Mathematical modelling for academic performance status reports in learning analytics

Abstract

The fast changing nature of the educational environment and the subsequent increase in the volumes of generated learner data, have found existing data analysis techniques lacking in certain fields. These techniques form part of the analysis and reporting phases of learning analytics and need to adapt to accommodate the changing face of education. In this paper, a set of interrelated algorithmic solutions that utilise mathematical programming models to generate and provide learning feedback in the form of academic performance status reports, is presented. Three existing mathematical models, more specifically the benchMark program, an outputs-only data envelopment analysis and a traditional analytic hierarchy process were evaluated for providing the information required to assist students in improving their academic achievement. The requirements include providing students with their current academic performance status, setting interim improvement goals and calculating improvement targets towards reaching those goals. The evaluated models did not address the requirements satisfactorily. The solution proposed in this paper consists of an algorithm that implements a linear programming model to generate performance status reports based on the current assessment scores of a group of students in a module. The output is used
in a second algorithm that utilises the remaining improvement opportunities available to generate a participation future time perspective. The resulting schedule together with each individual student's current assessment scores, is used to calculate discrete improvement goals for each student as well as targets towards reaching those goals. A third algorithm provides a lecturer with some insight into the mastering of module content.

Keywords: Analytic hierarchy process, data envelopment analysis, educational feedback, learning analytics, linear programming, non-linear programming