892 REPORT—1885. 
no doubt that the remedy he suggests would be effectual. In the higher teaching, 
which interests me most, I have to complain of the utter neglect of the all-important 
notion of algebraic form. I found, when I first tried to teach University students 
co-ordinate geometry, that I had to go back and teach them algebra over again, 
The fundamental idea of an integral function of a certain degree, having a cer- 
tain form and so many coefficients, was to them as much an unknown quantity 
as the proverbial 2. I found that their notion of higher algebra was the solution 
of harder and harder equations. The curious thing is that many examination 
candidates, who show great facility in reducing exceptional equations to quadratics, 
appear not to have the remotest idea beforehand of the number of solutions to be 
expected; and that they will very often produce for you by some fallacious 
mechanical process a solution which is none at all. In short, the logic of the 
subject, which, both educationally and scientifically speaking, is the most important 
part of it, is wholly neglected. The whole training consists in example grinding, 
What should have been merely the help to attain the end has become the end 
itself. The result is that aleebra, as we teach it, is neither an art nor a science, 
but an ill-digested farrago of rules, whose object is the solution of examination 
problems. 
The history of this matter of problems, as they are called, illustrates in a 
singularly instructive way the weak point of our English system of education. 
They originated, I fancy, in the Cambridge Mathematical Tripos Examination, as 
a reaction against the abuses of cramming bookwork, and they have spread into 
almost every branch of science teaching—witness test-tubing in chemistry. At 
first they may have been a good thing; at all events the tradition at Cambridge 
was strong in my day, that he that could work the most problems in three or two 
and a half hours was the ablest man, and, be he ever so ignorant of his subject in 
its width and breadth, could afford to despise those less gifted with this particular 
kind of superficial sharpness. But, in the end, it came all to the same: we were 
prepared for problem-working in exactly the same way as for bookwork. We 
were directed to work through old problem papers, and study the style and 
peculiarities of the day and of the examiner. ‘The day and the examiner had, in 
truth, much to do with it, and fashion reigned in problems as in everything else. 
The only difference I could ever see between problems and bookwork was the 
greater predominance of the inspiriting element of luck in the former. This 
advantage was more than compensated for by the peculiarly disjointed and, 
from a truly scientific point of view, worthless nature of the training which was 
employed to cultivate this species of mental athletics. The result, so far as 
problems worked in examinations go, is, after all, very miserable, as the reiterated 
complaints of examiners show ; the effect on the examinee is a well-known enerva- 
tion of mind, an almost incurable superficiality, which might be called Problematic 
Paralysis—a disease which unfits a man to follow an argument extending beyond 
the length of a printed octavo page. Another lamentable feature of the matter is 
that an enormous amount of valuable time is yearly wasted in this country in the 
production of these scientific trifles. Against the occasional working and pro- 
pounding of problems as an aid to the comprehension of a subject, and to the 
-starting of a new idea, no one objects, and it has always been noted as a 
praiseworthy feature of English methods, but the abuse to which it has run is 
most pernicious. 
All men practically engaged in teaching who have learned enough, in spite 
of the defects of their own early training, to enable them to take a broad view of 
the matter, are agreed as to the canker which turns everything that is good in our 
educational practice to evil. It is the absurd prominence of written competitive 
examinations that works all this mischief. The end of all education nowadays is 
to fit the pupil to be examined; the end of every examination not to be an 
educational instrument, but to be an examination which a creditable number of 
men, however badly taught, shall pass. We reap, but we omit to sow. Con- 
sequently our examinations, to be what is called fair—that is, beyond criticism in 
the newspapers—must contain nothing that is not to be found in the most miserable 
text-book that any one can cite bearing on the subject. One of my students, for 
