572 



SCIUNGE, 



[Vol. IX., No. 227 



process, the teacher may look at it to see where 

 the, form might have been improved, how it might 

 have been curtailed, what steps were superfluous, 

 and so on. So long as any fault in reasoning has 

 to be corrected, it is premature to examine inele- 

 gancies. I do not advise correcting too many mis- 

 takes at once. It disheartens a pupil to have too 

 many faults found at once. One mistake in each 

 exaruple is ordinarily enough. The faults of rea- 

 soning are to be first corrected, then mistakes in 

 work, and, last of all, mere matters of arrange- 

 ment. I know that this order is distasteful to 

 some pupils, who like first to be told how to put 

 their work down. I recommend the other order : 

 let them first reason out the proposition in the 

 way which they can follow by themselves, and 

 make no mistake about it ; then they are able to 

 appreciate the advantage of particular modifica- 

 tions of their process that a more experienced 

 mathematician may suggest to them, 



" As an example of what I mean. I may refer to 

 division by a binomial factor, such as x — a. A 

 pupil will at first naturally imitate long division 

 in arithmetic ; he may then be shown how the 

 abbreviated, or synthetic method, as it is called, 

 is a mere re-arrangement and curtailment of what 

 he has done before ; whereas, if he had been 

 taught the shorter method as a rule from the first, 

 it vvould have been a mere un-understood rule of 

 thumb. 



" It has been for a long time my practice, due 

 to a hint from the late Mr. Todhunter, always to 

 require to see an attempt and an exact statement 

 of his difficulty from a pupil, of any problem that 

 he says he is unable to solve, and which appears 

 to me to be within his reach. The reason is, first, 

 that I may see where the precise difficulty is, and 

 so know what it is that I have to explain ; and, 

 still more, because in the act of setting forth the 

 difficulty the obscurity has a habit of disappearing. 

 A student may think he is unable to solve a prob- 

 lem because he cannot see his way from the be- 

 ginning to the end ; but he can generally draw 

 some conclusion from the data of the question. 

 I can then 'give him just the help he needs, where- 

 as otherwise I am liable to explain to him what he 

 really understands, not knowing what it is that 

 stops him. 



"The influence of examinations is not wholly 

 bad, as at first sight one might be tempted to 

 think. A teacher who has not the prospect of an 

 examination of his pupils before him is apt to 

 think that it is suffi.cient if his pupils understand 

 the subject, and that requiring them to reproduce 

 it is superfluous. In this they are liable to lose 

 the great advantage which the necessity of writ- 

 ing out would have given them, and the teacher 



is extremely likely to credit them with a knowl- 

 edge that the examination would have shown that 

 they do not possess. As a test of knowledge,, 

 then, an examination is useful ; nay, it is most 

 valuable. But when the examination is made an 

 end in itself, and when the object aimed at is to 

 produce a semblance of knowledge to deceive an 

 examiner, where the reproduction is made a pri- 

 mary object instead of a secondary one, in sub- 

 servience to the mental education, then the in- 

 fluence of the examination is mischievous. 



"However intelligent and teachable a pupil 

 may be, he will occasionally make mistakes. The 

 commonest forms of these annoying but compara- 

 tively innocent mistakes are misoopying either 

 the question or their own work, arithmetical 

 slips, and mistakes with the signs -1- and — . 

 These mistakes do not always imply ignorance or 

 inattention, and a teacher is unwise to attach too 

 much importance to them : a few of them are 

 quite consistent with a sound appreciation of 

 principle. The effort should be made to under- 

 mine the causes of these faults, rather than to cor- 

 rect them when made. The chief of them is 

 hurry. This is a growth of our age which sends 

 down the fibres of its rootlets even to the minut- 

 est arrangements of school-life. Set before your 

 pupils that accuracy is preferable to pace ; ac- 

 custom them to the habit of exact speaking and 

 writing, even to the dotting of i's and crossing of 

 fs, — and such faults will largely disappear." 



THE STUDY OF LANGUAGE. 



Human language is wholly a psychological pro- 

 cess. As von Humboldt long ago pointed out, it 

 is nothing innate, but a function ; it is no concrete 

 object, but exists only in the soul of the indi- 



Die praktische Spracherlernung auf Grund der Psy- 

 chologie und der Physiologie der Sprache. Von Felix 

 Fbanke. Heilbi-onn, 1884. 



' Sprachentwickeluug, Spracherlernung, Sprachtild- 

 ung,' von F. Techmer, in hreizehnter Bericht il'oer die ho- 

 here Schule fur Mddctien zu Leipzig. Leipzig, 1885. 



'On the practical study of language,' by H. Sweet, 

 M.A., in Transactions of the Philological society, 1882-84. 

 [The President's annual address for 1884.] London, Triib- 

 ner, 1885. 



Der Sprachunterricht muss umkehren ! Ein Beitrag 

 zur Ueberbiirdungsfrage von Quousque Tandem (Wilhelm 

 Viator). Zweite um ein Vorwort vermehrte Auflage. Heil- 

 bronn, 1886. 



' Techmer's und Sweet's Vorschlage zur Reform des- 

 Unterrichts im En;4lische,' von H. Klinghardt, in Eng- 

 lische Studien, baud x., heft i. Heilbronn, 1886. 



German prontmciation : practice and theory. By Wil- 

 helm ViETOR. Heilbronn, 1885. 



Elemente der Phonetik und Orthoepie des Deutsch^n,. 

 Englischen, und Franzosichen mit Riicksicht auf die Be- 

 dUrfnisse der Lehrpraxis. 2d ed. Von Wilhelm Vietoe. 

 Heilbronn, 1887. 



