Glazov, Izhevsk, Russian Federation
BISAC EDU000000 General
The article offers the method for assessing the complexity of mathematical reasoning in various educational texts. It provides for counting the number of mathematical statements (or other elementary judgments) in the conclusions being drawn and taking into account the semantic complexity of the terms denoting the quantities included in the formulas. This allows to calculate the heuristic complexity of the text, depending on the number and complexity of mathematical conclusions, and find the heuristic indicator. To determine the semantic complexity of the entire text and the mathematical reasoning presented in it, a computer is used, which refers to a dictionary-thesaurus – a special file containing terms with an indication of their complexity. This takes into account the volumetric complexity of the formulas, the number of elementary sentences (equations) in mathematical reasoning, as well as the fact that some premises (formulas) are absent, and the pupil must guess before them on his own. Several examples of using the proposed method for analyzing text fragments in physics are considered.
didactics, semantic information, complexity, text, textbook, formula, heuristics
1. Gel'fman E.G., Kholodnaya M.A. Psikhodidaktika shkol'nogo uchebnika. Intel-lektual'noe vospitanie uchashchikhsya [School textbook psychodidactics. Intellectual education of students]. St. Petersburg: Piter Publ., 2006. 384 p.
2. Getmanova A.D. Logika [Logic]. Moscow: KnoRus Publ., 2016. 236 p.
3. Mayer R.V. Metod otsenki slozhnosti logicheskikh rassuzhdeniy [Method for as-sessing the complexity of logical reasoning]. Nauchnye issledovaniya i razrabotki. Sotsial'no-gumanitarnye issledovaniya i tekhnologii [Research and Development. Social and humanitarian research and technology]. 2020, I. 3 (32), pp. 35-40.
4. Mayer R.V. Otsenka didakticheskoy slozhnosti dokazatel'stva teorem shkol'nogo kursa geometrii [Assessment of the didactic complexity of proving theorems in a school geometry course]. Standarty i monitoring v obrazovanii [Standards and moni-toring in education]. 2020, I. 1, pp. 29-35.
5. Mayer R.V. Didakticheskaya slozhnost' uchebnykh tekstov i ee otsenka [Didactic complexity of educational texts and its assessment]. Glazov: GGPI Publ., 2020. 149 p.
6. Mikk Ya.A. Optimizatsiya slozhnosti uchebnogo teksta: V pomoshch' avtoram i redaktoram [Optimization of the complexity of educational text: To help authors and editors]. Moscow: Prosveshchenie Publ., 1981. 119 p.
7. Mikheeva S.A. Sistema formalizovannykh kriteriev otsenki shkol'nogo uchebnika [The system of formalized criteria for assessing a school textbook]. Voprosy obra-zovaniya [Education Issues]. 2015, I. 4, pp. 147-183.
8. Myakishev G.Ya., Bukhovtsev B.B., Charugin V.M. Fizika 11 klass: ucheb. dlya obshcheobrazovat. Organizatsiy [Physics grade 11]. Moscow: Prosveshchenie Publ., 2019. 432 p.
9. Naumov I.S., Vykhovanets V.S. Otsenka trudnosti i slozhnosti uchebnykh zadach na osnove sintaksicheskogo analiza tekstov [Assessment of the difficulty and com-plexity of educational tasks based on the syntactic analysis of texts]. Upravlenie bol'shimi sistemami [Management of large systems]. 2014, I. 48, pp. 97-131.
10. Fedorov B.I. Formal'no-logicheskoe predstavlenie voprosno-otvetnykh struktur nauchnogo znaniya [Formal-logical representation of question-answer structures of scientific knowledge]. Logiko-filosofskie shtudii [Logical and philosophical studies]. 2010, I. 8, pp. 5-19.
11. Fizika 11 klass: ucheb. dlya obshchebrazovat. uchrezhdeniy i shk. s uglubl. izucheniem fiziki: profil. uroven' [Physics grade 11: textbook. for general education. institutions and schools. with deepening the study of physics: profile. level]. Moscow: Prosveshchenie Publ., 2011. 416 p.
12. Cherneyko L.O. Lingvofilosofskiy analiz abstraktnogo imeni [Linguophilosophi-cal analysis of an abstract name]. Moscow: LIBROKOM Publ., 2010. 265 p.
13. Shalak V.I. Sovremennyy kontent-analiz. Prilozheniya v oblasti: politologii, psikhologii, sotsiologii, kul'turologii, ekonomiki, reklamy [Modern content analysis. Applications in the field of: political science, psychology, sociology, cultural studies, economics, advertising]. Moscow: Omega-L Publ., 2004. 272 p.
14. Checkland P., Scholes J. Soft System Methodology in Action. John Wiley & Sons Ltd. - 1990. - 346 p.
15. White M.D., Marsh E.E. Content analysis: A flexible methodology // Library trends. - 2006. - Vol. 55. - I. 1. - pp. 22-45.
