April 17, 1914] 



SCIENCE 



579 



death or get drowned or killed right away or a 

 little later on. 



That he underwent great inconveniences 

 and sufferings goes without saying. Such a 

 trip can not he made in a tropical country 

 without them; but it is questionable whether 

 readers should be bothered with his mosqui- 

 toes, his ants, his cattle ticks, and his run- 

 away mules. 



The photographs are the one redeeming 

 feature of the book. J. C. Branner 



A Text-hooh on the Teaching of Arithmetic. 

 By A. W. Stamper. New York, American 

 Book Co. Pp. 1 + 284, including bibli- 

 ography and index. 



This book is a real contribution to pedagogy, 

 for although its author disavows novelty in 

 theory and completeness in scope, he has come 

 nearer to writing a text-book in the teaching 

 of arithmetic for beginners than has any other 

 writer. It differs from the other excellent 

 works on the same subject, such as those listed 

 in the author's bibliography, in that it gives 

 more space to instruction in the details of 

 method and in class-room practise than to in- 

 spirational matter. It summarizes and applies 

 the results of pedagogical research instead of 

 dwelling upon their origin. In comparison 

 with other books on the teaching of arithmetic, 

 it is a manual of method rather than a refer- 

 ence book for the teacher's professional library. 

 As to its fitness for this purpose, it covers 

 well the courses in the teaching of arithmetic 

 given in our better normal schools. It is a 

 well-rounded and well-balanced treatment of 

 school. It is in general accurate as to fact, 

 and sound in doctrine. The author has prof- 

 ited by his labors at Teachers College, Colum- 

 bia University, particularly by his access to 

 the great collection of original arithmetical 

 works gathered there. These sources, supple- 

 mented by the accurate digests and classifica- 

 tions, and the collections of related mathe- 

 matical apparatus, constitute the most sig- 

 nificant assemblage of historical material on 

 the subject of arithmetic to be found any- 

 where in the world. 



But with all this the book is a chart of the 



beaten path. It will serve to help the laggards 

 rather than to blaze a new trail. To some the 

 book will seem to be written wrong end to. 

 As it stands the order of discussion is : Origin 

 (Chap. I.), Logic (Chap. II.), Subject Matter 

 (Chaps. III.-VI.), Method (Chaps. VIII.-X.), 

 Purpose (Chap. XI.). But among these topics 

 why should not the last be first? The author 

 makes aim or purpose the first consideration 

 in his typical method lessons, and states (pp. 

 248-249) the controlling aim in the teaching 

 of arithmetic. If the discussion of the selec- 

 tion, presentation and study of subject matter 

 had been controlled from the start by the real 

 purpose, it would not have greatly modified the 

 conclusions of this volume. But it would have 

 thrown a flood of light on why we are told to 

 teach or not to teach certain things, and why 

 we are told to teach in a prescribed way. The 

 subject, if approached from this stand-point, 

 would necessitate discussing, to a greater ex- 

 tent than the author does, the attitude of the 

 pupil, who, after all, is the first consideration, 

 the chief beneficiary and the sole legatee in the 

 teaching of arithmetic. 



The following more specific references may 

 be of value : Pp. 9-18 : A pragmatic treatment 

 such as indicated above would relegate these 

 meager nine pages of history to subordinate 

 notes under related topics in later chapters. 

 P. 18, questions 5 and 6, are of little value. 

 P. 20 : The worhing definitions explained at the 

 bottom of the page should be emphasized as 

 the kind of most value in arithmetic. P. 29 : 

 It would help the teacher, if the author had 

 admitted that counting is measuring in the 

 broadest sense. P. 30 : the last paragraph 

 could be strengthened thus : To the statement, 

 " The multiplicand and the product being con- 

 crete," add " and of the same kind." Also to 

 the statement, " The dividend is always con- 

 crete," should be added, " if either of the other 

 terms are." P. 43: Young teachers may be 

 led to overvalue work in artificial scales. P. 

 44 : The expression, " When the first nine," 

 would better be " when the column at the left." 

 P. 51 : The teaching of casting out nines is of 

 doubtful value as a pratical check required in 

 the universal course of study. P. 58 : Ke- 



