Factor Analysis of Students' Knowledge Assessment Based on the Results of Online Entrance Testing in Mathematics to the University under the Conditions of COVID-19

After the COVID-19 pandemic emerged, many educational institutions switched to distance learning, which led to the problem of organizing entrance examinations for universities. When conducting entrance examinations online, applicants have many more opportunities for fraudulent activities (cheating on the exam and using outside help). This article is devoted to the factor analysis of the assessment of students' knowledge in mathematics enrolled in 2020 at the Altai State Technical University (Barnaul, Russia) based on the results of online entrance testing during the COVID-19 pandemic using an Internet browser and the webcams of applicants. The study used statistical methods, including groupings and comparisons. The analysis revealed that the spread of students' entrance ratings and their grades at the end of examination sessions in the first year increased by 2.7 times compared to previous years when entrance testing was held offline at the university. Such a large spread can be justified by 37% of the personal problems of applicants (difficulty adapting to the educational process at the university, lack of time, change of interests, etc.) and by 17% of a partial transition to distance learning in the current COVID-19 pandemic. There is a 46% imperfection rate of online testing as a mechanism for competitive selection of applicants. Despite the moderator's constant control over the progress of testing by monitoring the video from the cameras of applicants, some students probably used outside help in the exam. A correlation analysis showed that the propensity to such behavior is influenced by such characteristics as the age of the applicant, the level of previous education, knowledge of Russian for foreigners, degree of adaptation to life, and education in another country. In addition, the analysis of the correctness of answers to the tasks of the online test made it possible to identify several tasks that can additionally serve as a detector of independence when passing the test, called "traps".