23 FEBRUARY 1929, Page 31

Arithmetic

THERE can rarely have been so entertaining or so instructive a book for teachers of arithmetic as Dr. P. B. Ballard's Teaching the Essentials of Arithmetic (University of London Press, lls.). The primary purpose of the book is to help in the class room. All the methods of teaching the subject are investigated and compared, and Dr. Ballard gives the results of his own researches. ,What is most unusual; however, is the spiritedness and the interest with which the author' approaches such apparently dry things as multiplidation or_ vulgar fractions. He shows a catching enthusiasm ; and almost every page is full of cheerfulness and wit..

It is a book therefore which we can earnestly recommend to all teachers. They will learn from it, not only how to interest their pupils, but also how to instruct them with the most economy and greatest certainty. It is a book, too, which would make an excellent present for any child who displays unusual alertness in mathematics.

Dr. Ballard has also prepared a , series of seven school books at prices from 10d. to ls. 4d. in paper, and ls. tc ls. 6d. in limp cloth, under the title of Fundamental Arith.. metic (University- of London Press).- The series carries a ' pupil from his multiplication tables to logarithms. Messrs. Bell- send us an Everyday Arithmetic in four books, copiously illustrated with diagrams and pictures, beginning with- problems in addition and ending with- fractions and graphs. The exercises are based on the full-page pictures of big stores, farmyards, playgrounds, docks and other such scenes. The same publishers send to A Practical School Algebra (4s. Gel.), by Mr. Clement V. Durell, a three-year elementary course, simply written, and illustrating, wherever possible, the practical applications of algebra.