Drawing is used in connection with arithmetic to illustrate magnitudes, and to explain processes; in geography, to illustrate by diagrams, maps, etc., to make the conceptions of cosmography, etc., more clear. It is used also to illustrate natural science.

The French theory of drawing outlined [sec. 10], insists on the unity of all drawing, on the recognition of geometry as its foundation, on the necessity of freehand drawing, on the great importance of visual observation, and on the reaction of this last upon manual observation. Hence it attaches considerable weight to geometrical drawing in the development of the programme, this, however, being executed at first freehand.

On the other hand it has been urged by some German authorities that geometrical drawing should not be taken early since it imperils the aesthetic sense; some go even so far as to propose the abolition of geometrical drawing in the lower classes. [Chap. XXI, sec. 14]. In some countries objects belonging to various periods in the history of art, are drawn so as to give some idea of the development thereof [scc. 16].

Perspective drawing is widely taught, both for its value as geometry, and its great value in guiding one in freehand drawing.

In the development of forms borrowed from the vegetable and animal kingdoms, the method usually followed is to first draw the object, and then to conventionalise it; beautiful decorative patterns are evolved in this way. Some of the recent drawing of this character in English schools is excellent, and was occasionally comparable to anything seen elsewhere. Teachers are thoroughly prepared for teaching the subject, its methodology being fully treated in the normal schools [sec. 17]. Of the advantages to any teacher, of the ability to draw, it is needless to speak; it is also important that he should be educated in the general theory of pædagogy.

It may further be pointed out that many of the drawing exercises are directly valuable in connection with arithmetic, algebra, geometry, physics, and natural history, and the drawing lessons should be co-ordinated with the others as much as possible. Especially is this true of geometry, geography, etc., while graphic arithmetic and algebra can be made of service as one of the technical forms of drawing.

14. Teaching of Languages.-The general practice throughout Europe is to restrict languages to the mother-tongue in the case of people who desire to qualify themselves for unskilled labour only, or who intend to follow only trade avocations. In a democratic country, however, it becomes necessary to constitute the ordinary primary school a preparatory school for higher education, and, therefore, at a suitable stage languages should be taught to those who desire such instruction. If, however, they are taught at all, the teaching should be thorough. The difficulties of unlearning erroneous quantity or accent in Latin or Greek, or mispronunciation in French or German, are far greater than those of correctly learning the elements. [Chap. XXII, secs. 15, 15].

The general question of language-teaching, at least so far as French and German are concerned, was recently very carefully considered by an American committee of twelve language-professors, who, two years after their appointment, presented a report on the subject. In Chapter XXII a synoptical statement of their opinions is given, and the question is further discussed in the light of subsequent experience.

If one analyses the various methods of teaching languages, they may be divided [Chap. XXII] as follows, viz., into :—

(a) The grammatical method, viz., that in which an attempt is made to learn the language through its grammar. This is the method generally adopted, and is also the poorest method [sec. 6].

(b) The reading or empirical method in which the grammar is to some extent dispensed with, and the language is learnt by reading it and from its vocabulary. This method is also common [sec. 7].

(c) The so-called "natural" or conversational-method in which it is attempted to learn a language as one learns the mother-tongue. This has elements of value, but in its simplest form is by no means satisfactory [sec. 8]. (d)

(d) The psychological or visualising method in which one associates the heard and printed forms of the word with the object or action represented, and endeavours to form in that way an indissoluble association [sec. 10]. (e) The phonetic or vocal-analysis method, which starts by drill in phonetics, aims at securing accurate pronunciation, by overcoming the difficulty introduced by the vocal habits engendered in learning one's own language [sec. 12.] In a highly-developed form this last is taught in Sydney for German by Mr. F. Bender.

There is a method which seems to give good results generally known as the Berlitz method [sec. 11]; and in Sydney M. Périer has a method based upon psychological principles for learning French which also gives good results. latter is, in a quasi-official way, taught at Fort-street school.1

The

The psychology of the relation between thought and its expression as applied

to learning languages is indicated in section 9.

The teaching of languages in other countries is very successful, and leads to an idiomatic knowledge of the language and to accurate accent and pronunciation. English people when properly taught are also able to learn foreign languages with facility.

The methods adopted by different classes of teachers have been indicated. It is well known that the ordinary or classical method of learning through grammar is one of the most tedious and unsuccessful of all possible methods. On the other hand, the psychological-conversational method leads to excellent results, especially if supplemented by phonetic suggestions as to pronunciation. It has quite lately been pointed out that this method will lead to a far more rapid acquirement of languages than is possible under the old system, and Professor Postgate of Cambridge gives it as his opinion that children who are taught by this method will hopelessly outdistance their competitors. Further, grammar should be learnt after some acquirement of the language-not before.

In a country such as ours, and bearing in mind the present state of education, the importance of securing correct methods of pronouncing Latin or Greek, and French or German, suggests the use of the phonograph. This has lately been largely called into requisition for the teaching of languages, apparently with good results [Chap. XXII, sec. 14].

The question of the importance of teaching the dead languages and modern languages is touched upon in Chapter XXII. It may be said that the great difficulty of finding sufficient time for the teaching of Latin (and Greek), and also for teaching modern languages, will be much alleviated by better methods of teaching. Whatever languages are to be learnt, lessons therein should commence at 10 years of age, or, if attention has been paid to etymology beforehand, they might, perhaps, be deferred till 12. Properly taught, language is not a difficult subject.

Wherever modern languages are taught by teachers unfamiliar with the correct pronunciation, the phonograph should be made available. Seeing, as previously stated, how much more difficult it is to unlearn erroneous pronunciation or quantity, than to initially learn correctly, the pronunciation should be most carefully attended to at the commencement of the instruction.

15. Teaching of Geometry.-By the great majority of European countries, the use of Euclid's Elements as a means of learning geometry has, for a long time, been wholly abandoned. England has retained this method, and though the unwisdom of this retention has been pointed out, and though it has also been obvious that mathematical education in England has been placed at a great disadvantage thereby, it is only lately that it has been admitted that we must follow in the footsteps of European method. The matter has been the subject of a long debate, in which a great number of persons, whose opinions have weight, have taken part, and the whole issue has been discussed by the British Association for the Advancement of Science. The recommendations of a committee, specially appointed by that Association, approves such abandonment. [Chap. XXIII, secs. 43-46].

The defect of a text-book of Euclid's Elements is that it teaches, after all, very little geometry, and that in a most tedious way. Its scheme of demonstration, while affecting to be extremely rigorous, is not really so (e.g., the 5th proposition

cannot

A general arrangement permitting special teaching in the schools of the Department would be an excellent one. The lessons are not actually given in the Fort-street school buildings,

cannot be proved except by the introduction of a new postulate allowing the rotation or inversion of a figure); by false construction (not obviously false) impossible results can be established by the scheme of reasoning followed. [See Sir John Gorst's remarks, Chap. XXIII, sec. 31].

Not only can nearly the whole of such geometry be taught intuitively, but by a different scheme of demonstration the proofs can be more readily and more obviously reached. [Chap. XXIII, pt. 2, secs. 48–60].

French and German treatises on geometry of quite a moderate size teach a great deal more of the subject than can be gleaned from Euclid, and there is no doubt that the abandonment of Euclid's Elements will not only make it possible to handle the subject more interestingly, but also to learn it more thoroughly and more comprehensively. [Chap. XXIII, secs. 5, 6].

Since the greater part of Euclidean geometry can be reduced to almost selfevident propositions, so that the teaching may be made intuitive, quite small children may learn a considerable body of geometrical truth in an interesting way, and very easily. The widespread dislike for Euclidean geometry is largely responsible for the indifferent appreciation of the subject and for a general absence of geometrical knowledge. Moreover it ought to be said that the reading of the books of Euclid occupies a considerable time in the primary schools, (though in the end but little geometry is learnt), and the more interesting branches of the subject are left absolutely untouched.

16. Geography. The methodology of the teaching of geography in Europe is very thorough, the subject being made interesting by being taught in relationship to allied subjects. In many places it commences in the kindergarten, the morphological element receiving first attention; then the idea of locality, the orientation of places known to the child being dwelt upon. His local knowledge is then extended to surrounding regions, of which he has some knowledge; from these to his country generally, and from his country to the empire, and from that to the world at large. In every way possible it is made interesting. Dry repetition is avoided. History is taught in connection therewith, each subject helping and making significant the other. By little exercises in geographical drawing, sometimes made from his own survey, the child learns also how maps are built up. The maps of Europe, it may be said, are excellent.

The European view, viz., that it is of the first importance to have a realistic and thorough knowledge of one's own country, of its characteristic features, its ways of communication, its touch with the outer world, its natural wealth, and its general resources, should govern the teaching of the subject in this State also. By explanations of its historical and commercial relationships, our country should be connected with England, and the possibilities of the mission of English-speaking people should be broadly outlined. Then the relation of the British Empire to the rest of the world could be made intelligible, viz., through subjects giving a real interest in the issues that lie open to any great race. In this way national dignity of character, a very necessary corrective to blind national prejudice, may be developed.

The characteristics and resources of other countries, in relation to our own, will not be without interest to children. If all branches of geography were, as far as possible, taught simultaneously, its educative value might be made very high indeed; and here again is seen the need for well-educated teachers with broad outlook, such as a scheme of training, similar to that of other countries, can assure.

Wherever history is taught, maps illustrating historical movements, and pictures giving reality to geographical forms, and giving general information, should be largely used. In this connection may be mentioned historical, ethnographical, and similar pictures. To give a vivid idea of the world's morphology, or the real appearance of different places, the Commissioners saw nothing better than the beautifully coloured, photographically reproduced scenes, known as Photochromes. [Chap. XXIV, sec. 10, Chap. LI, sec. 3], and a small selection was made at the instance of the Commissioners, and supplied to the Department at a remarkably low cost.

Physical geography is always taught. The place of the world in the solar system, and of the solar system in space, are explained, thus carrying onward the conceptions of children into the larger reaches of time and space.

An

An important aspect of the subject is its dualistic nature [Chap. XXIV, sec. 2], touching abstract science on the one hand, and human relationships on the other. This is obvious from the following:

Some idea of the perfection of maps may be had from Chap. XXIV, sec. 4. It may be mentioned that in the rural schools of France, and many of the schools of Switzerland, elementary surveying is taught, so that the people can measure up their crops, etc., and undertake any simple surveying desired. [Chap. XXIV, sec. 5.

Another feature of great interest is the practice of taking school children for geographical excursions. With teachers who know something of geology, physical geography, history, general science, etc., such excursions are extremely interesting and very instructive. [Chap. XXIV, sec. 17]. The mere copying of maps is everywhere falling into deserved discredit, but map drawing may be made educative. [Chap. XXIV, sec. 13]. This subject is worthy of our serious attention, and if the State Railways made the opportunity here, it would be an excellent thing for both teachers and scholars.

The equipment for the teaching of the subject consists of a black globe, a tellurium, a planetarium, an armillary sphere, a ura notrope, sometimes a relief globe of the moon, pictures, photographs, lantern slides, etc. [Chap. XXIV, sect. 18, to which reference should be made].

Reference is made to the special method of teaching the blind geography. By a special series of maps this subject is most successfully taught to them [Chap. XXIV, sec. 19], and often their achievements in the subject are surprisingly

excellent.

17. Arithmetic and Algebra.-In the school system of New South Wales, arithmetic is taught early and algebra comparatively late. It is desirable, however, that subjects, the logical elements of which are so fundamentally identical, should as far as possible be taught together, although in the early stages of the teaching the algebra need not be formal. The mode of teaching these subjects in other countries is briefly outlined in Chap. XXV. Perhaps the characteristic difference between the European and our teaching is the weight attached in the former place to mental arithmetic, and it is often required that mental processes shall be followed unless they are liable to lead to mistake or are tedious. It may be remarked that the lengthy arithmetical sums often given with us are practically valueless, since in practical computations professional computers have no difficulty in making use of abbreviated methods. The educative value of arithmetic lies in the thinking involved. The principles underlying arithmetical and algebraical processes are very carefully handled in European schools, stress being laid upon the importance of the children thinking accurately. Endeavour is made to give the children concrete ideas of the significance of number. The mere writing down or utterance of such a number, say, as 10,000, has no meaning for a small child; if, however, he be taught to represent it to his mind as groups of real objects, the numerical conception acquires reality.

Examples in arithmetic, to be of direct interest to the child, must have some practical value, be in concrete form, or concerned with something in which he is interested. Mere rule-of-thumb processes are to be avoided, such, for example, as certain forms of compound multiplication, duo-decimal multiplication, etc. It is better to take simple cases that are thoroughly understood, and expound the rule when the intelligence is sufficiently advanced.

It is, of course, eminently desirable that no arithmetical or algebraical examples leading to false conception of physical phænomena should be given. Some English treatises on arithmetic offend in this particular, an example being

given in the chapter on "Reform in the Training of Teachers" [Chap. XL, sec. 13]. A question leading to false physical conceptions will not be given when the proponent has a proper knowledge of physics, and similarly for other sciences; and hence the necessity for thorough education in general elementary principles, even for the proper teaching of arithmetic. Questions for arithmetical practice should be always normal cases.

The nature and laws of arithmetical operations may readily be explained to quite young children, provided they are thoroughly understood by the teacher, are put in proper form, and are suitably illustrated. The aim in Europe and America is to make every step rational.

Special care is taken in Europe not to develope mere "parrot-memory" of multiplication and other arithmetical tables. Unfortunately, all English children are greatly handicapped by the English systems of weights and measures-systems that, so long as they are retained, must place our people at a disadvantage, both industrially and commercially. By teaching the metric system to children in schools it will be very easy, even in one generation, to eliminate the difficulty and to avoid the inconveniences of the present cumbrous system.

In the German methodology of arithmetic, distinction is made between the introduction to arithmetical ideas, facility in arithmetical operations, and the application of arithmetic to various problems. As far as possible the whole range is covered in the earliest classes, the arithmetic, however, being so developed that the cases, simple at first, become more and more complex as the pupil passes into higher classes. Mental arithmetic receives the greatest possible attention, the arithmetical problems being drawn as much as possible from other branches of instruction [Chap. XXV, secs. 2 and 6].

In dealing with mathematics generally, the British Association for the Advancement of Science recommend a constant appeal to concrete illustrations. They strongly urge the introduction of the metric system, the abandonment of the elaborate manipulation of vulgar fractions, the introduction of the ideas of ratio and proportion concurrently with vulgar fractions, the early introduction of decimals, the use of contracted methods and the exhibition of the method of finding result true to a limited number of figures, the use of tables of simple functions-for example, of logarithms, circular functions, etc. These recommendations must commend themselves to everyone who has given the matter any attention. [Section 6].

In algebra they recommend the testing of formulæ by arithmetical applications, the use of graphs, the method of commencing with simple illustrations, the abandonment of extravagantly complicated algebraical expressions, of elaborate resolutions into factors, of difficult combination of indices, of equations that demand considerable ingenuity and manipulations; and so on. [Section 6].

It is desirable that the connection between algebra and geometry should also be more clearly indicated in teaching, so that the three subjects-arithmetic, algebra, and geometry-may be closely inter-related in the scheme of instruction.

Vector algebra is not taught in this State in the primary schools, but it would be very easy to make children understand its elementary conceptions-a matter of great importance as an element of mathematical thought. Some little idea also could easily be given of the significance of determinants. Naturally, all this involves a training of our teachers comparably to the training in Europe and America.

18. Natural Science. The place of natural science in the curriculum for primary schools is receiving increasing recognition in the United Kingdom and is well recognised in Europe and America. [Chap. XXV, scc. 1]. That it should find a place in the curriculum of this State is evident if reference be made to the work done in other countries. A special committee of the British Association for the Advancement of Science, consisting of eminent scientists and educationists, strongly recommended in 1902 the introduction of science teaching in English elementary schools. This has been done in recognition of the fact that such teaching is essential to enable the community as a whole to respond to the demands of existing conditions in commerce and industry. The very serious consequences to Great Britain of national neglect of scientific knowledge has been pointed out in no unmistakable terms by Lord Rosebery, Mr. Joseph Chamberlain, Dr. Haldane, Sir Norman Lockyer, and many others, who fully recognise the necessity of English industry and commerce more fully availing itself of scientific

knowledge