Student Performance Predictions for Advanced Engineering Mathematics Course With New Multivariate Copula Models

Abstract

Engineering Mathematics requires that problem-solving should be implemented through ongoing assessments; hence the prediction of student performance using continuous assessments remains an important task for engineering educators, mainly to monitor and improve their teaching practice. This paper develops probabilistic models to predict weighted scores ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WS</i> , or the overall mark leading to a final grade) for face-to-face (on-campus) and web-based (online) Advanced Engineering Mathematics students at an Australian regional university over a 6-year period (2013–2018). We fitted parametric and non-parametric D-vine copula models utilizing multiple quizzes, assignments and examination score results to construct and validate the predicted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WS</i> in independently test datasets. The results are interpreted in terms of the probability of whether a student’s continuous performance (i.e., individually or jointly with other counterpart assessments) is likely to lead to a passing grade conditional upon joint performance in students’ quizzes and assignment scores. The results indicate that the newly developed D-vine model, benchmarked against a linear regression model, can generate accurate grade predictions, and particularly handle the problem of low or high scores (tail dependence) compared with a conventional model for both face-to-face, and web-based students. Accordingly, the findings advocate the practical utility of joint copula models that capture the dependence structure in engineering mathematics students’ marks achieved. This therefore, provide insights through learning analytic methods to support an engineering educator’s teaching decisions. The implications are on better supporting engineering mathematics students’ success and retention, developing evidence-based strategies consistent with engineering graduate requirements through improved teaching and learning, and identifying/addressing the risk of failure through early intervention. The proposed methods can guide an engineering educator’s practice by investigating joint influences of engineering problem-solving assessments on their student’s grades.