Grading that Takes into Account the Need to Learn from Mistakes

It is well known that the best way to learn the new material is to try it, to make mistakes, and to learn from these mistakes. However, the current grading scheme, in which the overall grade is a weighted average of the grades for all the assignments, exams, etc., does not encourage mistakes: any mistake decreases the grade on the corresponding assignment and thus, decreases the overall grade for the class. It is therefore desirable to modify the usual grading scheme, so that it will take into account -- and encourage -- learning by mistakes. Such a modification is proposed in this paper. Specifically, we suggest that the overall grade be -- as now -- the weighted average of the grades corresponding to different parts of the material, but each of these parts-grades is now calculated differently: instead of the weighted average of grades corresponding to different assignments in which this material is tested, we suggest using the largest of the grades corresponding to all these assignments