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Mathematics learning in physics classrooms of Russian schools: a changing landscape from the Soviet period to the present

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Abstract

For a long time, Soviet students learned ‘pure’ mathematics in their mathematics classrooms, while applications of mathematics were introduced in their science (mainly physics) classrooms. This approach was a part of a uniform and rigid national curriculum. Even when in the 1990s the world was moving towards including applications in school mathematics, Russian students continued to engage in pure mathematics learning in their mathematics classrooms. It was physics teachers’ responsibility to teach applications of mathematics; therefore, physics courses were highly mathematics-intensive, making extensive use of mathematics from algebra to calculus in the formulation of scientific laws and the investigation of their consequences. The collapse of the Soviet Union and some liberalization in educational policy led to changes in graduation requirements in mathematics and physics as well as diversity in mathematics and physics curricula in schools. Based on a review of textbooks, standards, curriculum documents, and other resources, in this paper we analyze changes that affected the teaching and learning of mathematics in physics classrooms in Russia from the Soviet period to the present.

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Notes

  1. The surveys were in Russian; the quotes included in the paper were translated by the authors.

References

  • Abramov, A. M. (2010). Toward a history of mathematics education reform in Soviet schools (1960s–1980s). In A. Karp & B. R. Vogeli (Eds.), Russian mathematics education: History and world significance (pp. 87–140). World Scientific.

  • Alimov, Sh. A., Kolyagin, Yu. M., Sidorov, Yu. V., Fedorova, N. E., & Shabunin, M. I. (1992). Algebra i nachala analiza. Uchebnik dlya 10-11 klassv srednei shkoly [Algebra and elements of analysis Textbook for the 10th–11th grades of secondary schools]. Prosveshenie.

  • Atanasyan, L. S., Butuziv, V. F., Kadomtzev, C. B., Poznyak, E. G., & Yudina, I. I. (1992). Geometriya. Uchebnik dlya 7–9 klassov [Geometry. Textbook for 7–9th grades]. Prosveshenie.

  • Baker, A. (2011). Explaining the applicability of mathematics in science. Interdisciplinary Science Reviews, 36(3), 255–267.

    Article  Google Scholar 

  • Barbin, E., & Pisano, R. (Eds.). (2013). The dialectic relation between physics and mathematics in the XIXth Century (Vol. 16). Springer (History of Mechanism and Machine Science).

  • Bashmakov, M. (2010). Challenges and issues in post-Soviet mathematics education. In A. Karp & B. R. Vogeli (Eds.), Russian mathematics education: History and world significance (pp. 141–186). World Scientific.

  • Beichner, R. J. (1994). Testing student interpretation of kinematic graphs. American Journal of Physics, 62(8), 750–762.

    Article  Google Scholar 

  • Bodriakov, VYu., & Fomina, N. G. (2010). O kachestve matematichsekoi podgotovki uchashihsya v komplekse “shkola-vuz”: vzglyad c pozitzii rabotnika vysshego pedagogicheskogo obrazovaniya [On regards of the quality of students’ mathematical preparation in a “school-university” complex: The teacher educator’s point of view]. Matematika v shkole, 2, 56–61.

    Google Scholar 

  • Burmistrova, T. A. (Ed.). (2014). Algebra. Sbornik rabochih program. 7–9 klassy. Basovyi i uglublennyi urovni. FGOS [Algebra. Curriculum. Grades 7–9. Basic and specialized levels. FGOS]. Prosveshenie.

  • Burmistrova, T. A. (Ed.). (2015). Geometriya. Sbornik rabochih program. 10–11 klassy. Basovyi i uglublennyi urovni. FGOS [Geometry. Curriculum. Grades 10–11. Basic and specialized levels. FGOS]. Prosveshenie.

  • Burmistrova, T. A. (Ed.). (2016). Algebra. Sbornik rabochih program. 10–11 klassy. Basovyi i uglublennyi urovni. FGOS [Algebra. Curriculum. Grades 10–11. Basic and specialized levels. FGOS]. Prosveshenie.

  • Burmistrova, T. A. (Ed.). (2020). Geometriya. Sbornik rabochih program. 7–9 klassy. Basovyi i uglublennyi urovni. FGOS [Geometry. Curriculum. Grades 7–9. Basic and specialized levels. FGOS]. Prosveshenie.

  • Cherednichenko, G. A. (1999). Shkolinaya reforma 90-h godov: Novovvedenija i sotzialinaya selektziya. [School reform of the 90s: Innovations and social selection]. Sotziologicehskii Journal, (1–2), 5–22. Retrieved from https://cyberleninka.ru/article/n/shkolnaya-reforma-90-h-godov-novovvedeniya-i-sotsialnaya-selektsiya

  • Dalinger, V. A. (2017). Podgotovka uchitelei matematiki v usloviyah novyh gosudarstvennyh standartov po napravelniyu “Pedagogicheskoe Obrazovanie”, profil “Matematicheskoe Obrazovanie”. [Preparation of teachers of mathematics in the conditions of new federal standards for the major “Pedagogical Educaion”, specialization “Mathematics Education”]. Sovremennye problem nauki i obrazovaniya, (1), 1–13. Retrieved from http://www.science-education.ru/ru/article/view?id=26089

  • Dirkova, EYu. (1991). Edinyi matematicheskii podkhod k opisaniyu yadernykh protsessov [Single mathematics approach to description of nuclear processes]. Fizika v shkole, 2, 34–37.

    Google Scholar 

  • Dneprov, E. (1994). The reform of education in Russia and state policy in the educational system: Background, goals, principles and stages of implementation. Journal of Education Finance, 19(4), 36–45.

    Google Scholar 

  • Dobudko, T. V., & Tyuzhina, I. V. (2013). Razvitie shkolnoy matematiki v SSSR kak predposylka sovremennogo sostoyaniya rossiyskogo matematicheskogo obrazovaniya [Development of secondary school mathematics in the USSR as a premise of the current Russian mathematics education]. Teoriya i Practika Obshestvennogo Razvitiya, 10, 190–193.

    Google Scholar 

  • Egupova, M. (2015). Prakticheskie prilojenija matematiki v shkole [Practical applications of mathematics in school]. Prometey.

  • Filonovich, N. V., & Gutnik, E. M. (2017). Fizika. 7–9 klassy: rabochaya programma k linii UMK A.V. Peryshkina, E.M. Gutnik. [Physics. 7–9th grades: Curriculum for the textbook by A.V. Peryshkin, E.M. Gutnik]. Drofa.

  • Gingras, Y. (2015). The creative power of formal analogies in physics: The case of Albert Einstein. Science & Education, 24(5/6), 529–541.

    Article  Google Scholar 

  • Glavnoe upravlenie shkol SSSR. (1985). Programma odinatzatiletnei shkoli: Fizika [Program for the eleven-year school: Physics] Fizika v shkole, 6, 21–37.

  • Gosudarstvennyi komitet SSSR po narodnomy obrasovaniyu. (1991). Programma srednei obsheobrazovatelinoi shkoli: Matematika [Secondary school program: Mathematics]. Prosveshenie.

  • Gupta, A., & Elby, A. (2011). Beyond epistemological deficits: Dynamic explanations of engineering students’ difficulties with mathematical sense making. International Journal of Science Education, 33(18), 2463–2488. https://doi.org/10.1080/09500693.2010.551551

    Article  Google Scholar 

  • Hansson, L., Hansson, Ö., Juter, K., & Redfors, A. (2015). Reality-theoretical models-mathematics: A ternary perspective on physics lessons in upper-secondary school. Science & Education, 24(5/6), 615–644.

    Article  Google Scholar 

  • Karp, A. (2014). Mathematics education in Russia. In A. Karp & G. Schubring (Eds.), Handbook on the history of mathematics education (pp. 303–322). Springer.

  • Karp, A. (2020). Russian mathematics education after 1991. In A. Karp (Ed.) Eastern European mathematics education in the decades of change, international studies in the history of mathematics and its teaching. (pp. 173–227). Springer Nature. https://doi.org/10.1007/978-3-030-38744-0_5

  • Kikoin, I. K., & Kikoin, A. K. (1992). Fizika: Uchebnik dlya 9 klassa [Physics: Textbook for the 9th grade]. Prosveshenie.

  • Kjeldsen, T. H., & Lützen, J. (2015). Interactions between mathematics and physics: The history of the concept of function—Teaching with and about nature of mathematics. Science & Education, 24(5/6), 543–559.

    Article  Google Scholar 

  • Kline, M. (1981). Mathematics and the physical world. Dover.

  • Kneubil, F., & Robilotta, M. (2015). Physics teaching: Mathematics as an epistemological tool. Science & Education, 24(5/6), 645–660.

    Article  Google Scholar 

  • Kolesnikova, E. M. (2008). Demonopolizatsiya rynka obrazovatel'nykh uslug v postsovetskoy Rossii [Demonopolisation of the services of the educational market in post-Soviet Russia]. In Sotsiologiya obrazovaniya: Khrestomatiya (pp. 207–217). HSE University.

  • Korobov, V. A. (1991). Opyt primeneniya matematiki v prepodavanii fiziki [Experience of applying mathematics in teaching physics]. Fizika v shkole, 4, 23–27.

    Google Scholar 

  • Korolev, M. Yu. (2019). Problema prepodavaniya distziplin “Fizika” i “Estesstvennonauchnaya kartina mira” pri podgotovke bakalavrov po napravleniyu “Pedagogicheskoe obrazovanie”. [Problems of teaching subjects of “Physics” and “Scientific picture of the world” in preparing undergraduates majoring in education]. In V. A. Stepanov (Ed.) Proceedings of all Russian scientific-practical conference “actual problems of physics and technology in education, science and production” (pp. 86–88). Riazan State University named after S.A. Esenin.

  • Kostenko, I. P. (2009). Korni, vetvi i “yagodki” reform—1970 [Roots, branches, and “berries” of the 1970 reform]. Matematicheskoe Obrazovanie, 50(2), 14–23.

    Google Scholar 

  • Kostenko, I. P. (2011). Dinamika kachestva matematicheskogo obrazovaniya. Prichiny degradatzii [Dynamics of the quality of the mathematics education. Reasons for degradation]. Matematicheskoe Obrazovanie, 58(2), 2–13.

    Google Scholar 

  • Kozhekina, T. V. (1987). Vzaimosvyazi obucheniya fizike i matematike v odinnadtzatileetnei shkole [Interconnectedness of teaching physics and mathematics in eleven-year school]. Fizika v shkole, 5, 65–68.

    Google Scholar 

  • Levshina, S. V. (2016). Izmenenie soderjanija shkolinogo estestvennonauchnogo obrazovanija pri reformirovanii shkola v period 20–90kh gg. XX veka [Changes in the content of school science education during school reforms in 1920s–1990s of the 20th century. Izvestija of Russian State Pedagogical Univerity named after A. I. Gertzen, 181, 55–60.

    Google Scholar 

  • López-Gay, R., Martínez Sáez, J., & Martínez-Torregrosa, J. (2015). Obstacles to mathematization in physics: The case of the differential. Science & Education, 24(5/6), 591–613.

    Article  Google Scholar 

  • Lützen, J. (2011). The physical origin of physically useful mathematics. Interdisciplinary Science Reviews, 36(3), 229–243.

    Article  Google Scholar 

  • Martinez-Torregrosa, J., Lopez-Gay, R., & Gras-Marti, A. (2006). Mathematics in physics education: Scanning the historical evolution of the differential to find a more appropriate model for teaching differential calculus in physics. Science & Education, 15(5), 447–462.

    Article  Google Scholar 

  • McDermott, L. C. (1991). Millikan lecture 1990: What we teach and what is learned—Closing the gap. American Journal of Physics, 59(4), 301–315.

    Article  Google Scholar 

  • McDermott, L. C., Rosenquist, M. L., & van Zee, E. H. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American Journal of Physics, 55(6), 503–515.

    Article  Google Scholar 

  • Meredith, D. C., & Marrongelle, K. A. (2008). How students use mathematical resources in an electrostatics context. American Journal of Physics, 76, 570–578.

    Article  Google Scholar 

  • Myakishev, GYa., Bukhovtzev, B. B., & Charugin, V. M. (2019b). Fizika. 11 klass: Uchebnik dlya obsheobrazovatelinyh uchrezhdenii [Physics. The 11th grade: Textbook for the general education institutions]. Prosveshenie.

  • Myakishev, GYa., Bukhovtzev, B. B., & Sotskii, N. N. (2019a). Fizika. 10 klass: Uchebnik dlya obsheobrazovatelinyh uchrezhdenii [Physics. The 10th grade: Textbook for the general education institutions]. Prosveshenie.

  • Neretin, Yu. (2008). EGE: Perspektivy i evolutzia. [USE: Perspectives and evolution]. Nauka i zhizn, (4). Retrieved from https://www.nkj.ru/archive/articles/13582/

  • Odintzova, N. I., & Yakovetz, E. E. (2007). Matematicheskie zatrudneniya shkolinikov pri izuchenii fiziki i puti ikh preodoleniya [Mathematical difficulties of students in learning physics and methods of overcoming them]. Fizika v shkole, 3, 22–29.

    Google Scholar 

  • Pereira de Ataıde, A. R., & Greca, I. M. (2013). Epistemic views of the relationship between physics and mathematics: Its influence on the approach of undergraduate students to problem solving. Science & Education, 22(6), 1405–1421.

    Article  Google Scholar 

  • Peryshkin, A. V., & Gutnik, E. M. (2014). Fizika. 9 klass: Uchebnik [Physics. The 9th grade: Textbook]. Drofa.

  • Peryshkin, A. V., & Rodina, N. A. (1989). Fizika: Uchebnik dlya 7 klassa [Physics: Textbook for the 7th grade]. Prosveshenie.

  • Pontryagin, L. S. (1980). O matematike i kachestve ee prepodavaniya [About mathematics and quality of teaching it]. Kommunist, 14, 99–112.

    Google Scholar 

  • Quale, A. (2011). On the role of mathematics in physics. Science & Education, 20(3/4), 359–372.

    Article  Google Scholar 

  • Redish, E., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24(5/6), 561–590.

    Article  Google Scholar 

  • Safronova, L. V. (1987). Svoistva treugolinikov i geometricheskaya optika [Properties of triangles and geometric optics]. Fizika v shkole, 2, 76–77.

    Google Scholar 

  • Sharonov, N. V., & Adzhemyan, G. A. (2016). Primenenie matematicheskih zadach c fizicheskim soderjaniem dlya podgotovki mladshih podrostkov k izucheniyu fiziki [Application of mathematics problems with physics context for preparing young teens to study physics]. Fizika v shkole, 4, 25–36.

    Google Scholar 

  • Shatalina, A. V. (2017). Fizika. Rabochie programme. Predmetnaya linia uchebnikov serii “Klassichseckii kurs” 10–11 klassi [Physics. Working programs. Textbook series “Classic course” 10–11 grades]. Prosveshenie.

  • Shurygin, VYu., & Shurygina, I. V. (2016). Activation of physics and mathematics intersubject communications as the means of forming students’ metasubject competences. Karelski Nauchnyi Jurnal, 5(4), 41–44.

    Google Scholar 

  • Shurygina, I. V., & Funt, I. P. (2016). O ponyatiakh vektora i vektornoi velichiny v shkolinoi matematike i fizike [On the concepts of vectors and vector quantity in school mathematics and physics]. Innovatzionnaya Nauka, 3, 228–229.

    Google Scholar 

  • Solodnikov, V. V. (2015). The Unified State Examination experiment. Russian Education & Society, 51(3), 9–24.

    Article  Google Scholar 

  • Tomashev, B. I. (1980). Nekotorye voprosy svyazi mezhdu kursavi fiziki i matematiki [Some questions about connection between physics and mathematics]. Fizika v shkole, 2, 54–56.

    Google Scholar 

  • Trenogin, V. A. & Yagoda, A. G. (1988). O soveshanii-seminare prepodavatelei vuzov Severo-Zapadnogo raiona SSSR [About the meeting of higher education faculty in Northwest region of USSR]. In V. A. Il’in (Ed.) Sbornik nauchno-metodicheskih statei po matematike. Vypusk 15. (pp. 146–149). Vysshaya shkola.

  • Uhden, O., Karam, R., Pietrocola, M., & Pospiech, G. (2012). Modelling mathematical reasoning in physics education. Science & Education, 21(4), 485–506.

    Article  Google Scholar 

  • Vondracek, M. (1999). Teaching physics with math to weak math students. The Physics Teacher, 37(1), 32–33.

    Article  Google Scholar 

  • Zheleeva, A., & Odintzova, N. I. (2009). Kak preodoleti matematicheskie zatrudneniya pri izuchenii fiziki [How to overcome mathematical difficulties in studying physics]. Otkrytaya shkola, 6, 38–40.

    Google Scholar 

  • Zilbermintz, A. S. (1993). Iz opyta izucheniya kinematiki na osnove ponyatiya proizvodnoi [From the experience of learning kinematics based on the concept of derivative]. Fizika v shkole, 4, 51–52.

    Google Scholar 

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  1. Teachers College, Columbia University, New York, NY, USA

    Irina Lyublinskaya

  2. Moscow State Pedagogical University, Moscow, Russia

    Elena Petrova

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  1. Irina Lyublinskaya
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  2. Elena Petrova
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Correspondence to Irina Lyublinskaya.

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Lyublinskaya, I., Petrova, E. Mathematics learning in physics classrooms of Russian schools: a changing landscape from the Soviet period to the present. ZDM Mathematics Education 53, 1485–1498 (2021). https://doi.org/10.1007/s11858-021-01248-z

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