Mathematical modeling of systems with random variables: An analytical framework for studying non-deterministic behavior and its applications to improving academic achievement
Keywords:
Mathematical modeling, stochastic variables, student achievement, Monte Carlo simulation, statistical regression, student performance prediction, statistical analysis, stochastic models, MATLAB, SPSSAbstract
The main objective of this work is to investigate the extent of which the stochastic mathematical modeling can explain differences in students' achievements and to quantify the effect of a number of educational and behavioral factors on their achievements (study hours, attendance, motivation, usage of educational technology and test anxiety). Mathematical model which can describe the students' achievements when uncertainty and random phenomena are considered has also been developed. Data from students' achievements were gathered, and were then analyzed using a methodology relying on data collection and statistical analysis by use of software like SPSS and MATLAB). The study used regression models as mathematical models to show dependence of a student’s achievement on a number of variables and used Monte Carlo simulation technique for modeling educational achievements by different methods. The model was validated and evaluated using different indicators of validation (MSE, RMSE, MAE and R2). In all cases most of variables included in study were shown to affect the student achievements statistically significant. The contribution of most significant factors like study hours, motivation and educational technology on increasing the achievement of a student is positive, whereas the test anxiety negatively affects the achievements of students significantly. The simulation results further showed that the stochastic mathematical model used can significantly account for the variation in achievement, and to provide a quite good prediction of student achievement. Recommendations for the use of mathematical modeling and stochastic simulation in education and decision making were made, as well as recommendations to promote development of data-based learning strategies for the aim of reducing differences between students and improving educational process quality.
