45S REPORTS ON THE STATE OF SCIENCE. 



much character there is in me and how very useful I am. But 1 cannot 

 understand from your descriptions how you have cut me out, although 

 I must admit that most of you have cut me out very cleverly. Did 

 you look at me long enough to know me ? I fear not. Although I look 

 so simple, I am not easy to make. 



' You say I have four sides, each 4 inches long. Following your 

 description, I have cut out a piece of paper with four sides, each 4 inclies 

 long, l)ut it has not my shape at all. On looking at it you will say, 

 I think, that my corners are all of the same size and tliat the corners of 

 the piece I have cut out are not square corners. I see this is so. But 

 how, then, are square corners to be made ? What is the difference 

 between square corners and those of the shape I ha\e made ? Look at 

 them well and try to tell me. 



' 5. I notice that some of you say not only that my sides are equal 

 but also that my angles are of the same size. AVhat are angles ? Are 

 they corners ? Everybody knows this latter word, but angle is not a 

 common word. It would have been kind if you had told me, when using 

 the word for the fii-st time, what it meant and where it came from. I 

 have looked in the dictionary, and find it is from the Latin word for a 

 corner — anr/ulus. Why do English people use Latin words ? Can you 

 tell me ? In future, if you can, when you use new words tell me wliat 

 they mean and what language they come from. 



' G. I notice that some of you not only call my corners angles l>ut 

 tiiat you speak of them as right angles. What does this mean 1 Are 

 other angles than mine wrong angles ? I must object to be called by 

 names I do not understand and which need so much explanation. It 

 will be much lietter at pi-esent for you to call corners such as mine square 

 corners. When you have found out how to draw my corners properly 

 wo will talk about other kinds of corners.' 



Hecormnendations. 



The following recommendations may be considered as supplementary 

 to those made by the British and Mathematical Associations, and re- 

 printed earlier in this report ; — 



1. It is essential that a knowledge of aritlimetic should be leased upon 

 exercises involving the manipulation and measurement of actual objects. 

 At eveiy stage practical work performed by pupils individually should 

 be considered as of far greater importance than complexity of calcula- 

 tion. 



2. (ireat attention should be given to fundamental principles and 

 any rules required should be generalisations from work done by tlio 

 pupils. No written calculations .should be required until pupils are able 

 to give mental or approximate answers to the sums set. Frequent oral 

 exercises are therefore necessary. 



3. Complicated calculations presenting purely artificial diffioultie.s 

 .should be avoided. There should be a general simplification of the rules 

 and exercises usually included in school arithmetic and more Avork witli 

 small numbers to illustrate arithmetical principles. Less attention should 

 be given to currency calculations and more to the study of arithmetic 

 experimentally, in order that pupils may learn by their own experience 

 and acquire intelligent ideas of dimensions by realistic work and 



