504 
It is still more important to note the value 
of mathematical training from the point of 
view of good citizenship. American lower 
schools devote much more time to mathe- 
matics and other sciences than the correspond- 
ing schools of Germany and the “ German pri- 
mary and secondary education is more in- 
tensely classical and literary than is British.” 
Mathematics has for centuries been most 
highly appreciated in France and it has been 
most thoroughly mastered in the French 
schools. The account which the French sol- 
diers have given of themselves during the 
world war is therefore the more inspiring to 
us as teachers of this wonderful subject. 
The mathematics teachers are the mothers 
of mathematical progress, while the investi- 
gators are its fathers. Our teachers’ organi- 
zations are thus a kind of mothers’ clubs 
where we are inclined to discuss chiefly mat- 
ters relating to the interests of those com- 
mitted to our care. The highest devotion im- 
plies however, more than self sacrifice. It 
‘implies also thoughtful and arduous prepara- 
tion. In fact, such preparation tends to make 
our tasks much easier and the things that we 
ean do easily are usually done most efficiently. 
Hard intellectual work should be done only 
privately. All such public service should be 
easy as a result of thorough preparation. 
My principal object is to inspire some of you 
to form a new resolution to strive to grow 
more rapidly along mathematical lines. The 
scientific development of teachers is not only 
a state and national question of paramount 
importance but it is also of international 
significance. At the outbreak of the world 
war its instigator Germany offered several 
prizes for essays relating to the best ways of 
using the facilities already at hand and of 
‘providing additional facilities for advancing 
the interests of those engaged in teaching.? 
The glorious intellectual advances made by 
American secondary teachers during the last 
2W. J. Pope, ‘‘Science and the Nation,’’ 1917, 
p. 3. 
8 Zeitschrift fir naturwissenschaftlichen Unter- 
recht, Vol. 45, 1914, p. 521. 
SCIENCE 
[N. S. Von. XLVIII. No. 1249 
two or three decades is reflected in the rapid 
transformations of our universities in favor 
of teachers. These transformations have been 
so rapid and extensive as to give us little time 
to reflect upon their bearing and may have 
advanced already beyond the danger point. 
The summer sessions and the summer quar- 
ters of our universities have grown rapidly in 
importance and influence. The universities 
are enlisting more and more their best talent 
for teachers during the summer terms instead 
of allowing their less progressive members to 
utilize them to increase their salaries. 
Secondary teachers can not be urged too 
strongly to attend these summer sessions when- 
ever they can do so without endangering their 
health. Teachers of mathematics in partic- 
ular should aim to take at least one or two 
courses in the department of pure mathe- 
matics, and should not devote themselves too 
closely to the study of the methods or the 
history of teaching. The main element of 
interest about mathematics is the subject itself 
and the more advanced subjects throw the 
clearest light on the more elementary parts. In 
fact, these advanced subjects are only the ele- 
mentary subjects grown to manhood and we 
understand the boy better after we have 
watched him develop into aman. Methods, on 
the contrary, are simply the outer garments of 
our subject and no amount of dress will make 
a skeleton attractive. 
A child once watched a robin bearing a 
worm to its nest filled with little ones stretch- 
ing out their necks and widely opened mouths 
in eager expectancy. The mother robin gave 
little heed to these gaping mouths, and, after 
resting a few seconds on the edge of her nest, 
swallowed the worm herself. The child was 
exasperated and called the mother robin a 
horrid old thing, but the father of the child 
directed attention to the fact that if the 
mother robin would not preserve her strength 
the helpless little robins would soon have no 
one to provide for them. 
This simple illustration may serve to em- 
. phasize the need of looking after our own in- 
tellectual sustenance and growth. The help 
