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Decision Trees for Evaluation of Mathematical Competencies in the Higher Education: A Case Study

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  • Atanas Ivanov

    (Department of Applied Mathematics and Modeling, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

Abstract

The assessment of knowledge and skills acquired by the student at each academic stage is crucial for every educational process. This paper proposes and tests an approach based on a structured assessment test for mathematical competencies in higher education and methods for statistical evaluation of the test. A case study is presented for the assessment of knowledge and skills for solving linear algebra and analytic geometry problems by first-year university students. The test includes three main parts—a multiple-choice test with four selectable answers, a solution of two problems with and without the use of specialized mathematical software, and a survey with four questions for each problem. The processing of data is performed mainly by the classification and regression tree (CART) method. Comparative analysis, cross-tables, and reliability statistics were also used. Regression tree models are built to assess the achievements of students and classification tree models for competency assessment on a three-categorical scale. The influence of 31 variables and groups of them on the assessment of achievements and grading of competencies is determined. Regression models show over 94% fit with data and classification ones—up to 92% correct classifications. The models can be used to predict students’ grades and assess their mathematical competency.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:748-:d:355620
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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. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
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    Cited by:

    1. 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.
    2. Eugenio Vera-Salmerón & Carmen Domínguez-Nogueira & José L. Romero-Béjar & José A. Sáez & Emilio Mota-Romero, 2022. "Decision-Tree-Based Approach for Pressure Ulcer Risk Assessment in Immobilized Patients," IJERPH, MDPI, vol. 19(18), pages 1-9, September.

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