Marcu ‘14, 1912] 
dom now allowed to them, partly no doubt because 
of their long discipline under fixed syllabuses, probably 
partly also because in their work (chiefly arithmetic) 
there exists mo association like the public-spirited 
Mathematical Association, which has contributed so 
greatly to the solution of the problem of courses of 
mathematics in secondary schools. 
However, there is progress. Ten years ago, in 
answer to the simplest question not introduced by one 
of the mystic words, ‘‘multiply,’’ “‘add,’’ &c., pupils 
would reply, ‘‘I don’t know what rule it belongs to.” 
Or they would determine how long Mr. Gladstone 
lived by multiplying together the years of his birth 
and death. The two papers now under review show 
a great advance on that time. And if stocks and 
shares are still too much in evidence, and the por- 
tions of geometry and algebra selected for addition 
to the curriculum leave something to be desired, there 
is yet evidence of a great ferment, from which sooner 
or later good must come. In particular the new 
Central Schools are full of promise. 
The fifth pamphlet of the series, ‘‘The Algebra 
Syllabus in the Secondary School,” is a statesmanlike 
discussion by Mr. Godfrey of the reforms which are 
at present most urgent in school mathematics. The 
present ferment in education is acting not only on 
mathematical masters, but on all other masters, head- 
masters included. The number of subjects claiming 
recognition in the school is so great that all cannot 
be successful in their claims. The inquiry is made 
with regard to every subject, whether, by reason of 
its value for knowledge, training, or discipline, it 
deserves a place in the curriculum or no. Difficult 
as it is for the mathematician to believe, it is the fact 
that, so far as concerns non-mathematical boys, the 
verdict is in danger of going against algebra as at 
present taught. Many public schools would like 
to curtail seriously the time given to mathematics. 
Something is wrong when headmasters of position 
and judgment look back on their mathematical train- 
ing as the “transient but blighting shadow of x+ 
y. And those who believe in the value of a mathe- 
matical training for all boys must give earnest con- 
sideration to the remedy advocated by Mr. Godfrey, 
a remedy which is already applied in some schools. 
Algebra as at present taught is so abstract as to 
be incomprehensible to the majority of boys. It in- 
cludes also many portions which lead nowhere in par- 
ticular, and have no exceptional value as mental 
discipline. Mr. Godfrey reviews the customary 
algebra course, and shows severe pruning to be pos- 
sible and desirable. The time saved by this pruning 
it is proposed to utilise in giving a useful and educa- 
tional acquaintance with numerical trigonometry, 
mechanics on an experimental basis, and the ideas of 
the infinitesimal calculus. On the calculus Mr. God- 
frey’s proposals may be usefully studied along with 
the first pamphlet of this series. 
A paper on “The Correlation of Elementary Prac- 
tical Geometry and Geography”’ (6) is appropriately 
included in the series. Geography supplies many 
illustrations and problems for the use of the mathe- 
matical master. In return, when the geography 
master discusses maps and plans and their making, 
he finds as a result of the work of his mathematical 
cae a readier comprehension on the part of his 
pupils. 
Mr. Eggar’s views on “The Teaching of Elemen- 
tary Mechanics” (7) are shared by the _ best 
masters. That they are not more generally put into 
practice is mainly due to the backwardness of most 
examining bodies to recognise their merit. It is also 
partly due to the want of faith of the teacher, for a 
preliminary or concurrent practical course undoubtedly 
gives a better grasp, and fits a boy better than the 
NO. 2211, VOL. 89] 
NATURE 
45 
old plan, even for the oldest-fashioned theoretical 
examination in mechanics. The value of a practical 
course is placed beyond doubt when the two asso- 
ciations, which represent science and mathematical 
masters respectively, unite in so strong a recom- 
mendation as is contained in the report quoted by 
Mr. Eggar. 
Many words of wisdom are scattered through the 
paper. One valuable aspiration is that in the future 
mathematics and physics will be in the hands of one 
master. For the teaching of mechanics this has the 
merit of more complete correlation between the prac- 
tical and theoretical courses. For the mathematical 
master a knowledge of physics will give a breadth 
of understanding which is not always found at the 
present day. 
For details of the course Mr. Eggar’s paper must 
be consulted. We will only say here that he wisely 
follows the historical order in beginning with statics. 
(8) ‘Geometry for Engineers” is less pleasing than 
the preceding ones. The elaboration of the proposed 
treatment of conic sections, and (to a less extent) the 
time it is proposed to devote to synthetic geometry, 
would appear to necessitate the postponement to a 
very late stage of subjects so essential to an engineer 
as mechanics and the infinitesimal calculus. On the 
other hand, one sympathises with the author’s view 
of the importance of descriptive geometry, both on 
account of its direct usefulness and on account of 
the mental training involved in thinking in three 
dimensions. * 
(9) ‘‘ Mathematics in Secondary Schools for Girls.”’ 
Miss Story’s pupils are fortunate in having a mistress 
so well able to distinguish the gold from the dross. 
While selection of material is very desirable for boys, 
it is all-essential for girls. After half a century of 
attempts to fashion girls’ education on the lines fixed 
by tradition for boys, the country is now realising that 
it wants to have its girls made into good women and 
not into inferior men. : 
(10) ‘‘ Examinations from the School Point of View ” 
opens with the sound doctrine that qualifying and 
competitive examinations should be kept distinct, the 
former being intended to determine which pupils have 
attained a certain standard, the latter to pick out a 
certain number of the best. The union of the two 
tests in a single examination makes the questions too 
difficult to be a fair test of a moderate general educa- 
tion. On a given range of work fairly complete 
answers to easy questions are better evidence of 
ability and knowledge than fragmentary answers to 
difficult questions. : 
The author’s next proposition is more difficult of 
acceptance: that in a matriculation examination 70 
or 80 per cent. of the candidates should be passed. 
The object of such an examination being to test fit- 
ness to study at a university, the examiners are surely 
already generous in deciding that 50 per cent. possess 
that fitness. 
Objection to the technical bent of the Army Entrance 
Examination is possible only in a country which plays 
at keeping an army. In France and Germany the 
army is a highly technical profession, and the school 
education carefully arranged on that understanding. 
With the author’s statement that better ability cannot 
be secured by stiffening the examination we entirely 
agree; the remedy lies elsewhere. : 
In (11) Miss Stephens describes an interesting ex- 
periment on the ‘‘ Teaching of Mathematics to Young 
Children.” The excellent method of the ten-bundle 
and the hundred-bundle will no doubt lead up to the 
roo-times table, the 1000-times table, &c., which are 
more valuable than the 11- and 12-times tables. 
Davin BeveripcE Mair. 
