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to a problem of choice of profession studying the teacher it is extremely important to know the objective and subjective factors making the content of management. Treat objective factors: system of objectively operating regularities, living conditions of the subject, Wednesday, education, an economic environment and others. Treat subjective factors: possibilities of the subject, tendency, interests, abilities, intentions, motives, character, temperament, inclinations and other parties of the personality. That management of choice of profession was really effective, it is extremely important to understand in effect the composed parties of a subject of management stated above two. Management of choice of profession is impossible without knowledge of the personality, its structure.
Search of new solutions of the problem of psychology and pedagogical maintenance of self-determination of the studying youth in the conditions ofvocational guidance of training assumes:
- strengthening of integration of content of education with nonlearning practice of social and professional self-determination of school students;
- orientation to consolidation of resources and efforts of schools with other educational institutions (interschool educational plants, schools, colleges, lyceums, higher education institutions);
- ensuring profile training of school students on the basis of variability, taking into account the individual educational trajectories chosen by them corresponding to interests, tendencies, abilities of pupils and inquiries of labor market;
- ensuring the obligatory preprofile training of pupils including mastering school students idea of an image of the "I" about the world of professions, about labor market; acquisition of practical experience for the reasonable choice of a profile of training;
- rendering the psychology and pedagogical help to the teacher in reorientation of his activity of the creator, mentor to the activity directed to empathy; providing school student with support in the choice of a profile of training and further professional activity.
In the conditions of educational institution an effective type of the help to seniors in the professional choice are psychological and pedagogical support which are defined in world and domestic science and practice as the most effective. Fundamental in questions of the theory and practice of professional self-determination
of seniors in the context of vital self-determination V. I. Zhuravlev [1], V. A. Polyakov [3], N. S. Pryazhnikov [4] works, etc. are defined.
The rural school needs to provide the conditions stimulating human height therefore he could take the responsibility for the professional choice. Inner world at youthful age is autonomous and independent. It complicates process of psychology and pedagogical maintenance, children of this age do not wish to accept the help from the persuasive adult. Much more effective remedy for the solution of many psychological problems of rural school students are special methods of group work when the help proceeds not from the adult, and from children whose opinion for them is more significant. As an optimum method psychological trainings on development of consciousness of seniors, and also psychology and pedagogical and role-playing games in our opinion can serve. Also to a solution of the problem of choice of profession and a further educational route the course personally — professional self-determination, developed for pupils of 9-10 classes can promote. This course is complex according to contents as consists of two programs: 1) "Self-knowledge psychology" for the 10th classes; 2) "I and my professional choice" for the 9th classes. The course is offered to pupils for choice to create individual educational inquiry at the teenager, to develop ability to analyze and understand external circumstances.
Thus, psychology and pedagogical maintenance at rural school gains new quality. It is not only the most important component of education, but also its priority purpose. Also still serious easing of attention to questions personally — professional self-determination of pupils in all types of educational institutions, weak communication between an education system and labor market takes place. All this demonstrates that only the coordinated and purposeful work of pedagogical staff of Tarasinsky school positively affects the general improvement of quality of psychological and practical training of school students for conscious choice of profession.
Thus, the system of psychology and pedagogical maintenance at a stage of the professional choice has to be directed to activiza-tion of internal psychological resources of the personality, joining in professional activity, the person could fully realize himself in the chosen profession.
References:
1. Zhuravlev V. M. Questions of vital self-determination of graduates of high school / V. M. Zhuravlev. - Rostov N / Д: Publishing house of the - Rostov university, - 1972. - 200 p.
2. Klimov E. A. Way to profession / E. A. Klimov. - L.: LIE publishing house, - 1974. - 190 p.
3. Poles ofV. A., Chistyakova S. N. Professional self-determination / V. A. Poyakov S. N. Chistyakov // Russian pedagogical encyclopedia: in 2 t; гл.ред. V. V. Davydov. - M.: Nauch.Izd-vo "The big Russian encyclopedia", - 1999. - 2 t. - P. 212-213.
4. Pryazhnikov N. S., Pryazhnikova E.Yu. Psychology of work and human dignity: the education guidance for student. высш. уч. institutions/N. S. Pryazhnikov E.Yu. Pryazhnikova. - M.: Prod. Akademiya center, - 2001. - 480 p.
DOI: http://dx.doi.org/10.20534/ESR-17-3.4-79-84
Melkumyan Anaid, Gubkin Russian State University of Oil and Gas PhD in Physics and Mathematics, the Department of Physics E-mail: amelkumyan6@gmail.com
Joint analysis of Unified State Exam results and academic performance of technical university students by methods of nonparametric statistics
Abstract: The results of statistical data processing of the Unified State Exam (USE) scores, outcomes of university entrance control of school knowledge and academic performance of the first- and second-year students are analyzed in the article.
Methods of nonparametric statistics are used to assess the relationship between variables and the capacity of USE scores to predict the academic performance at university.
Keywords: engineering education, Unified State Exam, academic performance, nonparametric statistics.
1. Introduction.
Problems of modern engineering education in Russia have been studied in many papers [3; 11; 14]. It is noted not only a decrease in the number ofstudents in technical specialties [2], but also a deterioration in the quality ofengineering education [1].The quality ofengineer-ing education is related not only to the quality of teaching and knowledge control at university, but also with the level of students' preparation to the study of technical disciplines. Students of technical universities should have a basic knowledge of physics and mathematics and be able to use it actively. Accumulated data on students admitted to universities by USE results allows answer the question whether Unified State Exam an adequate assess of the student's academic potential. Various mathematical methods are used for processing and analysis oflarge data samples on USE scores, results of entrance control of knowledge and academic performance ofstudents at technical universities [9; 10]. The study [8] has shown that USE scores explain an average of 25-30% on the higher education progress scale, which is a rather high indicator, since academic progress is determined by a great number offactors apart from preliminary examinations. As applicants are ranked and selected by their USE scores, it is implied that students with higher scores are more talented and thus should demonstrate higher academic achievements after enrollment. Besides, the system is designed to select high school graduates based on their total USE scores in specific subjects required for admission. Therefore, it is expected that further performance is predicted equally in all subjects. The research using methods of regression analysis to assess how preliminary examinations (both composite USE scores and scores in specific subjects) affect academic performance in higher education have been provided at for about 19,000 students enrolled at five Russian universities of different profiles. The obtained results allow conclude the predictive capacity ofcomposite USE scores is high enough to accept this examination as a valid applicant selection tool. In the same time it has been found that USE scores in mathematics and Russian are better predictors of grades in almost all of the academic fields and, conversely, USE scores in field-specific subjects often appear to be poorly related to performance at university. The results of econometric study on predicting first-year average grades and dropout probability with USE scores are also presented in the paper [12]. Regression methods allow to conclude that using a sum of four exams — math, social studies, Russian language and foreign language — gives less accurate predictions than a sum of three exams, excluding foreign language. In models with separate exams as predictors, the greatest effect on dependent variable provides math grades. It should be noted that according to [16] 100-point scales for different subjects are inherently inconsistent. USE scores can be compared directly neither across subjects nor within one subject across different years. As regard to how long the impact of USE scores on the academic success is preserved, data on students of the first, second and third years has been analyzed and significance ofUSE results for prediction ofacademic performance and dropout probability after 2 or 3 years of study has been proved [17]. Analysis of changing correlation strength between USE scores and academic performance of first-year students through 2010 to 2014 has shown the decreasing of correlation in 2010-2012 and increasing in 2013-2014 [7]. With regard to decrease ofcorrelation, new techniques ofbypassing the requirements of the USE were created and developed every year. The violations include disseminating exam questions before the examination, using mobile phones (for Internet searches or SMS), receiving help from the onsite proctors, and reopening sealed test en-
velopes to correct mistakes [5]. Video cameras used during the USE from 2013 and control over Internet resources from 2014 have resulted the increase of the correlation. The statistically significant correlation between the USE results and academic performance allows identify groups "at risk" among first-year students [13]. Timely identification of first-year students that may potentially have low academic performance enables to organize early tutoring, counseling, training for these students. Monitoring academic performance and USE scores allows solve the problems of educational process associated with a varied approach to different groups of students, identifying violations and abuses, or, on the contrary, the positive effect of initiatives and interventions.
2. Methods and data.
Outcomes of a joint statistical analysis of USE scores, results of entrance control of school knowledge and students' academic performance are presented in this study. The analysis requires processing of large data sets taking into account the character of collected data. The raw data are often encoded in an ordinal or a nominal scale and their distribution significantly differs from the normality. Statistical techniques known as nonparametric statistics (or distribution free statistics because they make no assumptions about the distribution of the data) has been applied [4; 6; 15]. The methods include: computing Kolmogorov-Smirnov statistics to test whether the data fits a normal distribution; estimating quartiles of distributions; calculating Wilcox-on rank sum test and Kruskal-Wallis H test for testing the hypothesis that several groups have the same median; measuring the correlation with Spearman's rank-order coefficient; drawing histograms and box plots. With regard to the regression analysis, the method of logistic regression has been used for a prediction of a binary dependent variable and for capacity estimation of ordinal variables.
Data on USE scores on Physics, Mathematics and Russian language; results of Entrance Control of school knowledge on Physics and Academic Performance on Physics and Mathematics in the first and second semesters had been collected; Data Bases were created and the data has been processed. Data Base DB1 contains information about students of Mechanical Engineering Faculty. It contains six ordinal variables: USE scores on Physics, Mathematics and Russian language; Semester Rating, Examine Rating and Grade on Physics in the first semester. There are three nominal variables in DB1: Specialty, Gender and Admission to the Exam on Physics in the first semester. Semester Rating is the result ofknowledge control during the semester coded from 0 to 60 via 1. Exam Rating is coded from 0 to 40 via 1. Variable "Rating" obtained as a sum of Semester Rating and Exam Rating is used as the key Academic Performance indicator. Variable "Grade" is obtained from Rating according to the rule: from 0 to 49 -"fail", from 50 to 69 - "satisfactory", from 70 to 84 - "good", from 85 to 100 - "excellent" Admission to the Exam (0 - fail, 1 - success) is depended on the Semester Rating and results of laboratory works.
Data Base DB2 contains the information about students of six engineering Faculties: Petroleum Geology and Geophysics (Geology); Reservoir Engineering (Reservoir); Pipeline Engineering, Construction and Operation (Pipeline); Mechanical Engineering (Mechanical); Chemical and Environmental Engineering (Chemical); Automation and Computing Engineering (Computing). DB2 contains seven ordinal variables: USE scores in Physics and Mathematics; results of Entrance Control of school knowledge on Physics; Rating on Physics and Mathematics in the first and the second semesters. Entrance Control of school knowledge on Physics is
carried out for students of all engineering faculties except Chemical and requires resolving five simple problems from school program. There are four nominal variables in DB2: Faculty; Gender; Type of Admission (Budget - sponsored by State, Target - sponsored by Company, Contract - students pay tuition); Region of student's high school graduation (Central District, South District, Volga Region, Ural, Siberia, Far East, North Caucasus).
3. Results and discussion.
We have conducted a logistic regression analysis to predict the probability of getting the Admission to the Exam on Physics in the
first semester, using students' USE scores on Math, Physics and Russian language. The accuracy ofprediction is estimated by a parameter "sensitivity" obtained through dividing the number of confirmed outcomes by the number of all observed outcomes in the control group. Maximum of sensitivity has been obtained in prediction model using a sum of two exams: Physics and Russian language. In models with separate exams as predictors, USE scores on Physics have the greatest effect on the dependent variable. The latter is confirmed by Spearman rank-order coefficient estimations (Table 1). Median values of distributions of USE scores on Russian language are presented in Table 2.
Table 1. - Spearman rank -order coefficients between USE scores and Rating on Physics in the first semester, Mechanical Engineering Faculty
Unified State Exam Rating on Physics
Math Physics Russian
USE Math 1
USE Physics 0.4405 1
USE Russian 0.3063 0.3164 1
Rating on Physics 0.2759 0.5241 0.3214 1
Table 2. - Medians of distributions of USE scores on Russian language by categories of variable Grade on Physics in the first semester, Mechanical Engineering Faculty
USE scores on Russian language Grade on Physics in the first semester
fail satisfactory good excellent
min 73 65 71 70
median 87 84 84 82
max 100 98 100 90
Analysis of Table 2 and calculating the Kruskal-Wallis H test reveal that USE scores on Russian is significantly less for higher categories of variable "Grade". The share of students for whom the difference between the USE scores on Russian and on Physics is more than +20 points is about 40% of all students on the faculty. Most of these students had not been admitted or failed the exam on Physics in the first semester (Table 3). These results are confirmed by author's experience during teaching Physics at the Preparatory Courses of the University. Some students even had not attempted to solve problems of the second part of USE on Physics by declaring: "I find it easier to get high USE scores on Russian language than
to learn solving problems on physics". They were admitted to the university by the sum of three Unified State Exams (Math, Physics, Russian) and have not been able to perform the program on Physics in the first semester.
Results of Internal Control (IC) of students' knowledge in the university include Entrance Control and Academic Performance presented by variable "Rating" as a key indicator. In accordance with the generally accepted methodology for ordinal data, we assessed the relation between USE scores and results of Internal Control through measuring the correlation with Spearman's rank-order coefficient (Table 4).
Table 3. — Grades on Physics in the first semester and differences between USE scores on Russian language and Physics
Difference between USE scores in Russian language and Physics Grade on Physics in the first semester
Failed or not admitted to exam Satisfactory Good or excellence
> 20 54% 34% 12%
< 20 35% 33% 32%
Table 4. - Spearman's rank-order coefficients for USE scores and Internal Control results on Physics for students of five engineering faculties
Physics USE scores Entrance Control Rating 1st semester Rating 2 semester
Unified State Exam 1
Entrance Control 0.482 1
Rating 1st semester 0.395 0.574 1
Rating 2nd semester 0.315 0.566 0.777 1
The calculations were made for five engineering faculties (except Chemical). With a level of 0.05 we rejected the null hypothesis that USE and Internal Control scores are unrelated. It has been found that there is the tight correlation (0.777) of the Academic Performances in the first and second semesters. The correlation ofvari-ables "Rating" with variable "Entrance Control" (0.574/0.566) is stronger than with variable "USE scores" (0.395/0.315). Using
Chaddock scale of correlation tightness, we could say that the correlation between USE scores and results of Entrance Control is moderate, the correlation between results of Entrance Control and Semester Rating is salient, and the correlation between Ratings in the first and the second semesters is high.
Thus, the Entrance Control results are evaluating student's potential to study physics at university better than USE scores. The strong
correlation between the variables Rating 1 and Rating 2 confirms the sustainability and the fairness of assessment of students' knowledge of physics at university. Wilcoxon rank sum test reveals zero's shift between the distributions of the two variables. Hereinafter we are using the variable Rating 1 with the name "Rating" as an assessment of academic performance. Box plots of USE scores and IC results for
engineering faculties are represented on Fig. 1. The most significant disagreement between USE and IC is obtained for Pipeline Faculty, the best agreement - for Computing Faculty (Fig. 2). Perhaps it is due to the geography of student's high school graduation - in this sample the majority of students on Computing Faculty are from Moscow, on Pipeline faculty - from various regions of Russia.
Figure 1. USE scores and Internal Control results (the first semester of studying Physics)
Figure 2. USE scores and Rating points on Physics in the first semester
May be the situation on Pipeline Faculty is due to the fact that students from other regions should be adapting to life in Moscow during the first semester and have additional difficulties in their study. May be students on the Computing Faculty better learn math, and by their choice of specialty, are more interested in getting knowledge and problem-solving skills on physics. The majority of engineering students had been studying physics at school only for successful passing USE. Their motivation for obtaining
Table 5. - Contingency table of USE scores and Rating
deep knowledge and aspiration to learn solving problems, as a rule, are not great.
Contingency table (Table 5) with USE scores and Rating on Physics in the first semester reveals significant difference between the results of internal and external controls for students with the highest USE results: 40% of students with USE scores more than 80 got grades on Physics for the first semester "failed" or "satisfactory".
on Physics for Computing and Geological faculties
USE scores on Physics Rating on Physics at the first semester
0-59 60-79 80-100 SUM
0-59 65% 31% 4% 100%
60-79 59% 23% 18% 100%
80-100 40% 26% 34% 100%
It is not always like the results associated with fraud or violations of the USE. The gap between technical universities requirements and skills acquired at school is great and it is growing every year. It does not apply to special physical and mathematical schools but regular schools deliver students having neither sufficient theoretical knowledge nor ability to solve practical problems. The majority of high school students are performing only the first part of USE on physics, which is
not focused on solving problems, but is consisted of simple questions. It is not preparing students for studying physics in technical universities. As an example, author's observations of students of Chemical faculty (not required passing USE on physics) and Mechanical faculty (required positive scores of USE on physics). In the first semester most students of Chemical faculty were confused and scared, but they regularly attended special additional classes, learned to solve problems and
as a result in the second semester they passed the exam in physics with average rating better than students of Mechanical faculty.
Additional difficulties in the process of studying physics are caused by a low level of mathematical knowledge and the lack of
basic mathematical skills of students. Tables 6, 7 show values of Spearman rank-order correlation coefficients calculated for USE scores and Rating in the first semester of mathematics and physics for Mechanical and Computing faculties.
Table 6. - Spearman's rank-order correlation coefficients for USE scores and Rating on Physics and Mathematics for Mechanical faculty (N = 350 students)
N = 350 USE Physics USE Math Rating Physics Rating Math
USE Physics 1
USE Math 0.570 (2) 1
Rating Physics 0.403 (1) 0.382 (1) 1
Rating Math 0.379 (1) 0.411 (1) 0.793 1
Table 7. - Spearman's rank-order correlation coefficients for USE scores and Rating on Physics and Mathematics for Computing faculty (N = 200 students)
N = 200 USE Physics USE Math Rating Physics Rating Math
USE Physics 1
USE Math 0.627 (2) 1
Rating Physics 0.439 (1) 0.503 (1) 1
Rating Math 0.450 (1) 0.438 (1) 0.593 (2) 1
Calculating the significance test for Spearman rank-order correlation coefficients reveals that the variables are truly related in the populations with a level of 0.05. Statistical significance of differences between the correlation coefficients was tested using z-statistics with a level of 0.05. Correlation coefficients not significantly different from each other are marked with the same indices in the tables. According to Chaddock scale, the correlation between Rating on Mathematics and Rating on Physics is high for Mechanical faculty (0.793) and salient for Computing faculty (0.579); the correlation between USE
scores on these subjects is salient (0.570 and 0.627 resp.); the correlation between USE scores and rating for both subjects and both faculties is moderate. So we can conclude that the academic performance in two subjects is in good agreement and the same could be said about USE scores in these subjects. But the relationship between USE scores and Rating on Physics and Mathematics is significantly weaker.
Table 8 shows values of medians of distributions of USE scores and Rating on physics by classes of variable "Type of Admission" for three engineering faculties (Reservoir, Mechanical, Pipeline).
Table 8. - Medians of distributions of USE scores and Rating on Physics in the first semester for various values of variable "Types of Admission"
TYPE of ADMISSION F A C U L T Y
Reservoir Mechanical Pipeline
USE Rating USE Rating USE Rating
Budget 81 70 73 63 77 70
Target 57 64 52 53 61 56
Contract 54 54 53 50 50 50
Calculating Wilcoxon rank sum test, we have rejected the null hypothesis that the mean of the differences between the pairs is null. So, the medians have significantly different values for different types of admission. The largest gap between USE scores and Rating is observed for the Budget form of education, that is, for high USE scores. This is consistent with results of contingency tables (Table 5) and once again points to the need for careful checks to bad matching of high USE scores and poor academic performance at university.
With regard to the Regional factors, calculations show that students from Volga Federal District have the maximum median value for the USE scores (70) and Rating on physics in the first semester (70) and the minimal difference between them (0). The biggest difference (20) between the median values for the USE scores (70) and Rating on physics in the first semester (50) have students from the North Caucasus Federal District. These results are confirmed by the experience of author on Preparatory Courses for USE on physics in different regions of Russia including Volga Region and North Caucasus.
Conclusion
Nonparametric statistical methods take into account the specifics of the processed data — discrete variables encoded in an ordinal or a nominal scale; distribution does not fit the normal
law. Carried out with the help of these methods, data processing allows to:
1. test statistical significance for correlation and estimate the strength/direction of relationship between two variables;
2. calculate medians of the variable for different grades of factor;
3. compare medians of set of variables and test the hypothesis that several groups have the same median;
4. evaluate the predictive ability of individual variables and their combinations;
5. predict the value of a dependent dichotomous variable using a set of independent variables.
Data on the USE scores, results of entrance control of school knowledge and academic performance of the first- and second-year students were processed using these methods. The processing of the data included:
1. prediction of dichotomous variable "Admission to the Exam in Physics" with a method of binary logistic regression;
2. estimation ofprediction capacity ofvariables: USE scores on Physics, Mathematics, Russian language and their combinations, — to predict the Grade on Physics in the first semester;
3. calculation of rank-order correlation coefficients between USE scores on Physics, Mathematics, Russian language and Rating on Physics in the first semester (table 1);
4. estimation of medians of USE scores on Russian language for different values of Grade on physics in the first semester (tables 2, 3);
5. calculation of rank-order correlation coefficients between the USE scores on Physics, results of Entrance Control on Physics and Rating on Physics in the first and second semesters (table 4);
6. calculation of a contingency table on USE scores on Physics and Rating on Physics in the first semester (table 5);
7. calculation of rank-order correlation coefficients between USE scores on Physics and Mathematics and Rating on Physics and Mathematics in the first semester (tables 6, 7);
8. calculation of medians of two variables: USE scores on Physics and Rating on Physics in the first semester, — for different grades of variable "Type of Admission to the university" (table 8) and variable "Region" (Federal District where student graduated high school).
The results of the calculations made it possible to draw the following conclusions:
1. Prediction of the dependent variable "Admission to Exam in Physics" lets to preselect the first-year students who could be not-admitted to the session because of their poor academic performance during the semester. It makes possible to arrange extra classes in advance to help these students in passing tests, doing laboratory works and preparing to exams.
2. Analysis of relationships between USE scores on Russian language and Rating on Physics in the first semester leads to the conclusion that this exam is not such a good tool for selection of technical university students. May be using of USE scores on Russian language with a weight less than weight of scores on Physics and
Mathematics will improve assessing of student's academic potential for engineering university.
3. Compare of strength of correlation between results of internal and external knowledge control revealed that Entrance Control (which is performed in the form of a control work and requires problem solving skills) estimates student's capacity to study physics at the university better than the USE.
4. Analysis of contingency tables for the USE scores on Physics and Rating on Physics in the first semester shows an unreliability of high scores (>80) for a large number of students. This may be due to violations of requirements of the USE or because currently the USE variants are not good enough to prepare student for the physics course in engineering university.
5. Analysis of the difference between the USE scores and Rating in the first semester for various factors (Type ofAdmission, Region) lets to reveal groups of freshmen who do have problems of the first-year studying (domestic, social, psychological). Solving these problems helps students adapt more quickly to their studies in the university and protects them from academic failures. Results of this analysis help to highlight areas where the school is successfully preparing students for studies at technical university (Volga Region), and areas where the USE is performed with violations (in our case, North Caucasus).
6. Monitoring of academic performances on Physics and Mathematics on the first and second courses and of their connection with USE scores in these subjects enables to answer the question of how long USE results have an impact to academic achievements of students.
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