Cite this article as:

Igoshin V. I. To teach logic to prospective mathematics teachers (Part III). Izvestiya of Saratov University. Philosophy. Psychology. Pedagogy, 2022, vol. 22, iss. 2, pp. 202-207. DOI:

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).

To teach logic to prospective mathematics teachers (Part III)

Introduction. The article is the third part of the author’s article under the same title published in previous issues of this journal. It discusses the problem of forming the logical competencies of future mathematics teachers both at the undergraduate level and at the master’s level. Theoretical analysis. In this case, logic is considered in three aspects – classical Aristotelian logic, modern mathematical logic and its application to Aristotelian logic, non-classical logics. This part of the article proposes a number of measures related to the formation of the logical and didactic training content for future mathematics teachers at the undergraduate and graduate levels in order to make this training a system-forming factor in the entire system of their training. At the same time, training at the master’s level must meet the principle of continuity and become a natural continuation of training at the undergraduate level. Conclusions. Such an approach will signifi cantly increase the level of the logical and general professional competence of mathematics teachers who graduate from pedagogical and classical universities. Such teachers will be able to apply logical knowledge and skills in their pedagogical activities to educate logically and mathematically competent students at diff erent levels of general education capable of further self-development and creative activity.

  1. Igoshin V. I. About quality of teaching bachelors and post-graduated students of pedagogical education (mathematical education). Izvestiya of Saratov University. Philosophy, Psychology, Pedagogy, 2018, vol. 18, iss. 4, pp. 468–473 (in Russian).
  2. Igoshin V. I. Logika s elementami matematicheskoy logiki [Logic with Elements of Mathematical Logic]. Saratov, Nauchnaya kniga Publ., 2004. 144 p. (in Russian).
  3. Igoshin V. I. Matematicheskaya logika I teoriya algoritmov [Mathematical Logic and Theory of Algorithms: Textbook for students higher educational institutions]. Moscow, Akademiya Publ., 2010. 448 p. (in Russian).
  4. Igoshin V. I. Matematicheskaya logika [Mathematical Logic: Textbook]. Moscow, INFRA-M Publ., 2020. 399 p. (in Russian).
  5. Igoshin V. I. Elementy matematicheskoy logiki [Elements of Mathematical Logic: Textbook for students institutions of secondary vocational education]. Moscow, Akademiya Publ., 2016, 2018, 2021. 320 p. (in Russian).
  6. Igoshin V. I. Sbornik zadach po matematicheskoy logike i teroii algoritmov [Collection of Problems on Mathematical Logic and Theory of Algorisms: Textbook]. Moscow, KURS, INFRA-M Publ., 2017. 392 p. (in Russian).
  7. Manturov O. V., Isaeva M. A. On axiomatic method in school geometry. Matematika v shkole [Mathematics in School], 1988, no. 3, pp. 38–41 (in Russian).
  8. Gleizer G., Kalina A. On possibilities of logical construction of school geometries. Matematika (gazeta) [Mathematics], 2000, no. 14, pp. 1–4 (in Russian).
  9. Pouancare A. O nauke [About Science. Transl. from French]. Moscow, Nauka Publ., 1983. 560 p. (in Russian).
  10. Smirnov V. A., Markin V. I., Novodvorskiy A. E., Smirnov A. V. Logika i kompyuyter: dokazatelstvo i ego poisk. Kurs logiki i kompyuyterniy praktikum [Logic and Computer: Proof and Its Search. Logic Course and Computer Workshop]. Moscow, Nauka Publ., 1996. 254 p. (in Russian).
  11. Krantz S. Izmenchivaya priroda matematicheskogo dokazatelstva. Dokazat nelzya poverit [The Proof is in the Pudding. The Changing Nature of Mathematical Proof. Transl. from Engl.]. Moscow, Laboratoriya znanii Publ., 2016. 320 p. (in Russian).
  12. Fetisov A. I. Elements of logic in teaching mathematics. Izvestiya APN RSFSR. Voprosi obschey metodiki matematiki [Izvestiya APN RSFSR. Questions of General Methods of Mathematics], 1958, iss. 92, pp. 149–198 (in Russian).
  13. Boltianskiy V. G. Logical symbolic in mathematical definitions. Matematika v shkole [Mathematics in School], 1973, no. 5, pp. 45–50 (in Russian).
  14. Stoliar A. A. On some applications of logic in mathematical education. In: Logika i problemy obucheniya [Logic and Education Problems]. Moscow, Pedagogika Publ., 1977, pp. 125–139 (in Russian).
  15. Timofeeva I. L. Some notes about contradiction method proving. Matematika v shkole [Mathematics in School], 1994, no. 3, pp. 36–38 (in Russian).
  16. Igoshin V. I. On application of mathematical logic in converse theorems proving. Matematika v shkole [Mathematics in School], 2002, no. 10, pp. 26–28 (in Russian).
  17. Igoshin V. I. On points and vectors in geometry. Matematicheskoe obrazovanie [Mathematical Education Journal], 2017, no. 2 (82), April – June, pp. 27–43 (in Russian).
  18. Shzhedrovickiy G., Rozin V., Alekseev N., Nepomnyashzhaya N. Pedagogika i logika [Pedagogic and Logic]. Moscow, Kastal’ Publ., 1993. 416 p. (in Russian).
одобрено к публикации

Generator XML for DOAJ