Early Prediction of Mathematics Learning Achievement of Elementary Students Using Hidden Markov Model

Elementary students usually felt the fractions and decimals concepts were challenged concepts. This leads to misconceptions due to their symbolic representations and arithmetic rules being distinct from those of integers. This study utilized data mining and learning analytics methods to develop a learning system using a Hidden Markov Model (HMM), focusing on students' misconceptions in fractions and decimals lessons. The study aims to evaluate the efficacy of HMM in predicting students' mathematics achievement by comparing the Mean Squared Errors (MSE) of the HMM and a baseline model. There were seventy-eight fourth-grade students participating in Taiwan. Students answered forty mathematics questions using the system over eighty minutes, 6,246 time-series data points were collected. The baseline model used the ZeroR classifier as a benchmark. The first thirty learning behaviors were sequentially input into both models, calculating MSE relative to the students' mathematics achievement test scores. Subsequently, the Wilcoxon signed-rank test assessed significant MSE differences between models. The results showed that HMM significantly outperformed the baseline model in fractions and decimals, showing lower MSE. Furthermore, in graphical analysis, incorporating sequentially inputted behaviors, revealed a more pronounced reduction in MSE for the HMM model across lessons. These results highlight HMM's effectiveness in early math achievement prediction in elementary education.