406 SECTIONAL TRANSACTIONS.— L. 



(a) Miss F. Sater. — Group Work in Infants' Schools. 



(b) Miss C. T. CuMBERBiRCH. — The Dalton Plan. 



1. The recent tendency towards group and individual work in upper classes 

 in Elementary and Secondary Schools and in Training Colleges (leading on from 

 Miss Saj-er's paper) — seen in many directions and with varying aim — from 

 silent reading to simple research. 



2. Its concentration and development in the Self-Teaching Dalton Plan. A 

 terse survey of the Plan, giving its broad aims. 



3. The Plan — or modification — in local use. The work in four or five 

 schools and colleges, under conditions varying as to : Specialist teachers ; 

 specialist rooms ; allocation of free time ; nature of assigrunent, of graph, and 

 of test used. These points to be summarised. 



4. Summary of the opinions of the head teachers and teachers on the 

 development of the children and students in different subjects. 



5. Discussion raised on several debatable points : The effect of the Plan on 

 esprit de corps; the place and value in all teaching of : the class lesson, the 

 teacher's personality ; the difficulties met with in : (i) equipment, (ii) varying 

 standards of work in children; (iii) the transition from !Montessori to Dalton 

 schemes. 



6. Permanent value of the Plan ethically and intellectually. 



10. Joint Discussion with Section G on The Effect of Reformed 

 Methods in Teaching Mathematics. 



(a) Prof. T. P. NuNX. — The Principles of Formal Geometry. 

 The question whether there should be a return to a standard sequence of 



theorems in elementary geometry is of less importance than the question whether 

 the traditional basis of formal geometry should be retained. Euclid's system 

 (apart from the preliminary doctrine of points, lines, and planes) rests upon 

 two assumptions about the nature of space : (i) that it admits of congruent 

 figures; (ii) that it permits one and only one line to be drawn through a given 

 point parallel to a given line. There are strong reasons for, adopting, instead of 

 the latter, the assumption (ii) that space admits of similar figures. leaving the 

 properties of parallel lines to be deduced therefrom instead of deducing the 

 existence and properties of similar figures from the postulate of parallel lines. 



(b) Mr. E. C. Fawdry. — The Practical Result of the Reform. 

 The reforms in mathematical teaching originated in a revolt against Euclid, 



followed by the demand from Technical Colleges that the mathematical equip- 

 ment of the ever-increasing body of students should be wider in range and 

 more practical in character. 



The result was a reconsideration of the purport of mathematics as part of a 

 general education. The slow progress of the majority was due to a course 

 framed in the interests of specialists. The postponement of the more academic 

 portions has allowed the early introduction of trigonometry and mechanics, 

 and has enabled many to acquire a working knowledge of the calculus before 

 leaving school. 



Less emphasis is now laid upon bookwork ; the examples are of a more 

 interesting type and practical work has been introduced. The adoption of 

 the newer methods is still far from universal. The older teachers and some 

 Universities are still conservative, but progress is helped by the attitude of 

 the Board of Education, the Civil Service Commissioners, and the holiday 

 courses for teachers. 



(c) Prof. M. J. M. Hill. — Euclid's Exposition of the Theory of 



Proportion in the Vth Booh. 

 Euclid's Vth book has fallen into disuse not only in schools but also in 

 Universities : this is nrobably due t/O the inversion of the natural order of ideas, 

 to the omission of all explanation of the manner in which the fifth and seventh 

 definitions were originally obtained, and to the unnecessary use of the properties 

 of unequal ratios to prove properties of equal ratios. Although the book seems 

 to be unsuited for school use. it is probable that if the idea of proportion be 

 introduced from first principles the contents of the book would be of great 

 value to University students commencing the serious study of the calculus. 



