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Indiana University Studies 



who spend 65,000 minutes and achieve seventh place while similar 

 children spend not to exceed 55,000 minutes and achieve second 

 place, and still other children spend less than 50,000 minutes and 

 rank sixth? 



Taking these tables as a basis we can give a definite statement 

 as to how much time it is worth while to spend on arithmetic and 

 expect good results. Inasmuch as the ranking method often gives 

 first place on a very narrow margin, it is better to determine opti- 

 mal times by the inclusion of the first two ranks. This enables 

 us to give a minimum and a maximum for each grade. Following 

 this method we can make Table XLIX. 



TABLE XLIX 



Optimal Time to be Devoted to Study of Arithmetic from Beginning to 

 End of Several Grades as Determined by Ranks 1 to 2 of Reported 

 Schools. 



Grade 



Minimum 

 Time in 

 Minutes 



Maximum 

 Time in 

 Minutes 



Fifth 



30,000 

 40,000 

 45,000 

 50,000 



45,000 

 55,000 

 60,000 

 75,000 



Sixth 



Seventh 



Eighth 





Tables L and LI dealing with variabilities show essentially the 

 same thing as do the tables of medians, namely, that excellence in 

 the fundamentals of arithmetic as measured by these tests is not a 

 necessary correlative of long time spent on the subject. It more 

 often accompanies a time shorter than the maximum used by some 

 schools. We could, as in the case of the medians, make a table 

 showing optimal time for each grade. It would be essentially the 

 same table excepting a slight reduction in the seventh grade maxi- 

 mum. We may say, therefore, that Table XLIX represents the 

 optimal time for the study of arithmetic as shown both by the 

 median scores and per cent of variability. 



If one turns to the dependability the results are not particularly 

 different. One variation in grade 6 shows the pupils spending 

 maximum time to be second. The margin of superiority is so slight^ 

 however, as to be negligible. Tables LII and LIII therefore con- 

 firm the figures of Table XLIX. 



