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

Atanas Ivanov

doi:10.3390/math8050748

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.

Highlights

The training in mathematics during the first academic year at university has special characteristics.First-year students come from diverse high schools with different levels of knowledge and skills and varied personal attitudes toward mathematical education
The objective of this study was to investigate the importance of numerous factors such as the grades of students on individual test problems, students’ self-assessment of their mathematical competencies, their ability to use mathematical software, among others, on the obtained final grade, and the overall mathematical competency
The assessment test presented in this paper includes multiple-choice questions and problems to be solved in class, in the field of linear algebra and analytical geometry

Summary

Introduction

First-year students come from diverse high schools with different levels of knowledge and skills and varied personal attitudes toward mathematical education. Overcoming these differences is crucial to achieve the objectives of higher education—training highly qualified specialists for the labor market. In addition to knowledge and skills, students need to possess various abilities to apply their knowledge and skills to solving practical problems, too. The grouping of these requirements leads to a definition of the concept of mathematical competency. We note [2] where a general concept of mathematical competency is considered, describe the characteristics of the concept in detail, and give examples in the case of school mathematics

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Conclusion