Haggerty: Studies in Arithmetic 



99 



test and were better able to use all of their ability in making a 

 good showing. By examining Table IV it is seen that the pupils 

 of all grades and in all kinds of work almost without exception 

 made a greater gain in the second series of tests over their previous 

 work than they were able to make on the third series over the 

 second. This was on account of the condition just mentioned. 



The proper way to arrive at a proper answer to this problem 

 would be to give a class three sets of tests without drill at any time 

 and see what growth was shown between the second and third 

 tests. A little light, perhaps, is thrown on this by Table IV, 

 where we find that during the second six weeks while the grade 7 

 pupils were practicing on reasoning exclusively they made a gain 

 of 4.66 per cent on fundamentals, while during the same period 

 when grade 8 pupils were practicing on fundamentals they seemed 

 to have made no growth at all in reasoning. 



Comparative Progress with Drill and without. — Table VI gives 

 an unequivocal answer to the question as to whether drill is worth 

 while. The smallest difference in averages was shown in funda- 

 mentals where the fifth and sixth grades, who had drill during the 

 first six weeks, were able to excel themselves by only 4.356 per 

 cent more than the seventh and eighth grade pupils who were 

 being given no drill. In all other cases the gain is large. In reason- 

 ing where correct answers only are considered, the difference in 

 gain in favor of those groups that took regular drill is 32.7 per 

 cent. Evidently it pays to give regular drill work in arithmetic. 



TABLE VI.— COMPARATIVE PROGRESS WITH AND WITHOUT 

 DRILL. FIGURES BASED ON GAINS MADE IN SECOND 

 TEST OVER FIRST 





Grades 5, 6 



Grades 7, 8 



Difference 

 in favor of 

 Drill 



Drill 



No drill 



All tests, attempts and rights (see Table I) 



33.3 



16.2 



17. 1 



Fundamentals 



15.6 



11.3 



4.4 



Reasoning, attempts and rights 



58.0 



25. 1 



32.9 



Reasoning, rights only 



68.1 



35.4 



32.7 



Comparison of Progress with Drill on Fundamentals and Pro- 

 gress with Drill on Reasoning. — From Table VII it seems that about 

 the same progress was made by the two groups, the group that 

 had a drill daily in fundamentals and the group that had the 



