METHODS OF MATHEMATICAL STATISTICS AS A MEANS OF PROFESSIONAL COMPETENCE FORMATION OF STUDENTS-ECOLOGISTS

Introduction. Today, the worsening conditions of the human habitat are generating considerable interest in terms of the active development of the system of ecological education and education of the population. Special requirements in modern conditions are imposed to the qualification and competence of environmental professionals: to possess the skills for independent collecting reliable ecological information and to be able to analyze it by means of rigorous mathematical calculations; to perform necessary measurements and calculations within observations and experiments; to choose and to competently realize an adequate algorithm or a mathematical method for the solution of a specific ecological task; to make evidence-based forecasts of changes of environmental conditions. The aim of this publication is to reveal the potential of mathematical statistics methods application for the professional competencies formation of future ecologists. Methodology and research methods. Methodological framework of the research is made up of a competency-based approach to the preparation of high school specialists. The analysis of existing regulations and academic material sources focused on application of mathematical statistics methods for future ecologists’ training was carried out. The experience of such training in different universities of Russia was summarized. Results and scientific novelty. The main methodological and organizational problems in the training of environmental students in statistical data analysis are revealed: orientation of the existing training programs and methods of professional education towards the “average” student; insufficient quantity of professionoriented study guides; large volume of statistical information, necessary for studying, and limitation of temporary opportunities for its understanding and evaluation; a lack of future ecologists’ experience on application of mathematical statistics toolkit; etc. The conditions for the solution of these problems are planned: careful selection of professionally significant content of the academic discipline “Mathematics”; providing an optimum balance between mathematical tasks and theoretical material; training of students in competent interpretation of the received mathematical results in the context of ecology; efficient use of software in educational process. A number of the general methodical provisions which should be observed in mathematical statistics teaching are formulated to achieve a positive effect. The importance of a regional component of professional training of ecologists is emphasized. Detailed consideration of using the system of specially formulated tasks of a professional environmental orientation, in particular, based on official material sources on monitoring data of the Kirov region environment, is given. The possible directions of students’ independent research work organization in the study of mathematical statistics are presented. The ways for providing and strengthening of interdisciplinary and intersubject relations are highlighted. Practical significance. The results of the study can be used to improve the content of the academic discipline “Mathematics” included in education programs for ecological specialties.

1. Kasimov N. S., Popova L. V., Romanova E. P. Standards of higher professional environmental education in the direction “Ecology and Nature”. Vestnik Mi-ninskogo universiteta = Vestnik of Minin University [Internet]. 2015 [cited 2017 Nov 10]; 2. Available from: http://vestnik.mininuniver.ru/jour/article/view/36 (In Russ.)

2. Ivanova T. A., Perevoshchikova E. N., Kuznetsova L. I., Grigorieva T. P. Teoriya i tekhnologiya obucheniya matematike v sredney shkole = Theory and technology of teaching mathematics in high school. Nizhniy Novgorod: Nizhny Novgorod State Pedagogical University; 2009. 355 p. (In Russ.)

3. Bart A. G., Verbitskaya E. V., Solntsev V. N. On the state of affairs and perspectives of teaching statistical analysis of medical data. Mezhdunarodnyy zhurnal meditsinskoy praktiki = International Journal of Medical Practice. 2006; 2: 39–41. (In Russ.)

4. Varaksin A. N. Statistical analysis of biological and medical information: Problems and solutions. Mezhdunarodnyy zhurnal meditsinskoy praktiki = International Journal of Medical Practice. 2006; 2: 35–39. (In Russ.)

5. Vershinin V. I. Planirovanie i matematicheskaya obrabotka rezul’tatov hi-micheskogo eksperimenta = Planning and mathematical processing of the results of a chemical experiment. St.-Petersburg: Publishing House Lan’; 2017. 236 p. (In Russ.)

6. Leonov V. P. Common problems with the use of statistics in biomedicine or what is more reasonable: DAPP or DAPD? Jelektronnyj zhurnal Biometrika = Biometrics Online Journal [Internet]. 2015 [cited 2017 Oct 19]. Available from: http://www.biometrica.tomsk.ru/problem.htm (In Russ.)

7. Trukhacheva N. V. Matematicheskaya statistika v mediko-biologicheskikh issledovaniyakh s primeneniyem paketa Statistica = Mathematical statistics in biomedical research using the Statistica package. Moscow: Publishing House GEOTAR-Media; 2013. 384 p. (In Russ.)

8. Heiman G. W. Basic Statistics for the Behavioral Sciences [Internet]. Belmont, CA: Wadsworth Cengage Learning, 2011 [cited 2017 Nov 29]. 468 p. Available from: http://file.zums.ac.ir/ebook/352-Basic%20Statistics%20for%20the%20 Behavioral%20 Sciences,%206th%20Edition-Gary%20Heiman-0840031432-Wadsworth%20Pu.pdf

9. Lang T., Altman D. Basic statistical reporting for articles published in clinical medical journals: the SAMPL Guidelines. In: Smart P., Maisonneuve H., Pol-derman A. (eds). Science Editors’ Handbook, European Association of Science Editors [Internet]. 2013 [cited 2017 Nov 27]. Available from: http://www.equator-network.org/2013/03/20/basic-statistical-reporting-for-articles-published-in-biomedical-journals-the-statistical-analyses-and-methods-in-the-published-literature-or-the-sampl-guidelines/

10. Yusof Z. M., Abdullah S., Yahaya S. S. S., Othman A. R. A robust alternative to the t – Test. Modern Applied Science [Internet]. Published in Canadian Center of Science and Education. 2012 [cited 2017 Nov 29]: 5 (6): 27–33. Available from: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1014.7331 &rep= rep1&type=pdf

11. Leyzerman Zh. B. O prepodavanii teorii veroyatnostey i matematicheskoy statistiki na nematematicheskikh fakul'tetakh = On the teaching of probability theory and mathematical statistics at non-mathematical faculties [Internet]. [cited 2018 Jan 17]. Available from: http://geum.ru/next/art-215119.php (In Russ.)

12. Bakumenko L. P., Korotkov P. A. Statistical analysis of the influence of drinking water quality on population health in the region. Prikladnaya ekonometrika = Applied Econometrics. 2011; 2: 32–47. (In Russ.)

13. Bavrin I. I. Matematicheskaya obrabotka informatsii = Mathematical processing of information. Moscow: Publishing House Prometey; 2016. 262 p. (In Russ.)

14. Toropova S. I. Correlation and regression analysis in the training of future ecologists. Byulleten’ laboratorii matematicheskogo, estestvennonauchnogo ob-razovaniya i informatizatsii: materialy Mezhdunarodnoy nauchno-prakticheskoy konferentsii = Bulletin of the Laboratory of Mathematical, Natural Science Education and Informatization. Materials of the International Scientific and Practical Conference; 2015 Oct 22–23; Samara. Samara; Moscow: Samara Branch of Moscow City University; 2015. p. 390–400. (In Russ.)

15. Toropova S. I. Multiple correlation and regression analysis in professional training future ecologists. Prepodavaniye matematiki, fiziki, informatiki v vuzakh I shkolah: problem soderzhaniya, tekhnologii I metodiki: Materialy V Vserossiyskoy nauchno-prakticheskoy konferentsii = Teaching of Mathematics, Physics, Computer Science in Universities and Schools: Problems of Content, Technology and Methodology. Materials of the V All-Russian Scientific and Practical Conference; 2015 Dec 18–19; Glazov. Glazov: Glazovskaya tipografiya; 2015. p. 137–142. (In Russ.)

16. Toropova S. I. Regression models as a tool for analysis and forecasting of environmental phenomena. Matematicheskiy vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona = Mathematical Bulletin of Pedagogical Universities and Universities of the Volga-Vyatka Region. 2016; 18: 213–219. (In Russ.)

17. Kremer N. Sh. Teoriya veroyatnostey i matematicheskaya statistika = Theory of probability and mathematical statistics. Moscow: Publishing House YUNITI-DANA; 2006. 573 p. (In Russ.)

18. Toropova S. I. The peculiarities in the study of analysis of variance in mathematics lessons with students-ecologists. In: Aktual'nyye problemy razvitiya matematicheskogo obrazovaniya v shkole i vuze: materialy IX mezhdunarodnoy nauchno-prakticheskoy konferentsii = Actual Problems of the Development of Mathematical Education in School and University. Materials of the IX International Scientific and Practical Conference; 2017 Oct 17–18; Barnaul. Barnaul: Altai State Pedagogical University; 2017. p. 114–118. (In Russ.)

19. Toropova S. I. The organization of research activity of students-ecologists at the final stage of work with the task. Matematicheskiy vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona = Mathematical Bulletin of Pedagogical Universities and Universities of the Volga-Vyatka region. 2017; 19: 179–182. (In Russ.)

20. Brereton R. G., Jansen J., Lopes J., Marini F., Pomerantsev A., Rodionova O., et al. Chemometrics in analytical chemistry – part I: history, experimental design and data analysis tools. Analytical and Bioanalytical Chemistry [Inter-net]. 2017 [cited 2017 Nov 29]; 25 (409): 5891–5899. Available from: http://link.springer.com/article/10.1007/s00216–017–0517–1

21. Yelagina V. S. Formation of research competence in the process of professional training of students of a pedagogical university. Koncept = Concept [In-ternet]. 2012 [cited 2018 Jan 19]; 8 (Aug): 26–30. Available from: http://www.co-venok.ru/koncept/2012/12102.htm (In Russ.)

22. Puzachenko Yu. G. Matematicheskiye metody v ekologicheskikh i geog-raficheskikh issledovaniyakh = Mathematical methods in environmental and geographical research. Moscow: Publishing House Akademija; 2004. 416 p. (In Russ.)

23. Molchanova Ye. V., Kruchek M. M. Mathematical methods for assessing the factors affecting the health status of the population in the regions of Russia (panel analysis). Sotsial'nyye aspekty zdorov'ya naseleniya = Social Aspects of Health of Population [Internet]. 2013 [cited 2017 Oct 19]; 5 (33). Available from: http://vestnik.mednet.ru/content/view/513/30/ (In Russ.)

24. Zaripov Sh. Kh. Vvedeniye v matematicheskuyu ekologiyu = Introduction to mathematical ecology. Kazan: Kazan Federal University; 2010. 47 p. (In Russ.)