- Круглова, Наталія Володимирівна (orcid.org/0000-0002-9143-9398) and Диховичний, Олександр Олександрович (orcid.org/0000-0001-8505-2878) (2022) Selecting a mathematical model for analysis of test items of the type "embedded answers" for mathematical disciplines Інформаційні технології і засоби навчання, 1 (87). pp. 166-184. ISSN 2076-8184
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Abstract
The article examines the issue of choosing a mathematical model for the analysis of computer tests in mathematical disciplines. A feature of this study is the exploration of test items of the "embedded answers (cloze)" type. Such test tasks have several “steps” interconnected by a certain logic and have been used precisely for remote control of knowledge in mathematical disciplines during quarantine at NTUU “Igor Sikorsky Kyiv Polytechnic Institute”.The introduction of such tasks into the test raises the question for the teacher: how to analyze the quality of such tests? The authors built the study on the basis of the well-known methods of Classical Test Theory (CTT) and Item Response Theory (IRT), which have proven their effectiveness in pedagogical testing as well as in other industries in which the test approach is used. The study was carried out on the example of a modular test quizzes on probability theory for second-year students of the Faculty of Informatics and Computer Engineering of NTUU "Igor Sikorsky Kyiv Polytechnic Institute", formed on the MOODLE platform during distance learning in November 2020. In the course of the study, the following was done: the quality of the test was analyzed both as a whole and as individual test items; the latent parameters of the tasks were estimated, the adequacy of the corresponding models to the testing data was checked; characteristic and information curves were built; using information criteria, were selected the IRT models the most suitable for the analysis of computer tests with tasks of the "embedded answers" type; it has been proven that both Rush's dichotomous model and Muraki's political model are the most appropriate for the analysis of such tasks. The calculation was carried out using special libraries (packages) of R programming language, in which the KTT and IRT algorithms are implemented, namely, eRm, ltm, mirt. It is shown how the tasks with “embedded answers (cloze)” can be used to analyze certain skills and knowledge of students. The results of the study contribute to improving the competence of teachers in assessing the quality of tests in higher mathematics, which is very important when compiling tests in various disciplines, especially in the situation of student distance learning.
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