Transfer of Grades In the teaching profession one frequently encounters the situation where a student transfers between classes (or schools) or is taking a make-up exam. In many of these cases it is felt that the grades being transferred should be adjusted. Let us assume that the only factors which have influenced the previous grades of the student are the degree of difficulty of the exams given and the grading standards applied to them. In this case the grades of thestudent can be "put in perspective" by taking into account the differences of the grade distributions between the student's old class and the class he wishes to join. We assume here that the class averages are the only such information available tous. We wish t o find a formula which converts the grades based on these averages. Several criteria have to be applied t o find a suitable conversion formula. For example the relationship of being above or below averageshould be preserved in the conversion of thegrade. A total of four such criteria have been formulated. 11) I i a mldent hns a snm of 0, the ndpstsd amre ~ h d remain d 0. I ? ) If a student uhtami an arernge ymde in hw r h s i , his adjusted grade should he the rlnss nvernge o t t h e class he joins. (3) The higher of two scoresin the old class should remain thc higher of the two scores after both scores have been eonverted.
The above three criteria could be fulfilled by simply introducing a conversion factor. However, such a conversion factor would change the range of the grading scale. Evidently an additional criterion is required. (4) If a student has a perfect score, it should remain unchanged in the conversion
Let us assume that we have a grade from a student which has been obtained in a class with a class average of Aold. We want to convert this grade which we denote Goidto a grade G, which the student would likely have obtained in a class which had a class average of A,,. Let us try a formula of the form Gnew= ( B Gold)/(C
+ D Gold)
Using the criterialisted in (1) and (4) the parameters B, C, a n d D become B =An., (100 - A,I~); C = Aold (100 -Anew); and D =A, - Aold.where it has been assumed that the maximum grade is 100. If this is not the case, one can simply replace "100" in the expressions far B and C by the maximum grade of the grading scale. It can be shown that the criteria in (2) and (3) are fulfilled by the above conversion formula.
Peter Senn The University of Tennessee Knoxville, TN 37916
Volume 59
Number 7
July 1982
585
