studies in Arithmetic, 1916-1917 



31 



of the lines for the Best Five Cities is not so evident in the 

 lines for the entire state. At seven of the possible eight 

 points where the lines of achievement for speed in Figures 5 

 to 8 cross the vertical grades lines, these lines of achievement 



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FIG. 7, Showing Median Scores of Best Five Cities in Compari- 

 son WITH Indiana, Iowa, and Kansas Median Scores. Multiplication. 



FIG. 8. Showing Median Scores of Best Five Cities in Compari- 

 son with Indiana, Iowa, and Kansas Median Scores. Division. 



refract downward, whereas the same lines in Figures 1 to 4 

 refract downward at only six of the twelve possible points, 

 and at three of these the lines are practically straight. In 

 the lines for rights the same distinction holds. Do these facts 

 mean that growth from grade to grade in the systems that 

 rank highest is the least consistent and the most irregular? 



