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An Objective Study of Mathematical Intelligence 
marking based on an analysis of the intellectual processes involved in the answering 
of the questions as far as they could be detected by introspection ; according to 
this system, the maximum mark for any one process in any one answer was 10. 
(For samples of questions, analyses, and actual marks, see Appendices I. and III.) 
It was decided that the number of boys examined was not large enough to 
sustain a mathematical superstructure built on so detailed an analysis. The 
analyses were therefore subsumed under nine principal headings, viz., A, B, C, D, E, 
F, G, H, I, distributed as follows : — 
Geometry, 
A. Memory of definitions and general principles (e.g. principle of superposition) 
in Geometry. 
[1 (iii) + 3 (iii) + 5 (i) + 6 (i) + 8 (i) + 9 (i)] *. 
B. Memory of constructions in Geometry. 
[2(i) + 3(ii) + 4(i) + 5(iii) + 9(ii)]. 
C. Memory of preceding propositions, and power of applying them. Geometry. 
[1 (ii) + 2 (iii) + 3 (i) + 4 (iii + v) + 5 (ii + iv + vi) + 6 (ii) + 7 (i + iv) + 8 (ii + iii)]. 
D. Recognition of necessity of generality in proof, and power of recognizing 
general relations in a particular case. Geometry. 
[1 (i + iv) + 3 (iv) + 4 (iv + vi) + 5 (v) + 6 (iii) + 8 (iv)]. 
Arithmetic. 
E. Accuracy in Arithmetic. 
[1 (ii) + 2 (iii) + 3 (iv) + 4 (iii) + 5 (iv) + 6 (ii) + 7 (ii) + 8 (iii) + 9 (ii) + 10 (iv) 
+ 11 (ii)+ 12(iii)+13(ii)]. 
F. General memory of rules and power of applying them. Arithmetic. 
[1 (i) + 2 (i + ii) + 3 (ii) + 4 (i + ii) + 6 (i) + 8 (i + ii) + 10 (i + iii) + 11 (i) + 12 (i + ii) 
+ 13(i)]. 
G. Power of doing sums in percentage and proportion. Arithmetic. 
[7 (i) + 9(i) + 12(i + ii)]. 
Algebra. 
H. Accuracy in Algebra. 
[1 (iii) + 2 (iii) + 3 (ii) + 4 (iv) + 5 (ii) + 6 (iii) + 7 (iv) + 8 (iii) + 9 (ii) + 10 (iii)]. 
I. General memory of rules and power of applying them. Algebra. 
[1 (i + ii) + 2 (ii) + 3 (i) + 4 (ii + iii) + .5 (i) + 6 (ii) + 7 (i + ii + iii) + 8 (i)]. 
* See Appendix I for meaning of these numbers. 
