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Assessment of Students’ Achievements and Competencies in Mathematics Using CART and CART Ensembles and Bagging with Combined Model Improvement by MARS

Department of Mathematical Analysis, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria
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Mathematics 2021, 9(1), 62; https://doi.org/10.3390/math9010062
Received: 30 November 2020 / Revised: 23 December 2020 / Accepted: 26 December 2020 / Published: 30 December 2020
(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications)
The aim of this study is to evaluate students’ achievements in mathematics using three machine learning regression methods: classification and regression trees (CART), CART ensembles and bagging (CART-EB) and multivariate adaptive regression splines (MARS). A novel ensemble methodology is proposed based on the combination of CART and CART-EB models in a new ensemble to regress the actual data using MARS. Results of a final exam test, control and home assignments, and other learning activities to assess students’ knowledge and competencies in applied mathematics are examined. The exam test combines problems on elements of mathematical analysis, statistics and a small practical project. The project is the new competence-oriented element, which requires students to formulate problems themselves, to choose different solutions and to use or not use specialized software. Initially, empirical data are statistically modeled using six CART and six CART-EB competing models. The models achieve a goodness-of-fit up to 96% to actual data. The impact of the examined factors on the students’ success at the final exam is determined. Using the best of these models and proposed novel ensemble procedure, final MARS models are built that outperform the other models for predicting the achievements of students in applied mathematics. View Full-Text
Keywords: mathematical competency; assessment; machine learning; classification and regression tree; CART ensembles and bagging; ensemble model; multivariate adaptive regression splines; cross-validation mathematical competency; assessment; machine learning; classification and regression tree; CART ensembles and bagging; ensemble model; multivariate adaptive regression splines; cross-validation
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MDPI and ACS Style

Gocheva-Ilieva, S.; Kulina, H.; Ivanov, A. Assessment of Students’ Achievements and Competencies in Mathematics Using CART and CART Ensembles and Bagging with Combined Model Improvement by MARS. Mathematics 2021, 9, 62. https://doi.org/10.3390/math9010062

AMA Style

Gocheva-Ilieva S, Kulina H, Ivanov A. Assessment of Students’ Achievements and Competencies in Mathematics Using CART and CART Ensembles and Bagging with Combined Model Improvement by MARS. Mathematics. 2021; 9(1):62. https://doi.org/10.3390/math9010062

Chicago/Turabian Style

Gocheva-Ilieva, Snezhana, Hristina Kulina, and Atanas Ivanov. 2021. "Assessment of Students’ Achievements and Competencies in Mathematics Using CART and CART Ensembles and Bagging with Combined Model Improvement by MARS" Mathematics 9, no. 1: 62. https://doi.org/10.3390/math9010062

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