308 EEPORTS ON THE STATE OF SCIENCE. — 1916. 



requirements from children of particular ages. In regard to most 

 attainments such determinations present problems of gi-eat complexity. 

 Individual children vary greatly in their powers and in the circum- 

 stances of their out-of-school lives. So far as it is the outcome of 

 experience, knowledge can hardly be measured; and there is by no 

 means a general agreement about what ought to be taught to children 

 of eight or to children of eleven. In the case of the fundamental instru- 

 ments of social intercourse the problem is simpler. The mastery of 

 these is generally expected as a result of school training; progress in 

 these is more or less steady throughout the school career. Arithmetic, 

 reading, spelUng, and writing provide instances. Arithmetical skill 

 is largely dependent upon the rapid and accurate use of the funda- 

 mental processes — addition, subtraction, multiplication, and division — 

 which function best when they have reached the level of mechanical 

 habit. In reading and writing mechanical habit again plays a chief 

 part in their e,fficient use. But these subjects are psychologically more 

 complex; and it is disputable whether any real value can come from 

 isolating the ' habitual ' elements and attempting to measure progress 

 in the development of mere mechanism. In the case of the arith- 

 metical habits, no such disadvantage arises. Accordingly, the Com- 

 mittee has restricted its inquiries to the four ' fundamental rules ' of 

 arithmetic — addition, subtraction, multiplication, and division. 



General Principles. 



In constructing test-sheets for each kind of process a definite, written 

 scheme has been followed. Consequently, for the same kind of test it 

 is possible to construct any number of test-sheets of approximately 

 equal difficulty. 



As far as possible, all the available figures and combinations of 

 figures in pairs are used with equal frequency. The tests are so con- 

 structed that any child, after working through the first quarter (or in 

 some tests, half) of the paper, has worked through all possible pairs 

 of numbers (up to 9) once each. And, as far as possible, the pairs are 

 scattered over the paper by pure chance. Every other column for 

 addition sums involves 'carrying.' Similarly, half the pairs for sub- 

 traction involve ' borrowing. ' No ' remainders ' are involved in the 

 division sums. To facilitate computation of marks the sums were 

 printed in rows of five or ten. One mark was awarded for each correct 

 operation, — each column correctly added, each pair of figures correctlj' 

 subtracted, multiplied, or divided. 



The children worked the sums upon sheets already printed. The 

 tests were set, timed and marked by the investigators themselves or 

 under their immediate superintendence. 



London Schools. 



Four elementary schools were chosen : the boys' department of an 

 ordinary school attended by children in a ' good ' neighbourhood ; the 

 girls' department of an ordinary school in a 'poor' neighbourhood; 



