482 Indiana University Studies 



A. Time of Beginning Arithmetic 

 The questionnaire submitted on this topic was as follows : 



TIME OF BEGINNING STUDY OF ARITHMETIC 



City Reijorting 



ludicate the time when each class began the study of arithmetic. In 

 order that results may be uniform, consider a class as beginning aritlimetic 

 the term when tlie lirst arithmetic grades were given. If your records are 

 complete, this should be an easy matter. If i-ecords are at fault, estimate 

 as accurately as possible and place estimate after your mark. 



Eighth grade 



Seventh grade 



Sixth grade 



Fifth gradt' 



Each of the twenty cities returned the questionnaire complete. 

 As a result we have the school year when each class reported in 

 the tests began its arithmetic study in the school. This varies 

 from city to city and at times from grade to grade within the same 

 city. Thus one city reported that its eighth grade began arith- 

 metic in the first grade, but the fifth grade began in grade two. 

 We are able here to bring together the scores for all fifth grade 

 classes Avhich began their work in the first grade, for all who 

 began in the second grade, and for all who began in the third grade. 

 No city reported a class in any grade beginning as late as the 

 fourth grade. In Tables XLII to XLIV are gathered together all 

 the data resulting from this questionnaire. The first three hori- 

 zontal rows of figures of Table XLII are the medians. Reading 

 across the table : Fifth grade children beginning their work in 

 the first year of school, addition, attempts 6.9, rights 3 ; subtraction, 

 attempts 7.5, rights 5.3, etc. ; the total number of children included 

 being 492. The second and third rows are for children beginning 

 arithmetic in the second and third years of school respectively. 

 Then follow to the right similar data for sixth, seventh, and eighth 

 grades. 



Immediately below the medians are the ranks for the three 

 groups in the several points, and at the extreme right are the ranks 

 for each of the four grades and for the total of all grades. 



Similarly the variabilities and the ranks in variabilities follow 

 on the lower part of the table. 



If one judges by the tables of ranks it is clearly best for children 



