Data Mining for Statistical Evaluation of Summative and Competency-Based Assessments in Mathematics

Gocheva-Ilieva, Snezhana; Teofilova, Marta; Илиев, Антон; Kulina, Hristina; Voynikova, Desislava Stoyanova; Ivanov, Atanas; Atanasova, P. Kh.

doi:10.1007/978-3-030-20005-3_21

Cited by 3 publications

(6 citation statements)

References 15 publications

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“…The results obtained are comparable to those obtained by us in [6], where regressiontype CART models were constructed to predict the final exam results in linear algebra and analytical geometry for students in two other specialties at the same university, using a short mathematical competency test and mid-term test results. In [6], the models reached to fit the actual data with R 2 = 93%. The results obtained here are also similar to those in [11,13].…”

Section: Discussion With Conclusionsupporting

confidence: 80%

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

2020

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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.

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Section: Discussion With Conclusionsupporting

confidence: 80%

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

2020

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“…The development of specific approaches for assessment of mathematical competencies under the SEFI framework is presented in the recent publications [6][7][8][9][10]. These papers use specific examples to showcase the main aspects of the assessment standards and activities to implement an innovative pedagogical approach in engineering and science degrees.…”

Section: Introductionmentioning

confidence: 99%

“…The integration of the considered eight competencies using software for the education of students in the course for Software Systems in Mathematics is presented in Reference [8]. Results from a combined test for the assessment of mathematical competencies, processed using two data-mining techniques-cluster analysis and decision trees for statistical evaluation of summative and competency-based assessments-are presented in [9]. The authors of the recent publication [10] describe an experiment mixes game learning methodology (escape room), with engineering students learning linear algebra, calculus, or cryptography.…”

Section: Introductionmentioning

confidence: 99%

“…As far as the author is aware, in literature, the studies to assess mathematical competency in higher education by using data-mining methods are scant. Here, the results can be compared against Reference [9], where regression type CART models are built to explain the final exam results in linear algebra and analytic geometry of students in two other specialties at the same university, based on a short competency test with mathematical problems and midterm tests results. In [9], the models describe 92.6% and 93.4% of data variance, which concurs with our results.…”

mentioning

confidence: 99%

“…Here, the results can be compared against Reference [9], where regression type CART models are built to explain the final exam results in linear algebra and analytic geometry of students in two other specialties at the same university, based on a short competency test with mathematical problems and midterm tests results. In [9], the models describe 92.6% and 93.4% of data variance, which concurs with our results. Generally, in cases where other types of empirical data and data-mining techniques are used, similar model performance is achieved (see, for instance, [15,16,18]).…”

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confidence: 99%

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

Ivanov

2020

Mathematics

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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.

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Data Mining of Formative and Summative Assessments for Improving Teaching Materials towards Adaptive Learning: A Case Study of Programming Courses at the University Level

Tran,

Vu-Van,

Bang

et al. 2023

Electronics

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It is crucial to review and update course materials regularly in higher education. However, in the course evaluation process, it is debatable what a difficult learning topic is. This paper proposes a data mining approach to detect learning topics requiring attention in the improvement process of teaching materials by analyzing the discrepancy between formative and summative assessments. In addition, we propose specific methods involving clustering and noise reduction using the OPTICS algorithm and discrepancy calculation steps. Intensive experiments have been conducted on a dataset collected from accurate assessment results of the data structures and algorithms (DSA) course for IT major students at our university. The experimental results have shown that noise reduction can assist in identifying underperforming and overperforming students. In addition, our proposed method can detect learning topics with a high discrepancy for continuously improving teaching materials, which is essential for question recommendation in adaptive learning systems.

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Data Mining for Statistical Evaluation of Summative and Competency-Based Assessments in Mathematics

Cited by 3 publications

References 15 publications

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

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

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

Data Mining of Formative and Summative Assessments for Improving Teaching Materials towards Adaptive Learning: A Case Study of Programming Courses at the University Level

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