Complex numbers in the school course of Mathematics and in the perspective model of the final exam
- 8
- Complex numbers in the school course of Mathematics and in the perspective model of the final exam
- Babenko A.S., Margolina N.L., Matytsina T.N., Smirnova A.O., Shiryaev K.E. Complex numbers in the school course of Mathematics and in the perspective model of the final exam. Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics, 2022, vol. 28, № 2, pp. 60-68. https://doi.org/10.34216/2073-1426-2022-28-2-60-68
- DOI: https://doi.org/10.34216/2073-1426-2022-28-2-60-68
- УДК: 372. 8:51
- Publish date: 2022-06-19
- Annotation: The article is devoted to the use of the concept of a complex number in a school Mathematics course. Until recently, the topic of complex numbers had not been included in the state final exam, however studied in classes with in-depth study of mathematics. In connection with the introduction of tasks related to this concept into the prospective model of the unified state exam, it is now becoming topical. The article primarily touches upon the analysis of the presentation of material in school textbooks, in particular the concept of a complex number. Then there are several examples of problem solving, which was presented in a promising model of the unified state exam in Mathematics, using both analytical and geometric interpretation of a complex number. In addition, various approaches to solving the problem are shown, both algebraic (estimation method) and geometric (finding the altitude in a triangle, similarity method, methods of analytical geometry) methods, as well as methods of mathematical analysis (finding the largest or smallest value using the derivative). The article also contains some methodological recommendations for preparing on this topic and a system of tasks that can be offered both to teachers in preparing for the exam, and to pupils to consolidate the skill of solving tasks of this type.
- Keywords: perspective model, complex numbers, algebraic form of complex number, state final certification, unified state exam.
- Literature list: Ageeva E.S., Matycina T.N., Shirjaev K.E. Neskol'ko slov ob osobennostjah prepodavanija teorii verojatnostej v shkole [A few words about the peculiarities of teaching probability theory at school]. Aktual'nye problemy prepodavanija informacionnyh i estestvenno-nauchnyh discipline: materialy XIV Vseros. nauch.-metod. konf. [Actual problems of teaching information and natural science disciplines: materials of the XIV All-Russian Scientific method. conf]. Kostroma, Kostromskoj gos. un-t Publ., 2021, pp. 109–112. (In Russ.) Algebra i nachala matematicheskogo analiza. 11 klass: ucheb. dlja obshheobrazovat. uchrezhdenij (bazovyj i profil. uroveni) [Algebra and beginning of mathematical analysis. Grade 11: textbook. for general education institutions: basic and profile. levels], S.M. Nikol'skij, M.K. Potapov, N.N. Reshetnikov, A. V. Shevkin. Moscow, Prosveshhenie Publ., 2009, 464 p. (In Russ.) Algebra i nachala matematicheskogo analiza. 11 klass: ucheb. dlja obshheobrazovat. uchrezhdenij (uglublennyj uroven') [Algebra and beginning of mathematical analysis. Grade 11: textbook. for general education institutions: advanced level], A.G. Merzljak, D.A. Nomirovskij, V.M. Poljakov. Moscow, Ventana-Graf Publ., 2019, 415 p. (In Russ.) Babenko A.S., Kuznecova V.S., Shirjaev K.E. Shkola i VUZ: periodicheskie funkcii i shodimost' nesobstvennyh integralov [School and university: periodic functions and convergence of improper integrals]. Aktual'nye problemy prepodavanija informacionnyh i estestvenno-nauchnyh disciplin: materialy XIV Vseros. nauch.-metod. konf. Kostroma, Kostromskoj gos. un-t Publ., 2021, pp. 10–13. (In Russ.) Babenko A.S., Margolina N.L., Matycina T.N., Shirjaev K.E. Matematicheskij analiz: perspektivy i trudnosti cifrovogo obuchenija [Mathematical analysis: prospects and difficulties of digital learning]. Aktual'nye tehnologii prepodavanija v vysshej shkole: materialy nauch.-metod. konf. [Actual technologies of teaching in higher education: materials of scientific method. conf.], ed. by G.G. Sokova, L.A. Isakova. Kostroma, Kostromskoj gos. un-t Publ., 2019, pp. 14–16. (In Russ.) Babenko A.S., Margolina N.L., Matycina T.N., Shirjaev K.E. Nekotorye rekomendacii k rukovodstvu samostojatel'noj rabotoj studentov po algebre i geometrii [Some recommendations for the guidance of independent work of students in algebra and geometry]. Aktual'nye tehnologii prepodavanija v vysshej shkole: materialy nauchno-metodicheskoj konferencii [Actual technologies of teaching in higher education: materials of scientific method. conf.], ed. by G.G. Sokova, L.A. Isakova. Kostroma, Kostromskoj gos. un-t Publ., 2019, pp. 130–132. (In Russ.) Babenko A.S., Margolina N.L., Matycina T.N., Shirjaev K.E. Obuchenie uchitelej matematiki v uslovijah vvedenija professional'nogo standarta [Education of teachers of mathematics in the context of the introduction of a professional standard]. Vestnik Kostromskogo gosudarstvennogo universiteta. Ser.: Pedagogika. Psihologija. Sociokinetika [Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics], 2020, vol. 26, № 4, pp. 154–160. (In Russ.) Babenko A.S., Margolina N.L., Matycina T.N., Shirjaev K.E. Organizacija samostojatel'noj raboty studentov pri izuchenii discipliny «Geometrija» [Organization of independent work of students in the study of the discipline «Geometry»]. Aktual'nye tehnologii prepodavanija v vysshej shkole: materialy nauchno-metodicheskoj konferencii [Actual technologies of teaching in higher education: materials of scientific method. conf.], ed. by G.G. Sokova, L.A. Isakova. Kostroma, Kostromskoj gos. un-t Publ., 2019, pp. 133–135. (In Russ.) Babenko A.S., Margolina N.L., Matycina T.N., Shirjaev K.E. Differencial'nye uravnenija, teorija verojatnosti, topologija i matematicheskaja logika: vozmozhnost' ob#edinenija v kurse vysshej matematiki [Differential Equations, Probability Theory, Topology and Mathematical Logic: The Possibility of Combining in Higher Mathematics Course]. Aktual'nye tehnologii prepodavanija v vysshej shkole: materialy nauchno-metodicheskoj konferencii [Actual technologies of teaching in higher education: materials of scientific method. conf.], ed. by G.G. Sokova, L.A. Isakova. Kostroma, Kostromskoj gos. un-t Publ., 2019, pp. 11–13. (In Russ.) Vilenkin N.Ja. Matematika: algebra i nachala matematicheskogo analiza, geometrija. Algebra i nachala matematicheskogo analiza. 11 klass: uchebnik dlja uchashhihsja obshheobrazovat. organizacij (uglublennyj uroven') [Mathematics: Algebra and Principles of Mathematical Analysis, Geometry. Algebra and beginning of mathematical analysis. Grade 11: a textbook for students of educational organizations (advanced level)], N.Ja. Vilenkin, O.S. Ivashev-Musatov, S.I. Shvarcburd. Moscow, Mnemozina Publ., 2014, 312 p. (In Russ.) Koljagin Ju.M. Algebra i nachala matematicheskogo analiza. 11 klass: ucheb. dlja uchashhihsja obshheobrazovat. uchrezhdenij (profil'nyj uroven') [Algebra and the beginnings of mathematical analysis. Grade 11: textbook. for general education students. institutions (profile level)], Ju.M. Koljagin, Ju.V. Sidorov, M.V. Tkacheva, N.E. Fedorova, M.I. Shabunin. Moscow, Mnemozina Publ., 2010, 264 p. (In Russ.) Mordkovich A.G. Algebra i nachala matematicheskogo analiza. 10 klass: v 2 ch. Ch. 1: Uchebnik dlja uchashhihsja obshheobrazovatel'nyh uchrezhdenij (profil'nyj uroven') [Algebra and the beginnings of mathematical analysis. Grade 10: in 2 p. Part 1: Textbook for students of educational institutions (profile level)], A.G. Mordkovich, P.V. Semenov. Moscow, Mnemozina Publ., 2009, 424 p. (In Russ.) Muravin G.K. Matematika: algebra i nachala matematicheskogo analiza, geometrija. Algebra i nachala matematicheskogo analiza. Uglublennyj uroven'. 11 klass: uchebnik [Mathematics: algebra and principles of mathematical analysis, geometry. Algebra and beginning of mathematical analysis (deep level). Grade 11: textbook], G.K. Muravin, O.V. Muravina. Moscow, Drofa Publ., 2014, 318 p. (In Russ.) Perspektivnye modeli KIM EGJe 2022 [Perspective models of KIM Unified State Examination 2022]. URL: https://4ege.ru/materials_podgotovka/60888-perspektivnye-modeli-kim-ege-2022.html (access date: 17.01.2022). (In Russ.) Pratusevich M.Ja. Algebra i nachala matematicheskogo analiza. 11 klass: ucheb. dlja obshheobrazovat. uchrezhdenij: profil. uroven' [Algebra and the beginnings of mathematical analysis. Grade 11: textbook for general education institutions: profile. level], M.Ja. Pratusevich, K.M. Stolbov, A.N. Golovin. Moscow, Prosveshhenie Publ., 2010, 463 p. (In Russ.) Primernaja osnovnaja obrazovatel'naja programma srednego obshhego obrazovanija [Exemplary basic educational program of secondary general education]. URL: https://fgosreestr.ru/ (access date: 17.01.2022). (In Russ.)