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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

Author

Listed:
  • Snezhana Gocheva-Ilieva

    (Department of Mathematical Analysis, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

  • Hristina Kulina

    (Department of Mathematical Analysis, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

  • Atanas Ivanov

    (Department of Mathematical Analysis, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

Abstract

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.

Suggested Citation

  • Snezhana Gocheva-Ilieva & Hristina Kulina & Atanas Ivanov, 2020. "Assessment of Students’ Achievements and Competencies in Mathematics Using CART and CART Ensembles and Bagging with Combined Model Improvement by MARS," Mathematics, MDPI, vol. 9(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:62-:d:470399
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    References listed on IDEAS

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    1. Behr Andreas & Giese Marco & Teguim K Herve D. & Theune Katja, 2020. "Early Prediction of University Dropouts – A Random Forest Approach," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 240(6), pages 743-789, December.
    2. Atanas Ivanov, 2020. "Decision Trees for Evaluation of Mathematical Competencies in the Higher Education: A Case Study," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
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