An Application of the Generalized Rectangular Fuzzy Model to Critical Thinking Assessment

The authors apply the Generalized Rectangular Model (GRM) for assessing students’ critical thinking skills. GRM is a variation of the center of gravity (COG) defuzzification technique, which was properly adapted and used by them several times in the past as an assessment method, called here the Rectangular Model (RM). The central idea of the GRM is the “movement” to the left of the rectangles appearing in the membership function’s graph of the RM, thus making the adjacent rectangles to share common parts. This treatment reflects better than RM the ambiguous assessment cases of student scores being at the boundaries between two successive assessment grades (e.g. something like 84-85% being at the boundaries between A and B) and therefore belonging to the common parts of the above rectangles. In fact, in GRM, and in contrast to RM, assuming that these scores belong to both of the successive assessment grades, we consider twice the common parts of the rectangles for calculating the COG of the level’s section lying between the resulting graph and the OX axis. Our results are illustrated on the data of a classroom application performed in one of the Los Angeles Unified District High Schools and connecting the students CT skills with their language competencies.