Herald
South Ural State Humanitarian Pedagogical University bulletin ЧГПУ

ISSN: 2618–9682
Impact factor RSCI: 0.236

BACK TO ISSUE CONTENT | HERALD OF CSPU 2018 № 3 PEDAGOGICAL SCIENCES
SHOW FULL TEXT (IN RUSSIAN)
SHOW IN eLibrary
DOI: 10.25588/CSPU.2018.03.06
UDC: 512.23
BBC: 22.43
M.M. Isakova ORCID
Candidate of Sciences (Physical and Mathematical), Associate Professor, Kabardino-Balkarian State University named after H.M. Berbekov (Nalchik, Russia)
E-mail: Send an e-mail
R.G. Tlupova ORCID
the teacher, Kabardino-Balkarian State University named after H.M. Berbekov (Nalchik, Russia)
E-mail: Send an e-mail
F.A. Erzhibova ORCID
the teacher, Kabardino-Balkarian State University named after H.M. Berbekov (Nalchik, Russia)
E-mail: Send an e-mail
A.S. Ibragim ORCID
Master, Kabardino-Balkarian State University named after H.M. Berbekov (Nalchik, Russia)
E-mail: Send an e-mail
Non — traditional methods of irrational equations decisions
Abstracts

Introduction. Mathematics, like other subjects of the general education profile, aims at raising the general intellectual level, special mathematical training, developing a creative approach to solving the questions posed. During the study and practical solution of the equations, there are ample opportunities to form intuition, increase the logic of thinking.

Materials and methods. An extensive part of the mathematics program at the college is devoted to the study of equations. A particular case of algebraic equations is irrational equations. Described unconventional methods for solving irrational equations are based on the application of the Cauchy and Bernoulli inequalities. Equations with complete solutions based on the use of the indicated inequalities are presented.

Results. The solutions of irrational equations are the most difficult for students, not only in logic, but also in engineering. Their undisputed solution largely predetermines the successful result of the profile level of the USE. The psychological and pedagogical conditions for mastering non-traditional ways of solving irrational equations are considered.

Discussion. The use of non-standard ways of solving irrational equations in the classroom helps to increase the scales of achievement, improve the level of mathematical logic.

Conclusion. Students who have mastered non-traditional ways of solving irrational equations will successfully cope with tasks of increased complexity. The presented material can be a help in the work of teachers of specialized mathematical classes and provide significant assistance to the students.

Keywords

equation, inequality, method, irrational equation, logic

Highlights
  • The main types of irrational equations are considered;
  • Characteristics of general methods for solving irrational equations are given;
  • Inequalities of Cauchy and Bernoulli are presented;
  • The non-traditional application of the Cauchy and Bernoulli inequalities to the solution of irrational equations is shown;
  • Analogues of equations with solutions included in the profile level of the USE are presented.
REFERENCES

1. Zhafyarov A.Zh. (2016) Metodologiya i tekhnologiya vnedreniya kompetentnogo podhoda v matematicheskom obrazovanii [Methodology and technology for introducing a competent approach in mathematical education] Vestnik Novosibirskogo gosudarstvennogo pedagogicheskogo universiteta. 3, 105–115. Available from: http://vestnik.nspu.ru/article/1823 [Accessed 25th March 2018]. DOI: 10.15293/2226-3365.1603.10 (In Russian).

2. Shahmejsster A.H. (2011) Irracional’nye uravneniya i neravenstva [Irrational equations and inequalities] Moscow, Petroglif, Viktoriyaplus, MCNMO Publ. (In Russian).

3. Krylov A.N. (1979) Znachenie matematiki dlya korablestroeniya [The value of mathematics for shipbuilding] Moi vospominaniya.Leningrad, Sudostroenie Publ. (In Russian).

4. Hajdegger M. (2007) Vremya i bytie: Stat’i i vystupleniya [Time and Being: Articles and speeches] Saint Petersburg, Nauka Publ. (In Russian).

5. Bashmakov M.I. (2013) Matematika. Sbornik zadach profil’noj napravlennosti [Mathematics. Collection of tasks of profile orientation] Moscow, Akademiya Publ. (In Russian).

6. Firsov V.V. (1989) Planirovanie obyazatel’nyh rezul’tatov obucheniya matematike [Planning of compulsory learning outcomes for mathematics] Moscow, Prosveshchenie Publ. (In Russian).

7. Zhafyarov A.Zh. (2017) Realizaciya tekhnologii vnedreniya kompetentnogo podhoda v shkol’nom kurse matematiki [Implementation of a technology for introducing a competent approach in the school course of mathematics] Vestnik Novosibirskogo gosudarstvennogo pedagogicheskogo universiteta. 2, 71–84. Available from: http://vestnik.nspu.ru/article/2363 [Accessed 25th March 2018]. DOI: 10.15293/2226-3365.1702.05 (In Russian).

8. Puankare A. (1989) Matematicheskoe tvorchestvo [Mathematical creativity] O nauke. Ed. L.S. Portnyagina. Moscow, Nauka Publ. (In Russian).

9. Poja D. (1959) Kak reshat’ zadachu [How to solve the task] Moscow, Gosuchpedgiz Publ. (In Russian).

10. Skanavi M.I. (2013) Sbornik zadach po matematike dlya postupayushchih vo vtuzy [Collection of tasks in mathematics for those who enter the vetuz] Moscow, Mir i Obrazovanie Publ. (In Russian).

11. Boltyanskij V.G., Sidorov Yu.V., Shabunin M.I. (1974) Lekcii i zadachi po ehlementarnoj matematike [Lectures and tasks on elementary mathematics] Moscow, Nauka Publ. (In Russian).

12. Vasilevskij A.B. (1988) Obuchenie resheniyu zadach po matematike [Training in solving tasks in mathematics] Minsk, Vyshehjshaya shkola Publ. (In Russian).

13. Yashchenko I.V., Shestakov S.A. (2018) EGEh – 2018. Matematika. Profil’nyj uroven’. Metodicheskie ukazaniya [USE – 2018. Mathematics. Profile level. Methodical instructions] Moscow, MCNMO Publ. (In Russian).

14. Batueva K.S., ZakirovaN.M. (2017) Irracional’nye uravneniya i neravenstva v shkol’nom kurse [Irrational equations and inequalities in the school course] Matematicheskij vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona.Kirov. Vol. 19 (316), 204–209. (In Russian).

15. Bashmakov M.I. (2017) Matematika. Uchebnik [Mathematics. Textbook] Moscow, KnoRus Publ. (In Russian).

16. Shabunin M.I. (2005) Uravneniya: lekcii dlya starsheklassnikov i abiturientov [Equations: lectures for high school students and applicants] Seriya «Matematika».Moscow, Chistye prudy Publ. (In Russian).

17. Bashmakov M.I. (2014) Matematika: algebra i nachalo matematicheskogo analiza, geometriya. Zadachnik [Mathematics: algebra and the beginnings of mathematical analysis, geometry. Taskbook] Moscow, Akademiya Publ. (In Russian).

18. Kalinin S.I. (2013) Metod neravenstv resheniya uravnenij: uchebnoe posobie po ehlektivnomu kursu dlya klassov fiziko-matematicheskogo profilya [The method of inequalities in the solution of equations: a tutorial on the elective course for classes of physics and mathematics] Moscow, Moskovskij licej. (In Russian).

19. Zhafyarov A.Zh. (2007) Obuchayushchij zadachnik. Matematika. 10–11 klassy. Profil’nyj uroven’ [Learning task book. Mathematics. 10–11 classes. Profile level] Moscow, Prosveshchenie Publ.
(In Russian).

20. Erina T.M. (2018) Matematika. Profil’nyj uroven’, prakticheskoe rukovodstvo [Mathematics. Profile level, practical guidance] Moscow, UchPedGiz Publ. (In Russian).

21. Isakova М.М., Tlupova R.G., Kankulova S. H., Erzhibova F.A., Ibragim A.S. (2018) O sinteticheskom metode resheniya zadach [On the synthetic method for solving problems] Vestnik Chelyabinskogo gosudarstvennogo pedagogicheskogo universiteta. 1, 108–117. DOI: 10.25588/CSPU.2018.01.11 (In Russian).

22. Isakova M.M, Tlupova R.G., Erzhibova F.A., Kankulova S.H., Ibragim A.S. (2018) Primenenie analiticheskogo metoda pri poiske resheniya zadach [The application of the analytical method in the search for solving problems] Vestnik Chelyabinskogo gosudarstvennogo pedagogicheskogo universiteta. 2, 71–78. (In Russian).