Karmanova E. V. Technology for assessing the level of development of competencies of students studying in the system distance learning university // Concept. 22015.2No. 12(December).2ART15417. 20.3 p.l. 2URL: http://ekoncept.ru/2015/15417.htm.2ISSN 2304120X. 1
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Karmanova Ekaterina Vladimirovna,
candidate pedagogical sciences, Associate Professor, Department of Business Informatics and information technologies FSBEI HPE ©Magnitogorsk State Technical University named after. G. I. Nosova, Magnitogorsk [email protected]
Technology for assessing the level of development of competencies of students studying in the university’s distance learning system
Abstract. The article discusses the problem of organizing assessment of the level of development of competencies of students studying using distance learning educational technologies. The author substantiates a mathematical model for assessing the level of development of students' competencies, which takes into account the structure of existing electronic courses in the distance learning system of Magnitogorsk State Technical University. The main provisions of the technology for assessing the level of development of students' competencies are revealed. Key words: competency-based approach, competency assessment, mathematical model, technology, distance learning system. Section: (01) pedagogy; history of pedagogy and education; theory and methods of teaching and education (by subject areas).
With the introduction of a competency-based approach to the system Russian education Pre-educational institutions have faced a number of tasks that cannot be solved using traditional methods; one of these tasks includes the need to organize an assessment of the level of development of students’ competencies. Today, each university independently decides what will be the methodology for the formation and use of assessment funds to assess the level of development of students’ competencies. This problem also extends to the organization of the learning process using distance learning technologies, since this form of learning is legitimized at the level of the Law on Education of the Russian Federation, and therefore must comply with other requirements of Russian legislation in the field of education. An analysis of the literature showed that universities do not have a generally accepted technology that allows them to track the process of forming a separate competency; in addition, existing methods for assessing competencies are quite cumbersome and often do not take into account the specifics of the formation of the competencies themselves within the framework of the university’s distance learning system. The search for possible ways to resolve the identified problem determined the choice of the goal of our research: the need to develop a technology for assessing the level of development of competencies of students studying using the distance learning system (hereinafter referred to as DLS).
When developing technology for assessing competencies, we relied on the following provisions: since disciplines are the main form educational activities(not a single university introduced changes), and it is the level of student mastery academic disciplines is assessed by teachers, it is obvious that by assessing the level of training in disciplines it is possible to ultimately correctly establish the level of formation of competencies, in addition, in this case it is more convenient to adapt previously accumulated experience and use adapted diagnostic techniques Karmanova E. V. Technology for assessing the level of formation of students' competencies students studying in the university’s distance learning system // Concept. 22015.2No. 12(December).2ART15417. 20.3 p.l. 2URL: http://ekoncept.ru/2015/15417.htm.2ISSN 2304120X. 2
within the framework of a competency-based approach. Also, within the framework of our research, the task was to develop a technology that would allow, based on the existing structure of electronic courses, to “painlessly” introduce an assessment of the level of development of students’ competencies for a university’s LMS. For a clear understanding of the technology proposed below, we will describe the existing structure of electronic courses in the DMS of Magnitogorsk State technical university. In an LMS, an electronic course is a set of modules, each of which contains theoretical material, practical task and test for self-control. The electronic course necessarily ends with a final test for the entire discipline being studied (Fig. 1).
Rice. 1. Elements of an electronic course in the LMS
Let us describe the assessment methodology. When developing a mathematical model for assessing the levels of development of competencies, we used the points received by students based on the results of completing diagnostic materials for a separate competency, and the result of a control event (test or exam). Let us need to find out the level of development () of competence. This competence is formed through disciplines =(1,2,…,), where the discipline directly influences the formation of competence. The influence of a discipline on the formation of competence can be considered at the level of the number of modules (sections) that form a given competence and, accordingly, check the level of its development. As a rule, the number of such sections for an electronic course is determined by teachers (authors of the discipline), who, in turn, are guided by the labor intensity of the discipline. In accordance with the discipline, an electronic course is created in the LMS, which, based on work program The discipline contains modules and necessarily ends with a final test. Since each discipline module in the electronic course contains a practical task and a test, these components will be diagnostic materials for assessing competence within a given discipline: (1≤≤2+1) (see Fig. 2). Let us explain this entry: at a minimum, in a separate electronic course, the selected competence must be formed by at least one module of the course and, therefore, tested by at least one diagnostic material (either a test or a practical task), the maximum number of diagnostic materials can be all practical tasks and tests for each module plus a final test. However, the final test may not necessarily test this competency, and therefore is not necessarily included in the block of diagnostic materials for this competency. The influence of the results obtained from tests and practical tasks is different, so we will separately enter our weight for each of them: Determination of weights for test materials and Karmanova E.V. Technology for assessing the level of competency formation of students studying in the university’s distance learning system // Concept. 22015.2No. 12(December).2ART15417. 20.3 p.l. 2URL: http://ekoncept.ru/2015/15417.htm.2ISSN 2304120X. 3
Fig. 2. Example of a set of diagnostic materials for a specific competency
The result is also influenced by the final score obtained as a result of the final control (test or exam):. Thus, the mathematical model for assessing the level of competence formation will be presented in the following form: = ∑ (∑∙ = 1+), = 1 where n is the number of disciplines that form k competence; t is the number of diagnostic materials of the i discipline that test k competence; weight a separate th diagnostic material (test or practical assignment) for the control result in the ith discipline; a score received by the student based on the results of passing the th DM in the ith discipline; a score received in an exam or test in the ith discipline (this may also include a grade in course work, educational/industrial practice, final state certification). The result obtained can be compared with the maximum number of points that a student can receive based on the results of training, and presented as a percentage (70% work during the semester in the i-th discipline and 30% result of the examination test/test in the i discipline). For example, let the ith discipline have ∑∙=550=1 points, this is 70% of the total score of the discipline, then maximum value=236 points. As a rule, the assessment of Karmanova E.V. Technology for assessing the level of development of competencies of students studying in the university’s distance learning system // Concept. 22015.2No. 12(December).2ART15417. 20.3 p.l. 2URL: http://ekoncept.ru/2015/15417.htm.2ISSN 2304120X. 4
on the exam is given on a five-point scale, therefore, to convert it into course points, you must either indicate in percentage the rules for converting grades obtained on the exam to course points (for example, ©2ª 0%; ©3ª 55%; ©4ª 80%; ©5ª 100%), or the teacher also evaluate the exam results according to the course scale, which is more the right decision, however, increases the complexity of assessment. The procedure for calculating the level of competence development gives the final result after studying all the disciplines that form the competence. However, in the process of developing competence, it is very important to monitor and predict its possible assessment at any stage of training with subsequent correction of the process of developing competence. In addition, according to the requirements of federal government educational standards assessment of the quality of training of students and graduates should include current, intermediate and final state certification, which means that the level of competence development should be assessed. Therefore, a procedure is proposed for calculating the characteristics of the level of competence in the process of its formation. The contribution of the discipline to the competence: =∑∙=1+. Accordingly, the maximum and minimum possible contribution of the discipline to the competence is calculated using the formulas: brmin is the minimum possible score for assessing the knowledge and skills of students. Then the maximum and minimum possible assessment of competence at the current time is calculated using the formulas:=∑=1,
=∑=1,
where k is the number of disciplines that form competence and are studied at this moment time. This assessment will be calculated in points that teachers assigned in the disciplines that form this competency. The current assessment of competence is calculated according to formula (7) and measured in points of the score rating system adopted at the university for assessing disciplines: = ∑. = 1 The current contribution of all disciplines studied at a given time to the formation of competence is found using the expression:
Competencies can be developed at various levels; as a rule, there are three levels of formation of a separate competency: threshold (initial), basic and advanced. To convert students' quantitative assessments into competency levels, it is enough to determine the intervals of each level. As a rule, E. V. Karmanova, Technology for assessing the level of competency formation of students studying in the university's distance learning system // Concept. 22015.2No. 12(December).2ART15417. 20.3 p.l. 2URL: http://ekoncept.ru/2015/15417.htm.2ISSN 2304120X. 5
In the provisions of the university's point rating system, such intervals are presented as percentages. Any assessment technology must answer primarily the following questions: 1. What will be assessed? 2.Who or what evaluates? 3.When should an assessment be carried out? 4.Where and how should the assessment results be recorded? 5. By what criteria to evaluate (what is the evaluation methodology)? Figure 3 shows the main provisions of the proposed technology for assessing the level of development of competencies of students studying in the university's distance learning system.
Rice. 3. Technology for assessing the level of development of students’ competencies in the university’s LMS
The proposed technology for assessing the level of development of competencies of students studying in the university’s educational and educational system can also be used for full-time students. However, it is worth noting that the procedure for assessing student competencies must be supported by the automated control system that currently exists in almost every university. Automation in this case is necessary, since it is necessary to track quite a large number of competencies (40 on average) that need to be developed for each graduate; in addition, as a rule, the battery of diagnostic materials for assessing competencies is also large in size and manually processing it is labor-intensive.
Links to sources 1. Romanova E.P., Romanova M.V. About the concept of ©open Remote educationª in modern conditions training of students of classical universities // VIII International Conference ©Strategy of excellence in industry and masteryª: Materials: 3 volumes. T.II / administrators: T.S. Khokhlova, V.O. Khokhlov, Yu.A. Stupak. Dnipropetrovsk; Varna, 2012. P. 434436. Karmanova E. V. Technology for assessing the level of competency formation of students studying in the university’s distance learning system // Concept. 22015.2No. 12(December).2ART15417. 20.3 p.l. 2URL: http://ekoncept.ru/2015/15417.htm.2ISSN 2304120X. 6
2. Eliseev I.N. Mathematical models and software packages for automated assessment of learning outcomes using latent variables: dis. ... dra tech. Sciences: 05.13.18. Novocherkassk: SRSTU, 2013. 371 p. 3. Zakirova E.I. Information support for decision-making in the selection of students for a university master’s program based on a competency-based approach: dis. ...cand. tech. Sciences: 05.13.10.PNRPU: Tchaikovsky, 2014. 198 p.4.Permyakov O.E., Menkova S.V. Diagnostics of the formation of professional competencies. M.: FIRO, 2010. 114 p. 5.Pirskaya A.S. Methodology for assessing graduate competencies // Scientific and Technical Bulletin of St. Petersburg state university information technologies, mechanics and optics. 2012. No. 1(77). WITH. 124132.6.Sibikina I.V. Models and algorithms for the formation and assessment of competencies of a university graduate: dissertation... candidate of technical sciences. Sciences: 05.13.10. Astrakhan, 2012. 200 p.
Ekaterina Karmanova, Candidate of Pedagogic Sciences, Associate Professor at the chair of Business Informatics and Information Technologies, Nosov’s Magnitogorsk State Technical University, [email protected] for assessmentthe competenceslevel of students enrolled in university distance learning Abstract.The paper considers the problemofassessing the level of formationof students’organization competences using distance learning technologies. The author establishes thematic model for evaluating the level of formation of competences, taking into account the structure of the existing elearning courses in distance learning system of Nosov’sMagnitogorsk State Technical University. The basic provisions technologies assessing level of formation competences of students are revealed. Key words: competence approach, assessment of competence, mathematical model, technology, distance learning system. References 1. Romanova, E. P. & Romanova, M. V. (2012). “O ponjatii ‘otkrytoe distancionnoe obrazovanie’v sovremennyh uslovijah podgotovki studentsov klassicheskih universitetov”, VIII Mizhnarodna konferencija “Strategija jakosti u promislovosti i osviti”: Materiali: u 3 t.T. II / uporjadniki: T. S. Hohlova, V. O. Hohlov, Ju. A. Stupak, Dnipropetrovs "k, Varna, pp. 434436 (in Ukrainian). 2. Eliseev, I. N. (2013). Matematicheskie modeli i kompleksy programm dlja avtomatizirovannoj ocenki rezul" tatov obuchenija s ispol "zovaniem latentnyh peremennyh: dis. ... dra tehn. nauk: 05.13.18, JuRGTU, Novocherkassk, 371 p. (in Russian). 3. Zakirova, Je. I. (2014). . ... kand. tehn. nauk: 05.13.10, Chajkovskij, PNIPU, 198 p. (in Russian). 4. Permjakov, O. & Men "kova, S. V. (2010). Diagnostika formirovanija professional"nyh kompetencij, FIRO, Moscow, 114p. (in Russian). 5. Pirskaja, A. S. (2012). “Metodika ocenivanija kompetencij vypusknika”, Nauchnotehnicheskij vestnik SanktPeterburgskogo gosudarstvennogo universiteta informacionnyh tehnologij, mehaniki i opt iki, №1(77 ), pp. 124132 (in Russian). 6. Sibikina, I. V. (2012). (in Russian).
Gorev P. M., candidate of pedagogical sciences, editor-in-chief of the magazine ©Conceptª
Assessment of students' general competencies
methodologist at Cheboksary Electromechanical College
One of the key issues that arises in connection with the transition to a competency-based approach in education is the assessment tool. They are quite suitable for determining the level of development of students’ competencies. project work, business game, individual analysis of specific situations (when the student is asked to choose a certain strategy and tactics of action in the proposed situation), as well as expert observations.
The main difficulty in assessing the level of competence development is maintaining the principle of objectivity. To comply with this principle and get away from the human factor, it is necessary to place so-called “beacons” corresponding to each specific competency. And during the assessment process, the existing level of each student is compared with these “beacons”. But it should be noted that, again, these “beacons” may have a certain touch of subjectivity, and therefore they can only be used as a guide.
It is advisable to use a diagnostic interview, which should help clarify unclear points in the assessment. Students can be asked to conduct a self-assessment of the level of development of competencies. Let's consider this using the example of the general competence OK 6 “Work in a team and a team, ensure its cohesion, communicate effectively with colleagues, management, consumers” (FSES SVE), which relates to the field of social interaction.
Among the main indicators by which we can judge the level of development of this competence among students, we can highlight the following: establishes and maintains a good relationship with fellow students and teachers; shares his knowledge and experience to help others; listens to the opinions of fellow students and teachers and recognizes their knowledge and skills; actively contributes to the work of others. For each indicator we formulate three statements: “I do this rarely or never”, “I do this quite often”, “I always do this in any situation”. Each statement corresponds to a certain level of formation of the characteristic (low level is assessed as 1 point, average level– 2 points, high level- 3 points). Therefore, to self-assess competence, we invite students to choose one option from three statements for each main indicator of competence, and then, based on the answers received, we find the average value, which will be a self-assessment of the level of competence development.
The data obtained through self-assessment will help to present a complete picture for some students in the case where there are not enough materials to determine the level of competence development.
The existing system for assessing students' knowledge provides a clear picture of their performance, but does not allow assessing their personal characteristics. It is the curators of student groups, who directly communicate with students and know each of them individually, who can carry out such diagnostics. At the same time, curators can determine students’ motivation for learning, their leadership skills, relationships within the group. However, student evaluation is often based on academic performance. Even if the supervisors’ reports on the work done contain information on each student individually, then this information is not always conveyed to teachers at the beginning of training. Teachers are forced to determine their style of communication with students themselves (without prior knowledge). In this regard, I consider it advisable to bring the obtained data on the level of competence development among students to subject teachers. This will make it possible to determine how effective the teaching methods used are, and whether it is worth making certain adjustments to the teaching technology.
When assessing the competencies of students, it makes sense to rank the competencies according to the degree of their importance for employers - social partners, whom it is advisable to involve in the assessment (for example, during students’ practical training), since the process of assessing competencies requires the participation of not only teachers, but also third-party experts ( ideally, the HR manager of the employing company). Only then can the results obtained be truly objective.
It should also be noted that when assessing competencies, feedback is required, i.e. providing the student with detailed feedback on the work he has done, indicating strengths and weaknesses, as well as specific recommendations. Properly organized feedback can become an additional motivational factor for the student’s further learning and development within the framework of his chosen specialty.
Assessing the level of development of a student’s competencies provides an answer to the question: why does the student manifest himself in this way and show such results? Based on the assessments obtained, we can determine the size of the gap between the actual level of competence development and the expected one, which will allow us to see the step-by-step development plan for each student, the dynamics of this development, and also assess what issues (competencies) should be worked on in the future.
List of sources
1. , Jerry van Zantvoort. Modernization of vocational education: modern stage. European Education Foundation. – M., 2003.
2. Borisov - activity approach and modernization of content general education. // Standards and monitoring in education. – 2003. – No. 1, p.58-61.
3. Competence and competency: how many do Russian schoolchildren have? - http://vio. fio. ru/vio_l 7/resource/Print/art_l_6.htm
First level : The results of student learning indicate that they have acquired some basic knowledge of basic issues in the discipline. The mistakes and inaccuracies made show that students have not mastered the necessary system of knowledge in the discipline.
Second level : Level achieved Assessment of learning outcomes shows that students have the necessary system of knowledge and master some skills in the discipline. Students are able to understand and interpret the information they have mastered, which is the basis for the successful formation of skills and abilities for solving practice-oriented problems.
Third level : Students demonstrated results at the level of conscious mastery of educational material and educational abilities, skills and methods of activity in the discipline. Students are able to analyze, compare and justify the choice of methods for solving tasks in practice-oriented situations.
Fourth level : The achieved level of assessment of student learning outcomes in the discipline is the basis for the formation of general cultural and professional competencies that meet the requirements of the Federal State Educational Standard. Students are able to use information from various sources to successfully research and find solutions in non-standard practice-oriented situations.
Grading scale
|
Characteristics of levels of competence development |
||
|
Levels |
Manifestations |
|
|
Minimum |
The student has the necessary knowledge system and has some skills |
The student is able to understand and interpret the acquired information, which is the basis for the successful formation of skills and abilities for solving practice-oriented problems |
|
Base |
The student demonstrates results at the level of conscious proficiency educational material and educational abilities, skills and methods of activity |
The student is able to analyze, compare and justify the choice of methods for solving tasks in practice-oriented situations |
|
Advanced |
The achieved level is the basis for the formation of general cultural and professional competencies that meet the requirements of the Federal State Educational Standard. |
The student is able to use information from various sources to successfully research and find solutions in non-standard practice-oriented situations |
Level of development of knowledge, skills and abilities
The level of development of knowledge, skills and abilities in the discipline is assessed in the form of a point mark:
"Great" deserves a student who has demonstrated a comprehensive, systematic and deep knowledge of the educational program material, the ability to freely perform tasks provided by the program, who has mastered the basic and is familiar with additional literature recommended by the program. As a rule, an “excellent” grade is given to students who have mastered the interconnection of the basic concepts of the discipline in their meaning for the acquired profession, who have demonstrated Creative skills in understanding, presentation and use of educational material.
"Fine" deserves a student who has demonstrated complete knowledge of the educational program material, successfully completes the tasks provided in the program, and has mastered the basic literature recommended in the program. As a rule, a “good” grade is given to students who have demonstrated the systematic nature of knowledge in the discipline and are capable of independently replenishing and updating it in the course of further educational work and professional activities.
"Satisfactorily" deserves a student who has demonstrated knowledge of the basic educational program material to the extent necessary for further study and future work in the specialty, copes with the tasks provided for by the program, and is familiar with the basic literature recommended by the program. As a rule, a “satisfactory” grade is given to students who made errors in their answers on the exam and when completing exam tasks, but who have the necessary knowledge to correct them under the guidance of a teacher.
"Unsatisfactory" awarded to a student who has discovered gaps in the knowledge of the basic educational material, who has made fundamental errors in completing the tasks provided for in the program. As a rule, an “unsatisfactory” grade is given to students who cannot continue their studies or begin professional activities after graduation without additional classes in the relevant discipline.
Grade "passed" awarded to a student who has thoroughly mastered the provided program material; answered all questions correctly and with reason, giving examples; has demonstrated deep, systematized knowledge, masters reasoning techniques and compares material from different sources: connects theory with practice, other topics of the course, and other subjects studied; completed the practical task without errors.
A prerequisite for the grade given is correct speech at a fast or moderate pace. Additional condition obtaining a “pass” grade can lead to good success in completing independent and test work, systematic active work in seminar classes.
Grade "not accepted" Awarded to a student who failed 50% of the questions and tasks on the ticket and made significant mistakes in answering other questions. Cannot answer additional questions proposed by the teacher. The student does not have a holistic idea of the relationships, components, and stages of cultural development. The quality of oral and writing, as when giving a positive rating.
Bulletin of KhNADU, vol. 68, 2015
UDC 519.237.8
FORECASTING STUDENTS' ACHIEVEMENT BASED ON CLUSTER ANALYSIS METHODS
V.A. Shevchenko, associate professor, candidate of technical sciences,
Kharkov National Automobile and Highway University
Annotation. A methodology for predicting student performance based on cluster analysis methods is proposed. The results of the experiment are presented, confirming the effectiveness of the developed methodology for predicting academic performance.
Key words: forecasting, academic performance, cluster analysis, source data matrix, distance matrix.
PREDICTING STUDENTS' SUCCESS BASED ON METHODS
CLUSTER ANALYSIS
IN. Shevchenko, associate professor, candidate of technical sciences,
Kharkiv National Automobile and Highway University
Abstract. A methodology for predicting the success of students based on cluster analysis methods has been proposed. The results of the experiment were presented, which confirm the effectiveness of the developed methodology for predicting success.
Key words: forecasting, success, cluster analysis, output data matrix, output matrix.
PROGNOSTICATION OF STUDENTS PROGRESS ON THE BASIS OF CLUSTER
ANALYSIS METHODS
V. Shevchenko, Asso^ Prof., Ph. D. (Eng.),
Kharkiv National Automobile and Highway University
Abstract. The method of prognostication of students progress on the basis of methods of cluster analysis has been offered. The results of the experiment confirming the effectiveness of the developed method of prognostication have been given.
Key words: prognostication, progress, cluster analysis, matrix of initial data, matrix of distances.
Introduction
Currently, there are hundreds of forecasting methods. Kinds mathematical methods forecasting: correlation analysis, regression analysis, cluster analysis, factor analysis, etc.
Analysis of publications
The essence of forecasting in the field of education was considered by B.S. Gershun-
skiy, V.I. Zagvyazinsky, A.F. Juror, R.V. Mayer et al.
During the analysis of publications, it was concluded that cluster analysis methods are most suitable for reliably predicting student performance, since cluster analysis allows the division of objects not according to one parameter, but according to a whole set of characteristics. In addition, cluster analysis allows one to consider a variety of initial data of almost arbitrary nature.
Bulletin of KhNADU, vol. 68, 2015
Goal and problem statement
Based on the results of the analysis in the field of pedagogical forecasting, the following goals were set:
1. Develop a procedure for predicting student performance based on cluster analysis methods.
2. To test the effectiveness of the developed forecasting procedure, conduct an experiment to compare the actual and predicted student performance.
Choosing a cluster analysis method for predicting student performance
To solve the problem posed - developing a procedure for predicting student performance from a variety of clustering algorithms, the most suitable, in our opinion, is the McKean k-means algorithm, in which the user himself must specify the required number of finite clusters, denoted k. The classification principle is as follows:
k observations are selected or assigned to be the primary centers of the clusters;
The remaining observations are assigned to the nearest specified cluster centers;
The current coordinates of the primary cluster centers are replaced with cluster averages;
The previous two steps are repeated until changes in the coordinates of cluster centers become minimal.
However, McKean's algorithm assumes that cluster centers are selected from the existing data set for clustering. To solve the problem, this approach is not acceptable, since there may be groups of students with different academic performance; for example, groups where there are no poor students, or, conversely, no excellent students, or many three students. If you select cluster centers from the data of each student group, then for each group the distribution of students into clusters depending on their academic performance will be different, and it may happen that a student with good academic performance ends up in a cluster of poor academic performance and vice versa. It is necessary to determine such cluster centers, the values of which do not depend on the set of classified data and ensure
They distribute students into clusters in accordance with existing performance parameters: up to 60 points - poor, from 60 to 75 points - satisfactory, from 75 to 90 points - good, over 90 points - excellent.
In addition, according to the McKean algorithm, after adding any data to the cluster, it is necessary to recalculate the cluster center. In this case, the value of the cluster center will change, which will also lead to distortion of the clustering results.
Therefore, it is advisable to apply the McKean k-means method to solve the problem posed after some modification.
Modification of McKean's A-means method
We modify the McKean algorithm based on the following assumptions:
1. When solving the problem, it is necessary to set such cluster centers that represent the average values of each parameter for each class.
2. The specified centers must remain unchanged throughout the clustering procedure.
Formulation of the clustering problem
A set of objects X is known, representing data on the performance of n students, consisting of m features: X = X i, X 2,..., Xm). The set of objects X is described by the set of measurement vectors X j, j = 1, m. It is required to divide sample X into four typological groups characterizing student performance: “excellent”, “good”, “satisfactory” and “poor”. Therefore, we set the number of clusters k = 4.
Clustering procedure
1. Let's set the matrix of the initial data in accordance with formula (1), where Xj - jth parameter i-th object, m - number of parameters
Bulletin of KhNADU, vol. 68, 2015
ditch; n - number of students (clustering objects)
X11 X12. .. X1 j . 1 s
X21 X22. .. X2 j . ..X2m
Xi1 Xi 2 . .. Xj . ..Xm. (1)
Xn1 Xn2 . ..Xnj. ..Xnm
2. Let's assign primary cluster centers. To do this, for each cluster we define the reference values of the parameters as averaged data for each typological group of students, obtained by modeling the process of developing competencies among students. The reference values will be used as the centers of future clusters, around which the closest objects according to the values of the selected parameters are grouped. The reference values of clustering parameters are given in Table. 1.
where ztj is the normalized value of the j-th parameter of the /-th object; Xj - initial value of the j-th parameter of the i-th object; Xj is the average value of the j-th parameter for all objects; 4. For normalized data, construct a distance matrix D (3) " 0 d1,2 ... d1, n d1,n+4 d 2,1 0... d2,n d 2,n+4 D = dn,1 dn,2 . .. 0 dn,n+4 . (3) dn+4,1 dn+4,2 . .. dn+4,n 0 We calculate the distances between objects using the Euclidean metric (4) Table 1 Standards for forecasting Typologist. groups Initial knowledge Knowledge on the topic Number of passes Class 5 85 95 0 Class 4 75 85 0 Class 3 60 70 0 Class 2 40 40 2 Objects that are similar in their parameters are collected around the standards. The objects of clustering in this problem are students, and the parameters are factors whose values can be assessed at the initial moment of studying the discipline: Level of initial knowledge of students; The level of competencies developed by students on the first topic of the discipline; The number of absences from classes by students at the time of making the forecast. where d/j is the distance between the i-th and j-th objects; m - number of clustering features; zik - normalized value of the i-th object by k-th feature; Zjk is the normalized value of the j-th object according to the k-th attribute. 5. From the distance matrix, select the reference distance matrix, which is a matrix of distances (5) from each object to the reference data d1,n+1 d1,n+2 d1,n+3 d1,n+4 d 2,n+1 d 2,n+2 d 2,n+3 d 2,n+4 di,n+1 di,n+2 di,n+3 di,n+4 , (5) dn,n+1 dn,n+2 dn,n+3 dn,n+4 3. Since the selected characteristics have different units of measurement, we normalize the original data together with the standards added to them according to formula (2) i = 1, n + 4, j = 1, m where MEt is the reference distance matrix. 6. In the reference matrix, we determine the minimum value of the distance, the number of the object and cluster standard that are located at this minimum distance. 7. We will assign the selected object to the corresponding cluster. Bulletin of KhNADU, vol. 68, 2015 8. From the source data matrix and the reference distance matrix, we remove data about the object that was assigned to the cluster. We repeat steps 6 - 8 until all objects are separated into clusters. The developed procedure for predicting student performance is implemented in the form of a macro in VBA. Description and results of the experiment To test the effectiveness of the method of forming individual trajectories for independent work based on cluster analysis for organizing the individualization of independent work of a flow of students, an experiment was conducted with students of three groups (61 students in total) of the road construction faculty of KhNADU, studying computer science in the autumn semester. Three factors were used as initial data: the initial level of knowledge of students (assessed at the beginning of the first lesson), the knowledge acquired by students in the lesson on the first topic (assessed in the first laboratory work), and the number of absences from classes (the experiment was carried out in the second lesson). Based on these initial data, a forecast of academic performance was compiled for each student in the discipline “Informatics”. At the end of studying the discipline, the students’ predicted scores were compared with the scores that the students received in the computer science test. Comparative experimental data are given in table. 2 and in Fig. 1. Table 2 Credit and forecast data Excellent Good Satisfactory ОХОІГЦ Total Credit score 3 11 40 7 61 Predictive score 2 13 38 8 61 Rice. 1. Comparative chart of credits and forecast data Conclusion The results of the experiment showed that the predicted student performance differs from the actual one by no more than 3.3%. Therefore, the procedure based on the modified McKean's ^-means method is effective and can be used to predict student performance. Literature 1. Gershunsky B.S. Prognostic methods dy in pedagogy / B.S. Gershunsky. -K.: Vishcha School, 1979. - 240 p. 2. Zagvyazinsky V.I. Pedagogical pre- vision / V.I. Zagvyazinsky. - M.: Knowledge, 1987. - 77 p. 3. Juror A.F. Forecasting as function of a teacher (from a future teacher to a professional): monograph / A. F. Jury. - Chelyabinsk: Education, 2006. - 306 p. tov by cluster analysis method / R.V. Mayer // Problems of educational physical experiment: collection. scientific and method. works - 1998. - Issue. 5. - pp. 12-19. 5. Shevchenko V.A. Construction concept models of knowledge acquisition by students in the discipline “Informatics” / V. A. Shevchenko // Bulletin of KhNADU: collection. scientific tr. - 2012. - Issue. 56. - Reviewer: V.V. Bondarenko, professor, Ph.D., KhNADU.
