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

Atanas Ivanov
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Atanas Ivanov: Department of Applied Mathematics and Modeling, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria

Mathematics, 2020, vol. 8, issue 5, 1-16

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.

Keywords: mathematical competency; assessment; decision trees; classification and regression tree (CART) method; data mining; cross-validation; self-assessment; reliability; science and engineering education (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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