A Study on the Consistency and Efficiency of Student Performance Evaluation Methods: A Mathematical Framework and Comparative Simulation Results - Cecilia Leal-Ramírez; Héctor Alonso Echavarría-Heras; Enrique Villa-Diharce; Horacio Haro-Avalos (Applied Sciences)
Background: Consistent evaluation methods foster fairness, reduce bias, and enhance student understanding and motivation. Notably, mathematical inconsistencies, such as improper weighting, flawed averaging, and unsound scaling, can undermine the accuracy and reliability of assigned grades. This paper addresses the critical need for consistent student evaluation methods, with a primary focus on ensuring mathematical consistency within grading systems. Methods: We propose a scheme aimed at identifying inconsistencies in student evaluation related to the mathematical framework of the used grading method. To explain the functioning of our construct, we provide mathematical representation of conventional grading methods, including summative assessments, rubrics, and the Systematic Task-Based Assessment Method (STBAM) that we have recently developed, which incorporates both traditional and fuzzy logic-based grading modules. We introduce a Consistency Index <semantics>(CIM)</semantics> depending on the Mean Absolute Deviation of assigned scores <semantics>(MADM)</semantics> and a method’s Complexity Pointer <semantics>(CPM</semantics>). We also propose a method’s Efficiency Index <semantics>(βM)</semantics> expressed in terms of the Consistency Index and the latter indicator. We compared the mathematical consistency and efficiency of the methods addressed in this study through simulation runs. Results: We demonstrated how the proposed indices can reveal the strengths and weaknesses of each grading scheme analysed. Conclusions: The fuzzy logic-based modulus of the STBAM yielded the highest values of <semantics>CIM</semantics> and <semantics>βM</semantics>. However, performing a pending analysis of scalability, teacher training, and cultural adaptability would be essential to strengthen the potential of the STBAM to be adopted as a reliable grading alternative to conventional grading approaches. In the meantime, our approach could provide a clear, logical, and defensible framework for testing the mathematical consistency of student assessment methods.