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CAMBRIDGE LOCAL EXAMINATIONS, 1904.

Cicero.-Pro Archia. By A. H. ALLCROFT, M.A. Oxon., and F. G. PLAISTOWE, M. A. Camb. and Lond. 1s. 6d. Vocabulary, 1s. Translation, 1s. In One Vol., 38.

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and Lond., and A. H. ALLCROFT, M. A. Oxon. 2s. 6d.
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2s. 6d.
3s. 6d.
Livy.-Book VI. By W. F. MASOM, M. A. Camb. and Lond.
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Sophocles.-Antigone. By A. H. ALLCROFT, M.A. Oxon., and B. J.
HAYES, M. A. Camb. and Lond. 2s. 6d. Vocabulary, 1s. Translation,
1s. 6d. In One Vol., 4s. 6d.

Yergil.-Aeneid, Book I. By A. H. ALLCROFT, M.A. Oxon., and
W. F. MASOM, M. A. Camb. and Lond. ls. 6d. Vocabulary, 1s.
Translation is. In One Vol., 3s.
Shakespeare.-Richard II. By W. J. ROLFE, D.Litt.
Spenser.-The Faerie Queene, Book I. By W. H. HILL, M.A.

Lond. 2s. 6d.

COLLEGE OF PRECEPTORS' EXAMINATIONS, 1904. Caesar.-Gallic War, Books II., III. By A. H. ALLCROFT, M.A. Oxon., and W. F. MASOM, M. A. Camb. and Lond., and others. Is. 6d. each. Vocabulary, 1s. each. Translation, Is. each. In One Vol., 3s. each.

Euripides.-Alcestis.

By J. H. HAYDON, M.A. Camb. and Lond. In One Vol., 2s. 6d.

1s. 6d.

In

18. 6d. Translation, 1s. Horace.-Odes, Book I. By A. H. ALLCROFT, M. A. Oxon., and B. J. HAYES, M.A. Camb. Vocabulary, 1s. Translation, Is. One Vol., 3s. Vergil.-Aeneid, Book I. By A. H. ALLCROFT, M.A.Oxon., and W. F. MASOM, M. A. Camb. and London. Is. 6d. Vocabulary, 1s. Translation, 1s. In One Vol., 3s. Shakespeare.-Richard II. Edited by Prof. W. J. ROLFE, D.Litt.

2s.

OXFORD LOCAL EXAMINATIONS, 1904. Aeschylus.-Persae.

By J. H. HAYDON, M.A. Camb. and Lond. 3s. 6d. Translation, 1s. 6d. In One Vol., 4s. 6d. Caesar.-Gallic War. By A. H. ALLCROFT, M. A. Oxon., in collabo ration with F. G. PLAISTOWE, M. A., and others. Books I., II., III. 1s. 6d. each Book. Vocabulary, 1s. each Book. Translation, 1s. each Book. In One Vol., 3s. each Book. Cicero.-Pro Archia. PLAISTOWE, M. A. Camb. In One Vol., 38. Euripides.-Alcestis. 1s. 6d. Translation, 1s. Horace. Odes, Book I. By A. H. ALLCROFT, M. A.Oxon., and B. J. HAYES, Camb, and Lond. 1s. 6d. Vocabulary, 1s. Translation, 1s. In One Vol., 38. Sophocles.-Antigone. By A. H. ALLCROFT, M. A. Oxon., and B. J. HAYES, M. A. Camb. and Loud. 2s. 6d. Vocabulary, 1s. Translation, 1s. 6d. In One Vol., 4s. 6d.

By A. H. ALLCROFT, M. A. Oxon., and F. G.
ls. 6d.
Vocabulary, Is. Translation, 1s.

By J. H. HAYDON, M.A.Camb. and Lond.
In One Vol., 2s. 6d.

Yergil.-Aeneid, Book I.

By A. H. ALLCROFT, M. A. Oxon., and W. F. MASOM, M.A. Camb. and Lond. ls. 6d. Vocabulary, 1s. Translation, 1s. In One Vol., 3s. Dryden. Essay of Dramatic Poesy. Edited by W. H. Low, M.A.Lond. 3s. 6d.

SOUTH KENSINGTON EXAMINATIONS.

For the First Stage.

2s. each Volume.

Practical Plane and Solid Geometry, First Stage. By
G. F. BURN, A. M. Inst. M.E.
Building Construction, First Stage. By BRYSSON CUNNINGHAM,
B. E., Assoc. M. Inst.C.E.

Mathematics, First Stage. Edited by Dr. WM. BRIGGS, M.A.,
F.R.A.S.

Mechanics (Solids), First Stage. By F. ROSENBERG, M.A., B.Sc. Mechanics of Fluids, First Stage. By G. H. BRYAN, SC.D., F.R.S., and F. ROSENBERG, M.A.

Sound, Heat and Light, First Stage. By JOHN DON, M.A., B.Sc.

Magnetism and Electricity, First Stage. By R. H. JUDE, M. A., D.Sc. Second Edition.

Inorganic Chemistry (Theoretical), First Stage.

By G. H.
BAILEY, D.Sc. Lond. Edited by Dr. WM. BRIGGS, M. A., F.C.S.
Botany, First Stage. By A. J. EWART, D.Sc., Ph. D., F. L.S.
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Hygiene, First Stage. By R. A. LYSTER, M. B., B.Sc., D.P.H.
Price Is.

Inorganic Chemistry (Practical), First Stage.
BEDDOW, Ph.D., D.Sc.
Organic Chemistry (Practical). By GEO. GEORGE, F.C.S.

Price 1s. 6d.

By F.

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Chemistry, The New Matriculation. By G. H. BAILEY, D.Sc., Ph.D., and R. H. ADIE, M.A., B.Sc. Part I., 4s.; Part II., 2s. English Course, Matriculation. By W. H. Low, M. A. Lond.,

By A. F. 2s. 6d.

and JOHN BRIGGS, M. A. Camb., F.Z.S. 3s. 6d. Latin Authors, Matriculation Selections from. WATT, M.A. Oxon., and B. J. HAYES, M. A. Lond, and Camb. Latin Construing Book, Matriculation. 2s. 6d. [In preparation. Modern History, Matriculation. With Maps, Plans, and Tables. By C. S. FEARENSIDE, M.A.Oxon. 3s. 6d.

CENTRAL WELSH BOARD EXAMINATION, 1904. Caesar. Gallic War, Books I., II., III. By A. H. ALLOROFT, M. A. Oxon., and others. 1s. 6d. each. Vocabulary, 1s. each. Translation, 1s. each. In One Vol., 3s. each. Horace.-Odes, Book II. By A. H. ALLCROFT, M.A.Oxon., and B. J. HAYES, M. A. Lond. 1s. 6d. Vocabulary, Is. Translation, Is. In One Vol., 3s.

By T. M. NEATBY, M.A. Lond, and 2s. 6d. Vocabulary, 1s. Trans

Ovid. Fasti, Books III., IV. Camb., and F. G. PLAISTOWE, M. A. lation, 1s. 6d. In One Vol., 4s. 6d. Plato.-Ion. By J. THOMPSON, M.A., and T. R. MILLS, M.A. 3s. 6d. Vocabulary, 1s. Translation, Is. 6d. In One Vol., 5s. 6d. Sophocles.-Antigone. By A. H. ALLCROFT, M.A. Oxon., and B. J. HAYES, M. A. Lond, and Camb. 2s. 6d. Vocabulary, 1s. Translation, ls. 6d. In One Vol., 48. 6d. Chaucer.-Prologue to the Canterbury Tales, Knight's Tale. By A. J. WYATT, M. A. Lond. and Camb. 2s. 6d. Chaucer. The Nun's Priest's Tale, with the Prologue to the Canterbury Tales. By A. J. WYATT, M. A. Lond, and Camb. 2s. 6d.

Shakespeare.-Henry VIII. By W. H. Low, M.A. Lond. 2s.

ROYAL UNIVERSITY OF IRELAND MATRICULATION, 1904. Euripides. Hecuba. By T. T. JEFFERY, M.A. 3s. 6d. Translation, 1s. 6d. The Two Parts in Que Vol., 4s. 6d. Horace. Odes, Book I. By A. H. ALLCROFT, M. A. Oxon., and B. J. HAYES, M. A. Lond. and Camb. Is. 6d. Vocabulary, 1s. Translation, 18. In One Vol., 3s.

Horace. Satires. By B. J. HAYES, M.A. Lond, and Camb., and
F. G. PLAISTOWE, M.A. Lond. and Camb. 48. od. Vocabulary, Is.
Translation, 18. 6d. In One Vol., 6s. 6d.
Thucydides.-Book VII. By J. F. STOUT, B. A. Camb., and F. G.
PLAISTOWE, M. A. Lond, and Camb. 3s. 6d. Translation, 2s. 6d.
Yergil.-Aeneid, Book III. By A. H. ALLCROFT, M. A. Oxon., and
F. W. MASOM, M. A. Lond. Is. 6d. Vocabulary, Is. Translation, Is.
In One Vol., 38.

THE SCHOOL JUNIOR SERIES.

(Books suitable for the Oxford and Cambridge Junior Locals, and the College of Preceptors' Second Class, Certificates). Arithmetic, Junior. Adapted from the TUTORIAL ARITHMETIC. By R. H. CHOPE, B.A., of Kingswood School, Bath. 2s. 6d. Bookkeeping, Junior (or The Preceptors). CHALICE JACKSON, B. A., LL.B. Lond. Is. 6d.

By THOMAS

[In the Press.

English Course, Junior (or the Preceptors'). By W. H. Low,
M. A. Lond., and ARNOLD WALL, M.A.Loud."
French Course, Junior (or The Preceptors').
By ERNEST
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French Reader, Junior (or The Preceptors'). With Notes
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Complete Catalogues, and Lists of Books Classified for each of the following Examinations may be had free on application:LONDON UNIVERSITY MATRICULATION, Inter. Arts, and B.A., 1904 and 1905, Inter. Science, B.Sc., Royal University of Ireland, and Intermediate Education Board, Cambridge and Oxford Local, and College of Preceptors', Scotch Leaving Certificate, South Kensington fincluding Books for the Second Stage), and other Examinations. LONDON: W. B. CLIVE, UNIVERSITY TUTORIAL PRESS WAREHOUSE, 157, DRURY LANE,

W.C.

To face first matter.

The School World

No. 58.

A Monthly Magazine of Educational Work and Progress.

OCTOBER, 1903.

RECENT CHANGES IN THE ORDER FOR THE REGISTRATION OF TEACHERS.

TH

HE latest changes in the Order for the Registration of Teachers have without doubt gone very far towards removing most of the objections to the Order which have been made by teachers in secondary schools. The main objects of Column B of the Schedule being to determine what schools may appropriately be regarded as secondary schools, and what teachers may fitly be considered as secondary school teachers, we propose to point out in what manner the changes promulgated by the Board of Education in July help to accomplish these objects.

From the Report of the Teachers' Registration Council for 1902, presented to the Board of Education in January last, we learn that the Council found itself considerably hampered by the terms of the original Order. Although responsible for the registration of individual teachers, it possessed no discretionary power to modify regulations which in many cases produced hardship, and in effect defeated the very object for which the Order was made. On the Board of Education being satisfied with the Council's statement of the case, a Conference was arranged and held in October between the Council and the Consultative Committee. The outcome of the Conference is seen in the changes referred to, which at once temper the rigidity of the original Order and concede to the Council very considerable discretionary power.

It should be borne in mind that as regards secondary school teachers the Order both contemplates and arranges for two distinct sets of qualifications, differentiated in the main by the inclusion or non-inclusion of training. Up to March, 1906, Clause 4 is to remain in force, under which, training not being obligatory, applicants are admitted who possess certain specified academic qualifications and have had experience in teaching "other than teaching in an elementary school or teaching of a purely elementary character" for a specified period of three years.

Clause 3 makes training in some form or other compulsory; it requires a higher academic qualification, viz., a degree or its recognised equivalent, together with the pass certificate of some approved examination in the theory of teaching, and at least No. 58, VOL. 5.]

SIXPENCE.

one year's probation at a recognised school. These ideal conditions become compulsory, unless some further modification of the Order takes place, after March, 1906. We need, however, for the present only concern ourselves with Clause 4, which deals with existing teachers.

As regards such teachers, there were up to July two requirements, viz., an approved examination equivalent in general to the Intermediate Arts or Intermediate Science standard of the University of London, and an experience of three years in a recognised, i.e., secondary, school. Although about 3,000 teachers are already registered under these conditions, abundant evidence has been forthcoming to show that many excellent teachers, and indeed sections of teachers, would be excluded if both these conditions were insisted upon. For instance, the academic qualification bears with special hardship on experienced women teachers, inasmuch as the universities have not provided equal facilities for women as for men. After 1906 this difficulty can be reasonably provided for by scheduling the certificates approved for this purpose. The second condition presses with hardship upon teachers in private schools, since these schools having been hitherto exempt, both in theory and practice, from inspection, find it difficult all at once to fulfil the conditions for recognition. By 1906 these conditions will be sufficiently well known, and this difficulty also will have been reduced to very small proportions.

Of another class of teachers to whom registration will be specially valuable, viz., governesses and teachers of private students, it is not too much to say that the original regulations ignored their existence. The Order had too exclusive a regard to the qualifications held desirable for boys' schools of a public type, aided or aidable by grants from local authorities.

The latest amendments change all this, and it is hardly too much to say that the modifications revolutionise the regulations in a sense favourable to existing teachers, and it cannot be doubted that full advantage will be taken of the two main concessions before, having served their purpose, they are withdrawn in 1905 and 1906 respectively.

It will be convenient to deal with the modifications in the Order of the two clauses most concerned. In Clause 4 the requirement of three

FF

years' continuous experience of a recognised, i.e., secondary, school remains, with this alternative

"or for periods amounting altogether to not less than three years under circumstances which, in the opinion of the registration authority, render the periods equivalent to a period of three years next preceding application."

Here the Registration Council, referred to above as the registration authority, has discretion to sanction breaks in continuity of teaching, owing to such circumstances as illness, absence for study, change of school, &c. Thus each case as regards the three years' experience will be taken on its merits. The flexibility of this regulation is thus greatly increased by a change which at first sight seems almost unimportant, but which in practice proved an absolute bar to many applicants.

The principal concession, however, is to be found in sub-section (b) to Clause 5, a section originally framed to admit to the register men and women of rare and exceptional merit as teachers who had for some reason omitted to acquire the necessary qualifications. This power remains, but a new sub-section empowers the registration authority, until March, 1905, to admit any person to the register who does not fulfil all the conditions of registration, but

"has had experience, extending over a period of not less than ten years, of teaching (other than teaching in an elementary school or teaching of a purely elementary character), and has in their opinion shown ability to teach."

This sub-section gives the Registration Council a very free hand indeed, but it is to be noted that their discretion is limited in two important particulars in the first place, it has a very short time limit, viz., to March 31st, 1905, not 1906 as might have been expected; and secondly, the applicant must be able to prove not less than ten years of secondary experience, that is, either in a secondary school or in secondary teaching. It will be obvious enough that the determination of what in individual cases is to be considered secondary, as distinct from elementary, experience will not be an easy matter, and if the Registration Council had preferred their own ease to professional and other considerations, they have been badly advised to seek the wide discretion conferred by this change.

It may be hoped, however, that the means which the Council is taking to discharge faithfully its new obligation will commend themselves to those for whose benefit the new sub-section has been framed. The Council has drawn up a special Application Form for Registration under the new sub-section. Following its previous practice, the Form is numbered as in the Order itself. It is therefore called Form 5 (2) (b), and teachers who are qualified under this clause and not under one of the previous Clauses 3 or 4 are recommended to apply for this Form without delay to the Registrar, 49 and 50, Parliament Street, London, S.W. When they receive it they will find that this Form differs from the other Forms in its providing

a Statutory Declaration for use in certain cases. If the ten years' service has been held at a school recognised for the purpose of registration of teachers by the Board of Education (and, in cases of doubt whether a certain school has or has not been recognised, enquiry should be made of Secretary, Board of Education, South Kensington) there will be no need to use the Declaration. But in cases where certificates of service are not forthcoming by reason of death of the principal, of closing of the school, &c., the applicant himself is required to state on oath before a Justice of the Peace or a Commissioner for Oaths that the statements made by the applicant are correct. It may be noted that if the Declaration be made before a

J.P. no charge is made, if before a Commissioner the charge is Is. 6d. ; in addition the stamp costs 2s. 6d. Some teachers may perhaps feel objection to the Statutory Declaration, but it is not easy to work out any simpler plan by which a body like the Registration Council, with this duty to perform, can satisfy the profession and the public that the function has been discharged adequately and impartially. It is possible that the difficulty in some cases caused by the requirement to produce evidence satisfactory to the Council "of ability to teach" may lead to the appointment of Inspectors for the purpose. In such cases, however, a special additional fee would probably have to be charged, for the present fees are by no means adequate to meet the current expenses for salaries, rent, publication of the register, and ordinary printing.

With regard to Column A, it may be noted that no question about the registration on this Column comes before the Council, all such questions being determined solely by the Board of Education, which sends to the Council the names. There are many teachers who, though teaching in public elementary schools, claim to be admitted to Column B. Hitherto non-recognition by the Board of the school has proved an effective bar to admission. The Board itself, however, accords its recognition. to each School of Science, as, for instance, that contained in the Leeds Higher Grade School, and every teacher in all such schools is qualified to go on Column B. It is certain that under the reorganisation which the Education Acts, 1902 and 1903, render necessary, many schools lately under School Boards will become recognised as secondary schools. We have before us a Report made to the Education Committee on the Secondary and Higher Education of the City of Sheffield, by Prof. M. E. Sadler (Eyre and Spottiswoode, is.), in which occurs the following sentence :--

"By reason of its convenient situation and close connection with the public elementary schools of the city, the present Central School should, in my opinion, be converted into a secondary school of the kind described in the foregoing paragraphs. As part of their general scheme for the improvement of secondary education in Sheffield, I think that the City Education Committee should approach the Board of Education for recognition of the Central School, which is at present carried on under the Higher Elementary School Minute as a secondary school" (p. 30).

If this be done, and if this policy be in general adopted, the Register by its Columns A and B will find itself in complete adininistrative accordance with the new Education Act, which differentiates the form of administration of elementary from that of higher education.

One word in conclusion is necessary with regard to the "supplemental registers for teachers of music, drawing, physical training, manual instruction, cookery, needlework" [Clause 6]. For these the regulations are not completed, but it cannot be doubted that the Consultative Committee, which in the first instance has the matter in hand, will endeavour to apply to these subjects the main principles which have commended themselves to them in the formation of Columns A and B. These principles are two: first, that the applicant for registration in each subject must possess adequate knowledge, training and experience in teaching; and secondly, that for a limited period the requirement of training will not be compulsory and the minimum attainments test will probably be of an easier standard than that for admission after the expiration of the allotted term of grace.

PASS GEOMETRY AT OXFORD AND CAMBRIDGE.

By EDWARD M. LANGLEY, M. A.

Bedford Modern School.

long as the changes sanctioned by the universities affected only their non-gremial examinations, the success of reformers, though considerable, was still partial, in its range. It was considerable, for the many secondary schools whose curriculum is based on the regulations for the Locals" have come under the new influence at once, but it was partial, because those trained in the great Public Schools who did not look forward to enter the services, might still be taught to regard the reproduction of Euclid's text as the ultimate aim of geometrical teaching. The adoption of the report of the Syndicate appointed at Cambridge to consider "what changes,

if any, are desirable in the regulations that affect the mathematical portions of the Pass Examinations" (see THE SCHOOL WORLD for June, 1903), following the announcement of the corresponding changes in the examination for Responsions, so nearly completes the success of the movement for reform, so far as alterations in regulations are concerned, as to afford a favourable opportunity for taking a general view of the position created by the changes made, and for considering the way in which teachers should carry on their work, if the full possible advantage is to be gained from the concessions made by the authorities.

It is important that they should be guided, not merely by the letter, but by the spirit of these regulations. The mere fact that certain useless or mischievous propositions of Book I. may now be omitted, while certain others not in the

"Elements" have to be looked upon as part of the ordinary book-work, is of small importance compared with the recognition by the highest authority of the opinon strongly held by experienced teachers, that this study (ie, of formal demonstrative geometry) would be rendered more effective by some preliminary and concurrent work in practical geometry." in practical geometry." Personally, I hold the preliminary to be of even greater importance than the concurrent. The preliminary work will be to a great extent work by the teachers of the lower forms with their pupils; it will consist very little of work set by them to their pupils; and cannot be done by putting a text-book in the hands of the pupils and telling them to do this or that exercise. It cannot even be done by getting up a lesson from a text-book for reproduction to a class, though some admirable text-books exist, which should be carefully studied.

It will be convenient here to notice the twofold nature of this preliminary work. It is sometimes spoken of as experimental, sometimes as practical. These are not two different names for the same thing, but the names of two different things, both of which should precede courses of formal demonstration. The "experimental" is that begun in the kindergarten. At this stage the child is made to handle the simpler solids, and to observe some of their more obvious properties; to notice the simpler plane geometrical figures, not only of specially shaped cards and papers, but also of the common objects of the class room and the street; to see that il y a de géométrie partout, to get some ideas of measurement, to use technical terms correctly. The term practical seems to imply the actual use of instruments for definite geometrical constructions by the pupil himself. Using the terms thus, we see that the experimental should precede and accompany the practical, just as both should precede and accompany formal demonstrative geometry. They are to be regarded as intended to lead up to the demonstrative course, and should be arranged with that object in view. Hence a great deal of informal demonstration should accompany both; the teacher should lose no opportunity of getting his pupils to deduce consequences from principles already known. The course should be looked upon as preliminary not merely to mathematical training, but to any scientific training worthy of the

name.

It is true that the regulations can only enforce the concurrent study of practical geometry, but I believe they will be found to lead, in many cases directly, in more indirectly, to the systematic institution of preliminary work. Those responsible for the preparation of classes for examination will not be slow to perceive that a great deal may and should be done to prepare their pupils for profiting by the demonstrative course, and they will use their influence (if they are wise they will try also to use that of their science colleagues) in trying to get much of the experimental and practical work done beforehand. They will desire this preparation, not to save themselves work, but to render their

work more effective; it should be their task only to revise and complete it, and to join it on to the deductive work. But while we may fairly expect that in a not very distant future it will be the rule rather than the exception, that the lower forms should be taken through courses of practical and experimental geometry before they are allowed to attempt any formal course of deduction, it is, unfortunately, certain, that for some time to come many will be found whose training in this respect has been very faulty, or completely neglected. Hence the teacher must lose no opportunity of illustrating his theoretical work by practice and experiment.

Coming to the demonstrative course, I would urge the importance of not delaying long over the earlier theorems. Much harm is done to beginners by keeping them too long over these, under an entirely erroneous notion of the importance of thoroughness. Sound ideas of the nature of geometrical deduction, and ability to perform it, are much more likely to arise from a rapid course through the essential theorems of Book I., followed by a closer and more careful one, than by tedious and deadening iteration of propositions 4 and 5. The best plan, I believe, is to get on as quickly as possible to the propositions on equality of areas, for the reasoning in these seems more readily appreciated than that in the earlier ones. If the subject matter of Book I. is to be taken as a year's work, at least one half of it should be traversed in the first term, the other half, with repetition of the first, should be taken the second term; the third term should be occupied by revision of the whole. In the first term there should be very little writing out but much questioning, short trains of unprepared deduction should be started and followed, both directly and inversely. The time devoted to writing out must be greater in the second term, and must be used for riders as well as for book work; in the third term writing out will play a still more important part.

I suggest the following scheme of work as one that may be more or less closely adopted under present conditions. It will be seen that, though it goes beyond the limits of Responsions and the Previous, it is about that for the highest papers in the Locals. The Books of the "Elements" are named for convenience: it is to be understood that those propositions are to be omitted which the authorities no longer require.

The following table will probably appear ambitious to some, and too narrowly conceived to others. That with a staff of zealous and enlightened teachers for all the forms it is now possible, I am convinced. But its possibility depends on good work in the very lowest forms, and on each master doing what he can to meet new requirements, in spite of all discouragements. Too much must not be expected at first. The teachers of the lower forms have to deal with a great variety of subjects; in many cases they have only received a faulty geometrical training themselves, and have had neither time, opportunity, inclination, nor inducement to fit themselves for the work now required

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As to text-books, my own opinion is that up to the time of beginning his formal demonstrative course the pupil need have no text-book, though the teacher will probably find it best to use the course of some particular book in order to make his work systematic. But he should not be a man of one book; he should be ready to seize upon and fit into his class work any good idea which he comes across in his reading. Among current text-books that can be recommeded for the ex

perimental and practical course are Sundara Row's "Exercises in Paper Folding;" Spencer's "Inventional Geometry;" Mault's "Natural Geometry;" Paul Bert's "Experimental Geometry; Eggar's "Practical Exercises in Geometry;" Warren's "Experimental and Theoretical Course of Geometry; Barnard and Child's "New Geometry for Schools;" Godfrey and Siddons' Elementary "Elementary Geometry;' Geometry;" Pickel's

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"Geometrie der Volksschule;" Pressland's "Geometrical Drawing; " Harrison's "Practical Plane and Solid Geometry." Some older works, now out of print, and to be picked up occasionally for a few pence, are worth having, e.g., Dupin's "Geometry of the Arts" and Pasley's "Complete Course of Practical Geometry."

As soon, however, as a boy is fit to begin a course of formal demonstration, he is fit to begin to use a text-book, or at any rate to begin to learn how

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