Про обчислення складності завдань
Journal Title: Математичне моделювання - Year 2018, Vol 1, Issue 2
Abstract
ABOUT COMPATIBILITY OF TASKS COMPATIBILITY Shumeyko O.O., Iskandarova-Mala A.O., Lymar N.M. Abstract Student knowledge and skills control is one of the main elements of the learning process. The effectiveness of managing educational work and the quality of the training of specialists depends on the correct organization of the control. Through control, a "feedback" is established between the teacher and the student, which allows assessing the dynamics of learning the learning material, the actual level of knowledge, skills and abilities, and, accordingly, makes appropriate changes to the organization of the learning process. Testing is an important part of knowledge control methods. The testing system is a versatile tool for identifying students' knowledge at all stages of the learning process. In modern conditions, knowledge of testing techniques and the creation of test-bench bases is a necessary component of the teacher's work. The article is devoted to the search for methods for constructing a rating of tasks for checking the level of knowledge of students and students. The set of answers for each task is a point in a multidimensional space. All answers to all tasks form a cloud, in which you can find the main direction. The principal component method is used to search the main direction. It is proposed to use the iterative method of the main components. The projection of each point that corresponds to each task in the main direction allows us to reduce the point of the multidimensional space to a point in a straight line and thereby put in correspondence with each point a real positive number, which will characterize the rating of the task. The higher the number, the higher the rating. When using computer knowledge testing programs, there is a complex problem of evaluating each task in order to build an objective assessment scale for students. Since creating a set of tasks with the same complexity is impossible, it is desirable, in some way, to conduct a rating of complexity of tasks. The article proposes to consider the answer to each task as a point in a multidimensional space, the size of which coincides with the number of students who answered this question. In this way, all responses form a multidimensional cloud that extends along a certain direction. In the projection, it is proposed, as a rating of each task, to take the projection of the point of multidimensional space into this main direction. In addition, a filtration method is proposed that allows you to discard incorrect data, because a point that is far enough away from the received cloud does not characterize the complexity of tasks in general. The method of the main components can be interpreted as follows — we take an orthogonal basis and twist it until one of the directions gets the maximum variation. Just this direction we need. The classic method of the main components allows you to accurately solve the problem, but uses rather complicated algorithms when solving the problem with own numbers and own vectors, even though we only need one vector that corresponds to the largest eigenvalue. In view of the fact that the objective function is a quadratic function, the necessary and sufficient conditions for the extremum coincide. But the aggregated estimates of the complexity of the problem are based on the correlation data of the data, which is possible in the absence of emissions, that is, quite a bit different than the level of knowledge of pupils or applicants of higher education, and the level of complexity of tasks. In practice, both one and two conditions are usually not fulfilled. In this case, from the existing set of data it is necessary to delete the information that does not correspond to the main trend, that is, to filter the data. For this purpose, we use the value of the distance Mahalonobis of each point from the centroid of the set altogether. The Mahalanobis distance is calculated as the distance from the point to the center of gravity of the set of all points in the multidimensional space, which is determined by correlated (nonorthogonal) independent variables. If the independent variables are uncorrelated, the Mahalanobis distance coincides with the distance of Euclidean. In this case, this measure determines whether a given emission point is relative to other values of independent variables. As an experiment, we will examine the results of testing in the discipline "Economic Theory". The total test contains 30 questions and 4 answers, only one of which is true. The error stabilized at 4 iterations. The proposed method allows automating the evaluation of the complexity of the test for further analysis and improving the quality of tasks and testing. References [1] Applied statistics. Classification and Dimension Reduction. / S.A. Ayvazyan, V.M. Buchstaber, I.S. Enyukov, L.D. Meshalkin. – Moscow: Finances and Statistics, 1989. – 607 p. [2] Shumeiko AA, Sotnik S.L. Intellectual Data Analysis (Introduction to Data Mining). – Dnipropetrovsk: Belaya Ye.A., 2012. – 212 p. [3] Penny K.I. Appropriate critical values when testing for a single multivariate outlier using the Mahalanob distance // Applied statistics. 1996. V. 45, No. 1. P. 73–81. [4] Measurement in education: Textbook / Edited by O.V. Avramenko. – Kirovograd: Lysenko V.F., 2011. – 360 p. [5] Designing tests / L.О. Kuhar, VP Sergienko – Lutsk, 2010. – 182 p. [6] Shumeiko O.O., Iskandarova-Mala A.O. Construction of IRT profiles with the help of piecewise linear regression with free nodes / A.O. Iskandarova-Mala, O.О. Shumeiko // Collection of KNU. – 2016. [7] Shumeiko O.O., Iskandarova-Mala A.O. Influence of adaptive testing on the profile of IRT / A.O.Iskandarova-Mala, O.Shumeiko // Collection of KNU. – 2017. [8] Iskandarova-Mala A.O. On the choice of parameters of the EM algorithm for the division of a mixture of distributions / A.O. Iskandarova-Mala, O.О. Shumeiko // Mathematical modeling. – 2018. [9] Iskandarova-Mala A.O. Adaptive testing based on IRT profiles / A.O. Iskandarov-Malaya // Modern information and communication technologies in transport, industry and education: Abstracts of the XI International scientific and practical conference. – 2017. – No. 11. – C. 178.
Authors and Affiliations
О. О. Шумейко, А. О. Іскандарова-Мала, Н. М. Лимар
Keywords
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- EP ID EP444576
- DOI 10.31319/2519-8106.2(39)2018.154208
- Views 80
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