geography.—Dealing, then, with the world and not with any representation of it, dealing with it in such a way that his pupils may be educated to become good citizens, the teacher is forced to adopt such a scheme that the facts with which he is dealing can be arranged in an orderly fashion. Without orderly arrangement any study is useless : there must be some kind of grammar. The older geography had a grammar, the new geography must have a grammar also, though it need not be the same grammar, and in fact is very different. Grammar is not usually interesting. One does not expect it to be interesting in itself : all one asks is that it should be convenient. A series of numbered pigeon-holes is not interesting, though the pigeon-holes may contain interesting matter. There are at the present time two grammars