Reliability of Diagnosis of Certain Types of Errors in Long Division with a One-Figure Divisor

It is generally known that many errors which a pupil makes in dealing with the fundamental operations are due to chance. When an error of combination is due to chance, the correct response will occur at least as often as the in correct response. However, when a com bination occurs two or more times in a test and each response to the fact is in correct, the error is said to be constant. This study was made to determine if cer tain types of errors made in long divi sion were due to chance or if they were caused by a faulty knowledge of the com binations. In the latter case the error should be constant. A test was given in Grades V-XV, inclusive, (Grades XIII, XIV, and XV were in normal school) to determine if the long or the short form of division is better when the divisor Is a one-figure number. There were approximately 200 stu dents tested in each of the eleven grades sampled. About an equal number used the short and the long-division form. The re sults showed conclusively that the long division form was superior to the short form.l Then, a study was made of the types of errors2 which a pupil made when he divided in the long form with a one figure divisor. These errors were grouped under six different classifications. The classification which had the greatest frequency of errors was known as errors of combinations. These included errors of combinations in division, multiplica tion, and subtraction. The errors were made when the subjects used in the expe riment on short and long division solved the examples which follow*