224 INTERNATIONAL CONGRESS OF EDUCATION. 
Epwirp G. Hower, of Chicago: T have come here to learn and not to speak. But 
there is one thought that has come to me since these programmes were announced, and 
that is, as Professor Hailmann has said, we must consider what has gone before and what 
is to come after. The first thing the child is taught is arithmetic. He gets overwhelm- 
ing numbers ; he finds how difficult they are to handle, and he wants some shorter 
method to handle those great numbers. It seems to me that algebra should precede 
ceometry. Still I know so well, and was very glad to hear Herbert Spencer’s book 
mentioned, that inventional method in geometry can be given very early. How much it 
should precede algebra I don’t know. But let us not give these studies until we have 
brought our children where the study shall have a use. 
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Tar CralrMAN : I will say, in my own school inventional geometry has been repeat- 
odly taught before taking algebra. I think we should all be glad to know if there is 
any one here who has ever attempted to teach logical—that is, Huclidian—geometry 
sefore taking up the algebra ; it would be a matter of considerable interest to us all. 
" have never heard of it in this country. 
W. H. BarrHoLoMEW, of Louisville, Ky.: I have a certain conception in my own 
mind, as I Wnderstand it, of where there is a strong line of demarcation between the 
secondary school and the grammar school. In other words, there is not anything in the 
secondary school that ought to be in the grammar school. The grammar school has its 
function, and the secondary school has its function. The grammar school is to prepare 
tor the secondary school.” Now, with this in view, I am decidedly of the opinion, 
though I say that very cautiously, that there must be a certain preparation in the ele- 
mentary schools, and this must be decided in some way or other before the student 
anters upon the work of the secondary school. Now, this question arises as this discus- 
sion has been mapped out for us : Which ought to precede the other ? We have been 
oxperimenting in our school somewhat along this line, and we have reached about this 
conclusion : that what is known as elementary work—that part which lies very directly 
with the study of arithmetic—should follow that first in order. And then, following 
‘hat, comes plane geometry, and then the higher forms of algebra ; and, following that, 
analytical forms of geometry. I know the former plan was to take algebra for two 
years, and then geometry. But this failed to satisfy ; and with the experience we had 
last vear. we find it is more satisfactory to carrv these studies along together. 
W. B. Poynter, of Shelbyville, Ky. : I hope the gentleman who opened this discus- 
don will not misunderstand me when I say I didn’t understand anything he said. I 
ret at questions from the practical side entirely, and then at the theories afterward. 
[ liked him. But as to which subject should be taught first in the schools, I want to say 
‘rom my own experience I have adhered to the old plan of letting algebra follow arith- 
metic—two years for algebra, and one for geometry. Never having tried any other, I 
sould not say that is the better way. But my judgment is entirely on that side. After 
\lgebra, naturally following where arithmetic leaves off, and reviewing the principles of 
writhmetic, you are gradually developing the mind of the pupil. That is what we are 
Wfter. All we want to do is to get pupils to think ; then have algebra come in between 
\rithmetic and geometry, giving the mind a little more strength when it comes to geom- 
trv. the great logical study of the preparatory school. 
Dr. Hammany : You will permit me, perhaps, to say an additional word with refer- 
sce to a view of the subject which the gentleman who has just spoken takes. Of course, 
'n the view he takes, I presume he is right. In the view I have taken of that subject, 
paving for geometry an entirely different aim—in that view he wouldn’t be right. 
ProFESSOR WILLIAM KE. Story, of Clark University, Worcester, Mass.: I should like 
to emphasize the importance of beginning algebra as early as possible. Algebra is not 
a subject of itself ; it is arithmetic, and should be taken up as a part of arithmetic, as 
soon as the child knows enough about the fundamental principle of numbers to under- 
stand what algebraic symbols mean. Where it is taken up in the course of arithmetie, 
with the same problems, it could be treated by the so-called arithmetical algebraical 
process. 
JouN B. Patrick, Superintendent of Patrick Military Institute, Anderson, S. C.: Mr. 
President and Fellow- Teachers—In my earlier days I taught a school where the curricu- 
lum was regulated by State authorities. There it was a rule to complete arithmetic ; 
‘hen aloebra was taken and completed, and then geometry was taken and completed. 
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