FRACTAL GRADING SYSTEM AND ITS USE IN THE PHILIPPINES

Abstract

This paper proposes a new measure of “typical performance†and examines its behavior in comparison with the traditional method of grading. The new measure is based on the concept of a fractal statistics. When one of the test scores become extremely low or extremely high, the values obtained by using the sample mean will be adversely affected. This type of grading system is not fair to the student because he is unduly penalized for a single bad performance. Likewise, he is also unduly rewarded for a single lucky performance. In order to correct this situation, we attempt to control the amount of “reward†a student obtains for a single lucky performance. That is, we do not put the same weight on a single high score as the rest of the scores, but we, instead, adjust this reward as a function of his consistency in class. The study made use of a simulation design using Monte Carlo methods.  Outlier probability models are assumed so that student scores are generated from these models. Results revealed that a fractal grading system rationalizes the weights placed on examination scores as basis for the final marks given to students. The system uses the “worst†performance as base score and adds a „reward†component based on his consistency in performance as measured by his fractal dimension. In contrast, the traditional grading system ignores the “reward†component and computes the final marks of students based on an averaging or smoothing process.