Haggerty: Study in Arithmetic 



497 



What now is the meaning of these optimal times? It is clearly 

 this: under some conditions it is possible to do a good quality of 

 work in the fundamentals of arithmetic within the limits of time 

 set in this table for the several grades. It means also that in 

 case a school with a lower score and using less time desires to 

 improve its work it can probably do so by increasing the amount 

 of time devoted to the subject. It means further that in the case 

 of a school which takes longer time without achieving higher rank 

 something is wrong ^dth the school regime. Either the children 

 are deficient in ability due to ancestry or environmental condi- 

 tions, or the methods of school work are faulty and need to be 

 changed. Doubtless the latter is the fact in many cases. 



What changes should be made are, to be sure, not indicated. 

 It is something to have discovered, however, that there is a limit 

 to the amount of deficient results that can be charged to the lack 

 of time. The "crowded program" will not excuse bad results ex- 

 cept when the time for a given subject is reduced below a certain 

 minimum. It is worth much that we are discovering in the use of 

 standard tests a means of determining what that minimum should 

 be. Once we have determined what is the optimal time for a given 

 subject, it is incumbent upon a teacher or superintendent to justify 

 his use of more time or his failure to get normal results within 

 the time specified. In either case he is wasting not only public 

 funds but also the tim,e of children. 



Objection may be taken that the time reported covers different 

 things in the case of different cities. Thus in one city much time 

 may be given to partial payments, cube root, etc., while in another 

 city the time is given more exclusively to fundamental processes. 

 The children from a school giving a small amount of time may 

 thus do better in this particular test than the pupils giving more 

 time, whereas if we could give a reasoning test the results might 

 be reversed. Such objection is valid, but two things may be said 

 in reply. First, to what extent can you justify the dissipation of 

 a pupil's time over a larger range of arithmetical subjects with the 

 consequent danger of achieving low ability in the fundamentals? 

 Second, these figures must be regarded as tentative and subject to 

 alteration by subsequently collected data. Until thus corrected, 

 however, they should stand as the best authenticated standard to 

 date. 



Two methods of supplementing these data suggest themselves 

 First, we should have similar data from many other school sys- 



8—3102 



