Reliability of Diagnosis of Error in Multiplication of Fractions

In recent years, reports of comprehensive analyses of the errors made by pupils in various arithmetic processes have been made by Brueckner,1 Buswell,2 Morton,3 and others. The findings of these basic studies have suggested the necessity of extending the scope of the analysis of pupil errors to such questions as those related to the validity and reliability of the diagnosis made. In the earlier studies no attempt was made, for example, to determine the consistency with which a particular kind of error would appear in the pupil's work. Obviously, it is important to discover whether or not an error in procedure in solving a single example in a test is a chance error or one that will persist in other examples of a similar type. In an attempt to develop a method of studying the con sistency of error by pupils, the investigation herein reported was under taken. The procedure followed consisted in analyzing the errors made by fifth-grade pupils who had completed the subject on four examples of each of six of the forty different types included in the Brueckner Diag nostic Test4 in the multiplication of fractions. The six types used were as follows :