STATISTICAL MODELING OF INTERNET EXAMINATION CONDUCTED IN THE FRAMEWORK OF HIGHER SCHOOL CERTIFICATION

Currently many Universities of Russia are undergone the procedure of certification which is carried out in several directions including the test of students of their knowledge qualification level on fundamental disciplines. Mathematics is one of the fundamental disciplines. We present a description of students’ testing in mathematics in the framework of certification of higher education institution. 1) First, the learning groups put to the certification are defined. These groups were selected evenly from all the faculties. Thus, ten groups took part in the testing during the university certification. 2) The modal patterns of the test were laid out in the special website. Each student from the selected groups had the opportunity to familiarize with the tasks on mathematics and practice in the course. 3) The tasks of the test were categorized by the topics: 6 topics on mathematics. As the table shows, there are from 4 to 10 tasks for each topic. The student solves similar tasks during the test which are displayed on the computer screen. These tasks can be shuffled during the test. 4) The student should solve at least a half of all the tasks to pass the mathematics test. This test specificity has misled a number of students. Having solved 92% (35/38•100%) of all the tasks the student could not pass the test on condition that he solved, for example, only one task of the four on the topic “Differential equations”. 5) In the end of the test the students who did not pass the test were recorded. If the number of those students was greater than pr (pr ≈ 50%), the group was considered not to pass the certification, and the fact of negative certification in the group was determined. Otherwise, the fact of positive certification of the group is settled. 6) If at least one of the selected groups will not pass the test, it is believed that the university did not pass the certification. The testing depends on many parameters, such as: 1) knowledge qualification level ( θ ср) of students in the tested group; 2) heterogeneity of the group, determined by the range of knowledge qualification level; 3) level of test tasks difficulty; 4) heterogeneity of the test tasks, determined by the range of changes of difficulty level; 5) number of students in the tested group, 6) certification threshold of the pr group (see above). The objective of this work is to study the dependence of probability of positive certification of the group from the above parameters with the help of simulation using the Monte Carlo method. The following results are obtained: 1) If the determined parameters of the system be arranged in descending order of their importance for the probability p of positive certification of the students’ group, the result will be in the following sequence: a) the average level of the knowledge qualification level of students and the average level of difficulty of the test tasks (the highest value), b) the number of students in the group and the threshold certification (medium importance), c) the heterogeneity of the group and the heterogeneity of the test (low importance). 2) Prestigious universities ( θ av ≥ 62) will successfully pass the certification. 3) Certification of low-prestige universities ( θ av ≤ 56) will always lead to negative results.

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