Applied statistics to evaluate the quality of education

N. A. Bure ; N. L. Grebennikova ; K. Yu. Staroverova

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 4, pp. 325-333

Résumé

The application of statistical methods and machine learning to analyze the data describing the education process are considered. The solution of two problems typical of the educational process but different in the organization is shown. The first problem is to analyze the results of students' tests who study Russian as a foreign language to enter the university in Russia. The purpose of the analysis is to evaluate the adequacy of the teaching methods, in particular, the consistency of results gained for the elementary and intermediate tests with the result obtained for the advanced test. Data is transformed firstly, then the analysis of variance is conducted, finally, the clustering is built. Found structure shows that students successfully coping with elementary and intermediate tests are likely to pass the advances level test. In the second problem, the results of studying mathematics by junior pupils are analyzed. Classification of pupils is made based on their marks gained for the answer in the lesson. The classifier determines the pupil mark for the final control work. The predictive model is built as the ensemble of random forests trained on four samples: the first is a sparse matrix of estimates, the others are the transformation of the first obtained by principal component analysis within a nuclear structure.

Détail

Keywords: statistics, random forest, clustering, the methodics of studying Russian language and mathematics, the analysis of education progress.

Bibliographie

[1] Gurova G., Piattoeva N., Takala T., “Quality of education and Its evaluation: an analysis of the Russian Academic Discussion”, European Education, 47:4 (2015), 346–364 | DOI

[2] About forms of state testing on russian lunguage as foreign language, Order of RF ministry of education dated 18.06.2017 N 667, M., 2017 (In Russian)

[3] Andryushina N. P., Bitehtina G. A., Ivanona A. S. et al., Requirements on level of Russian as foreign language proficiency. I certification level. General skills, 2nd ed., Zlatoust Publ., M.–SPb., 2009, 32 pp. (In Russian)

[4] Vladimirova T. E., Nahabina I. I., Soboleva N. I. et al., State educational standart on Russian as foreign language. Elementary level, 2nd ed., Zlatoust Publ., M.–SPb., 2001, 28 pp. (In Russian)

[5] Nahabina M. M., Soboleva N. I., Starodub V. V. et al., State educational standart on Russian as foreign language. Basic level, 2nd ed., Zlatoust Publ., M.–SPb., 2001, 32 pp. (In Russian)

[6] Andryushina N. P., Bitehtina G. A., Vladimirova T. E. et al., Programm on Russian language for foreigners. The first certification level. General skills, Zlatoust Publ., M.–SPb., 2001, 176 pp. (In Russian)

[7] Kapitonova T. I., Moskovkin L. V., Methodology of teaching Russian as foreign language pre-university education, Zlatoust Publ., SPb., 2006, 360 pp. (In Russian)

[8] Esina Z. I., Ivanova A. S., Soboleva N. I. et al., Educational programm on Russian as foreign language. Elementary level. Basic level. The first certification level, M., 2001, 134 pp. (In Russian)

[9] Bartlett M. S., “Properties of sufficiency and statistical tests”, Proceedings of the Royal Statistical Society. Series A, 160 (1937), 268–282

[10] Raykov Y. P., Boukouvalas A., Baig F., Little M. A., “What to do when $K$-means clustering fails: A simple yet principled alternative algorithm”, PLoS ONE, 11:9 (2016), 28 | DOI

[11] Grebennikova N. L., Methods and approaches to deal with nonstandard problems, Sterlitamakskaya gos. ped. akademia im. Zajnab Biishevoj, Sterlitamak, 2010, 310 pp. (In Russian)

[12] Grebennikova N. L., Koscova S. A., Training of future teachers of primary school to implement the standards of the second generation, Educational monograph, Sterlitamakskaya gos. ped. akademia im. Zajnab Biishevoj, Sterlitamak, 2012, 245 pp. (In Russian)

[13] Grebennikova N. L., Koscova S. A., “Modern technologies of primary mathematics education”, Proceedings of V International extramural scientific and practical conference “Education in spaces of school and adult school: experience, problems and perspectives” (Bashkortostan, Sterlitamak, 21 April 2016), Bashkir State University, Sterlitamak, 2016, 82–83 (In Russian)

[14] Hastie T., Tibshirani R., Friedman J., The elements of statistical learning: data mining, inference, and prediction, 2nd ed., Springer-Verlag, New York, 2009, 746 pp. | MR | Zbl

[15] Cohen J., “A coefficient of agreement for nominal scales”, Educational and Psychological Measurement, 20:1 (1960), 37–46 | DOI