June 10, 1887.] 



SCI^J^CJi\ 



569-" 



in the room do the same work at the same time. 

 Every new mesh or stitch that is introduced is 

 first illustrated by the teacher before the class, on 

 a frame which is high enough for all to see. It 

 is rectangular, two feet by eighteen inches. 

 Heavy threads or cords are drawn through its 

 sides, crossing each other at right angles. After 

 the seventh year, crocheting of loose, open, and 

 close meshes, with one-colored yarn, is intro- 

 duced. Next party-colored yarn is used, from 

 which various beautiful figures are made, which 

 gradually leads them to crochet articles of many 

 beautiful patterns. 



From the twelfth to the fourteenth year (the 

 last year in the public schools), sewing is the chief 

 branch. The patching and mending of torn gar- 

 ments is most thoroughly taught. In the last 

 school-year the cutting and making of underwear 

 is taught. 



The specimens of work that come from those 

 young hands are simply wonderful in points of 

 neatness, skill, and taste. Any generous-minded 

 person will be at once convinced that the capacity 

 for happiness in those young girls is far superior 

 to that of the class who have never been taught 

 any thing else than mere book-knowledge. 



Sebastian Thomas. 



THE TEACHING OF ALGEBRA. 



Among the papers lately presented to the Edu- 

 cation society of London, is one on the teaching of 

 algebra, by W. H. H. Hudson. It contains a great 

 many passages of universal application, and such 

 deserve to be reproduced in this country for the 

 benefit of our teachers of mathematics. Mr. Hud- 

 son first answers the question. Why teach algebra 

 at all ? and, while fully recognizing the utility of 

 algebra, he maintains that algebra is not to be 

 taught on account of its utility, nor to be learnt 

 on account of any benefit which may be supposed 

 to be got from it, but because it is a part of mathe- 

 matical truth, and no one ought to be wholly alien 

 from that important department of human knowl- 

 edge. 



The next question is, When should algebra be 

 taught ? The answer is, At an early period of in- 

 tellectual development. The reason for this is 

 that algebra is a certain science, it proceeds from 

 unimpeachable axioms, and its conclusions are 

 logically developed from them : it has its own spe- 

 cial difficulties, but they are not those of weighing 

 in the balance conflicting probable evidence which 

 requires the stronger powers of a maturer mind. 

 It is possible for the student to plant each step 

 firmly before proceeding to the next ; nothing is 

 left hazy or in doubt : thus it strengthens the 



mind, and enables it better to master studies of a 

 different nature that are presented to it later. 

 jMathematics give power, vigor, strength, to the 

 mind. This is commonly given as the reason for 

 studying them. This is also the reason for studying 

 algebra early, that is to say, for beginning to 

 study it early. It is not necessary, it is not even 

 possible, to finish the study of algebra before com- 

 mencing another. On the other hand, it is not 

 necessary to be always teaching algebra : what 

 elementary teachers have to do is to guide pupils 

 to learn enough to leave the door open for further 

 progress ; to take them over the threshold, but 

 not into the innermost sanctuary. 



Children younger than nine will rarely be fitted 

 to take up algebra ; and, on the other band, it is 

 seldom advisable to defer its commencement until 

 after twelve years of age. Certain preliminary 

 acquisitions are essential for this study. The first 

 of these, in Mr. Hudson's opinion, is the power 

 of listening. 



" By this I mean the habit of attaching an idea 

 to what is said. Some pupils — I hope no teach- 

 ers — consider it sufficient if the pupil can repro- 

 duce the words that have been used, without at- 

 taching any idea to them. Such pupils will not 

 learn algebra. A pupil who has the habit of 

 listening will not allow a teacher to use unintel- 

 ligible language, and will be of great use in a class 

 by stopping the teacher and asking for things to 

 be repeated and strange words explained. It is 

 difficult for a teacher to realize that sometimes 

 he is using a vocabulary beyond his pupils. In- 

 terruptions of this kind, which, show that the pu- 

 pils are listening, are of great help to the teacher. 

 " This leads to the next essential preliminary: 

 the student should be able to speak. I do not 

 mean that a deaf-and-dumb person cannot learn 

 algebra, but he can only be taught under great 

 disadvantages. Thinking of the ordinary run of 

 boys and girls, I say that they cannot learn alge- 

 bra until they have learnt to speak. By speak, I 

 mean can ask questions and can answer questions,, 

 can say what they know, and can point out what 

 to them is obscure. It has been well said that a 

 pupil vvho cannot ask a question in his natural 

 voice is unteachable : my own experience confirms 

 this. Some pupils put on a lecture voice, in which 

 they answer questions put to them. I do not caU 

 this speaking. It is unnatural and artificial, and 

 is a serious bar to progress. It arises from timid- 

 ity, fear of the teacher, or fear of the rest of the 

 class ; and the latter is far more difficult to be got 

 rid of than the former. 



'* Moreover, a pupil must have a sufficient com- 

 mand of language to be able to frame a complete 

 sentence. I have heard of teachers who are satis- 



