706 TRANSACTIONS OF SECTION L. 
years. The intermediate curriculum includes seven subjects; English, history, 
geography, mathematics (including arithmetic), at least one language other than 
English, science, and drawing. ‘The post-intermediate includes at least four 
subjects, three of which must be English (including history), one language other 
than English, and mathematics or science. The intermediate certificate crowns 
the one course and the leaving-certificate the other. The award depends upon a 
written examination, a class oral examination, and the teacher’s opinion. ‘The 
papers are set on two standards, and excellence in one subject may compensate 
for deficiency in another. 
The intermediate certificate indicates the satisfactory completion of a well- 
balanced course of general education, suitable for those who leave school at the 
age of fifteen or sixteen. It also acts as a passport to certain technical institu- 
tions and continuation schools. The standard of examination practically pre- 
cludes the study of more than two foreign languages in the course. 
Leaving-certificate courses may be classified as general, linguistic, mathe- 
matical, scientific, artistic, or musical. There is no difficulty in selecting a group 
of subjects which meets the entrance requirements of the universities. 
3. Discussion on the Present Position of Mathematical Teaching. 
(i) The Reform of ihe Teaching of Trigonometry. 
By T. Percy Nunn, D.Sc. 
Few systematic attempts have been made to reform school trigonometry in the 
spirit of Professor Perry’s teaching. Yet in no branch is it easier to present 
mathematical truths as instruments of investigation and ‘intellectual control.’ 
What is chiefly needed is a complete departure from the traditional curriculum 
and method. To begin with, trigonometry should no longer be regarded as a 
separate ‘ subject,’ but should be incorporated in algebra. The inevitable effect 
of making it a distinct branch has been an over-elaboration of its formal side. 
This, in turn, has made it an ‘advanced’ subject, accessible only to specialists. 
There is no logical or pedagogical justification for this procedure. All boys and 
girls should study the sine and the tangent just as they study the square root or 
the cube—namely, as a means of appreciating the quantitative side of certain 
matters of wide human interest. The author has experimented with a programme 
of topics under the following heads: (1) surveying problems; (2) navigation 
problems; (3) map projections; (4) the analysis of wave-motions and other 
periodicities. The method is concrete and practical throughout and ignores the 
academic distinction between plane and spherical trigonometry. 
(ii) The Present Position of Mathematical Teaching. 
By P. Priyxerton, D.Sc. 
We are beginning to learn that current ideas regarding the teaching of 
mathematics are very like current ideas in other provinces, and that the move- 
ment towards reform is an index of the spirit of the times. It is fairly safe to 
say that mathematics used to be regarded by many as consisting of a body of 
sound doctrines logically articulated and appealing only to minds specially fitted 
to receive them. Literature, on the other hand, was supposed to be more human, 
more adapted to the tastes and capacities of the many. One of the results of 
looking closely into these matters, without subservience to tradition, is the con- 
clusion that a genuine appreciation of lancuage and literature is just as rare as 
a genuine appreciation of mathematics, and that the aims and ends of teaching 
are in both cases very much alike. 
A good though simple poem, such as Wordsworth’s ‘ Daffodils,’ serves to 
illustrate the various stages in the growth of ideas just as much as a good piece 
of elementary mathematics. The first verse describes a scene, the second the 
beauty of the scene; in the third the mind is attracted and interested; and in 
the fourth the scene is treasured ‘in the mind’s eye.’ The equation 3z + 4y = 7 
displays a scene of related z’s and y’s; the beauty of the scene is revealed when 
